Index A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z A a1() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) a2() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) a3() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) a4() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) a6() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) a_invariants() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) a_number() (sage.schemes.hyperelliptic_curves.hyperelliptic_finite_field.HyperellipticCurve_finite_field method) abelian_group() (sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field method) abelian_variety() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) absolute_degree() (sage.schemes.elliptic_curves.heegner.RingClassField method) absolute_igusa_invariants_kohel() (in module sage.schemes.hyperelliptic_curves.invariants) (sage.schemes.hyperelliptic_curves.hyperelliptic_g2.HyperellipticCurve_g2 method) absolute_igusa_invariants_wamelen() (in module sage.schemes.hyperelliptic_curves.invariants) (sage.schemes.hyperelliptic_curves.hyperelliptic_g2.HyperellipticCurve_g2 method) add_reductions() (sage.schemes.elliptic_curves.saturation.EllipticCurveSaturator method) additive_order() (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_field method) (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_finite_field method) (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_number_field method) adjusted_prec() (in module sage.schemes.hyperelliptic_curves.monsky_washnitzer) ainvs() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) all_values_for_one_denominator() (sage.schemes.elliptic_curves.mod_sym_num.ModularSymbolNumerical method) alpha() (sage.schemes.elliptic_curves.heegner.GaloisAutomorphismQuadraticForm method) (sage.schemes.elliptic_curves.height.EllipticCurveCanonicalHeight method) (sage.schemes.elliptic_curves.padic_lseries.pAdicLseries method) an() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) (sage.schemes.elliptic_curves.sha_tate.Sha method) an_numerical() (sage.schemes.elliptic_curves.sha_tate.Sha method) an_padic() (sage.schemes.elliptic_curves.sha_tate.Sha method) analytic_rank() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) analytic_rank_upper_bound() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) anlist() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) antilogarithm() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) ap() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) aplist() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) approximative_value() (sage.schemes.elliptic_curves.mod_sym_num.ModularSymbolNumerical method) archimedean_local_height() (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_number_field method) are_projectively_equivalent() (in module sage.schemes.elliptic_curves.constructor) as_morphism() (sage.schemes.elliptic_curves.hom.EllipticCurveHom method) at1() (sage.schemes.elliptic_curves.lseries_ell.Lseries_ell method) ate_pairing() (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_field method) atkin_lehner_act() (sage.schemes.elliptic_curves.heegner.HeegnerPointOnX0N method) automorphisms() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) B B() (sage.schemes.elliptic_curves.height.EllipticCurveCanonicalHeight method) b2() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) b4() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) b6() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) b8() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) b_invariants() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) bad_reduction_type() (sage.schemes.elliptic_curves.ell_local_data.EllipticCurveLocalData method) base_extend() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.hyperelliptic_curves.hyperelliptic_generic.HyperellipticCurve_generic method) (sage.schemes.hyperelliptic_curves.jacobian_homset.JacobianHomset_divisor_classes method) (sage.schemes.hyperelliptic_curves.monsky_washnitzer.MonskyWashnitzerDifferentialRing method) (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialHyperellipticQuotientRing method) base_field() (sage.schemes.elliptic_curves.ell_field.EllipticCurve_field method) (sage.schemes.elliptic_curves.heegner.GaloisGroup method) (sage.schemes.elliptic_curves.height.EllipticCurveCanonicalHeight method) base_ring() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) (sage.schemes.elliptic_curves.ell_modular_symbols.ModularSymbol method) baseWI (class in sage.schemes.elliptic_curves.weierstrass_morphism) basis() (sage.schemes.elliptic_curves.period_lattice.PeriodLattice_ell method) basis_matrix() (sage.schemes.elliptic_curves.period_lattice.PeriodLattice_ell method) bernardi_sigma_function() (sage.schemes.elliptic_curves.padic_lseries.pAdicLseriesSupersingular method) beta() (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlgEmbedding method) betas() (sage.schemes.elliptic_curves.heegner.HeegnerPoints_level_disc_cond method) Billerey_B_bound() (in module sage.schemes.elliptic_curves.gal_reps_number_field) Billerey_B_l() (in module sage.schemes.elliptic_curves.gal_reps_number_field) Billerey_P_l() (in module sage.schemes.elliptic_curves.gal_reps_number_field) Billerey_R_bound() (in module sage.schemes.elliptic_curves.gal_reps_number_field) Billerey_R_q() (in module sage.schemes.elliptic_curves.gal_reps_number_field) border() (sage.schemes.elliptic_curves.period_lattice_region.PeriodicRegion method) bound() (sage.schemes.elliptic_curves.sha_tate.Sha method) bound_kato() (sage.schemes.elliptic_curves.sha_tate.Sha method) bound_kolyvagin() (sage.schemes.elliptic_curves.sha_tate.Sha method) brandt_module() (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlg method) C c4() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) c6() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) c_invariants() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) cantor_composition() (in module sage.schemes.hyperelliptic_curves.jacobian_morphism) cantor_composition_simple() (in module sage.schemes.hyperelliptic_curves.jacobian_morphism) cantor_reduction() (in module sage.schemes.hyperelliptic_curves.jacobian_morphism) cantor_reduction_simple() (in module sage.schemes.hyperelliptic_curves.jacobian_morphism) cardinality() (sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field method) (sage.schemes.elliptic_curves.heegner.GaloisGroup method) (sage.schemes.hyperelliptic_curves.hyperelliptic_finite_field.HyperellipticCurve_finite_field method) cardinality_bsgs() (sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field method) cardinality_exhaustive() (sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field method) (sage.schemes.hyperelliptic_curves.hyperelliptic_finite_field.HyperellipticCurve_finite_field method) cardinality_hypellfrob() (sage.schemes.hyperelliptic_curves.hyperelliptic_finite_field.HyperellipticCurve_finite_field method) cardinality_pari() (sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field method) Cartier_matrix() (sage.schemes.hyperelliptic_curves.hyperelliptic_finite_field.HyperellipticCurve_finite_field method) change_ring() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) (sage.schemes.hyperelliptic_curves.hyperelliptic_generic.HyperellipticCurve_generic method) (sage.schemes.hyperelliptic_curves.monsky_washnitzer.MonskyWashnitzerDifferentialRing method) (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialHyperellipticQuotientElement method) (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialHyperellipticQuotientRing method) change_weierstrass_model() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) characteristic_polynomial() (sage.schemes.elliptic_curves.hom.EllipticCurveHom method) check_prime() (in module sage.schemes.elliptic_curves.ell_local_data) chord_and_tangent() (in module sage.schemes.elliptic_curves.constructor) class_number() (in module sage.schemes.elliptic_curves.heegner) clear_cache() (sage.schemes.elliptic_curves.mod_sym_num.ModularSymbolNumerical method) clebsch_invariants() (in module sage.schemes.hyperelliptic_curves.invariants) (sage.schemes.hyperelliptic_curves.hyperelliptic_g2.HyperellipticCurve_g2 method) clebsch_to_igusa() (in module sage.schemes.hyperelliptic_curves.invariants) cm_discriminant() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) cm_j_invariants() (in module sage.schemes.elliptic_curves.cm) cm_j_invariants_and_orders() (in module sage.schemes.elliptic_curves.cm) cm_orders() (in module sage.schemes.elliptic_curves.cm) codomain() (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlgEmbedding method) coeff() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.MonskyWashnitzerDifferential method) coefficients_from_j() (in module sage.schemes.elliptic_curves.constructor) coefficients_from_Weierstrass_polynomial() (in module sage.schemes.elliptic_curves.constructor) coeffs() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.MonskyWashnitzerDifferential method) (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialCubicQuotientRingElement method) (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialHyperellipticQuotientElement method) coleman_integral() (sage.schemes.hyperelliptic_curves.hyperelliptic_padic_field.HyperellipticCurve_padic_field method) (sage.schemes.hyperelliptic_curves.monsky_washnitzer.MonskyWashnitzerDifferential method) coleman_integral_from_weierstrass_via_boundary() (sage.schemes.hyperelliptic_curves.hyperelliptic_padic_field.HyperellipticCurve_padic_field method) coleman_integral_P_to_S() (sage.schemes.hyperelliptic_curves.hyperelliptic_padic_field.HyperellipticCurve_padic_field method) coleman_integral_S_to_Q() (sage.schemes.hyperelliptic_curves.hyperelliptic_padic_field.HyperellipticCurve_padic_field method) coleman_integrals_on_basis() (sage.schemes.hyperelliptic_curves.hyperelliptic_padic_field.HyperellipticCurve_padic_field method) coleman_integrals_on_basis_hyperelliptic() (sage.schemes.hyperelliptic_curves.hyperelliptic_padic_field.HyperellipticCurve_padic_field method) compare_via_evaluation() (in module sage.schemes.elliptic_curves.hom) complex_area() (sage.schemes.elliptic_curves.period_lattice.PeriodLattice_ell method) complex_conjugation() (sage.schemes.elliptic_curves.heegner.GaloisGroup method) complex_intersection_is_empty() (sage.schemes.elliptic_curves.height.EllipticCurveCanonicalHeight method) compute_codomain_formula() (in module sage.schemes.elliptic_curves.ell_curve_isogeny) compute_codomain_kohel() (in module sage.schemes.elliptic_curves.ell_curve_isogeny) compute_intermediate_curves() (in module sage.schemes.elliptic_curves.ell_curve_isogeny) compute_isogeny_bmss() (in module sage.schemes.elliptic_curves.ell_curve_isogeny) compute_isogeny_kernel_polynomial() (in module sage.schemes.elliptic_curves.ell_curve_isogeny) compute_isogeny_stark() (in module sage.schemes.elliptic_curves.ell_curve_isogeny) compute_model() (in module sage.schemes.elliptic_curves.ell_field) compute_sequence_of_maps() (in module sage.schemes.elliptic_curves.ell_curve_isogeny) compute_trace_generic() (in module sage.schemes.elliptic_curves.hom) compute_vw_kohel_even_deg1() (in module sage.schemes.elliptic_curves.ell_curve_isogeny) compute_vw_kohel_even_deg3() (in module sage.schemes.elliptic_curves.ell_curve_isogeny) compute_vw_kohel_odd() (in module sage.schemes.elliptic_curves.ell_curve_isogeny) compute_wp_fast() (in module sage.schemes.elliptic_curves.ell_wp) compute_wp_pari() (in module sage.schemes.elliptic_curves.ell_wp) compute_wp_quadratic() (in module sage.schemes.elliptic_curves.ell_wp) conductor() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) (sage.schemes.elliptic_curves.heegner.HeegnerPoint method) (sage.schemes.elliptic_curves.heegner.HeegnerPoints_level_disc_cond method) (sage.schemes.elliptic_curves.heegner.KolyvaginCohomologyClass method) (sage.schemes.elliptic_curves.heegner.RingClassField method) conductor_valuation() (sage.schemes.elliptic_curves.ell_local_data.EllipticCurveLocalData method) congruence_number() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) conjugacy_test() (in module sage.schemes.elliptic_curves.Qcurves) conjugate() (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlgEmbedding method) conjugates_over_K() (sage.schemes.elliptic_curves.heegner.HeegnerPointOnEllipticCurve method) contract() (sage.schemes.elliptic_curves.period_lattice_region.PeriodicRegion method) coordinates() (sage.schemes.elliptic_curves.period_lattice.PeriodLattice_ell method) copy() (sage.schemes.elliptic_curves.isogeny_class.IsogenyClass_EC_NumberField method) (sage.schemes.elliptic_curves.isogeny_class.IsogenyClass_EC_Rational method) count_points() (sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field method) (sage.schemes.hyperelliptic_curves.hyperelliptic_finite_field.HyperellipticCurve_finite_field method) count_points_exhaustive() (sage.schemes.hyperelliptic_curves.hyperelliptic_finite_field.HyperellipticCurve_finite_field method) count_points_frobenius_polynomial() (sage.schemes.hyperelliptic_curves.hyperelliptic_finite_field.HyperellipticCurve_finite_field method) count_points_hypellfrob() (sage.schemes.hyperelliptic_curves.hyperelliptic_finite_field.HyperellipticCurve_finite_field method) count_points_matrix_traces() (sage.schemes.hyperelliptic_curves.hyperelliptic_finite_field.HyperellipticCurve_finite_field method) CPS_height_bound() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) create_element() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialCubicQuotientRing method) create_key_and_extra_args() (sage.schemes.elliptic_curves.constructor.EllipticCurveFactory method) create_object() (sage.schemes.elliptic_curves.constructor.EllipticCurveFactory method) cremona_curves() (in module sage.schemes.elliptic_curves.ell_rational_field) cremona_label() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) cremona_optimal_curves() (in module sage.schemes.elliptic_curves.ell_rational_field) curve() (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_field method) (sage.schemes.elliptic_curves.ell_tate_curve.TateCurve method) (sage.schemes.elliptic_curves.ell_torsion.EllipticCurveTorsionSubgroup method) (sage.schemes.elliptic_curves.formal_group.EllipticCurveFormalGroup method) (sage.schemes.elliptic_curves.heegner.HeegnerPointOnEllipticCurve method) (sage.schemes.elliptic_curves.heegner.KolyvaginPoint method) (sage.schemes.elliptic_curves.height.EllipticCurveCanonicalHeight method) (sage.schemes.elliptic_curves.modular_parametrization.ModularParameterization method) (sage.schemes.elliptic_curves.period_lattice.PeriodLattice_ell method) (sage.schemes.hyperelliptic_curves.jacobian_homset.JacobianHomset_divisor_classes method) (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialHyperellipticQuotientRing method) curve_key() (in module sage.schemes.elliptic_curves.ell_egros) curve_over_ram_extn() (sage.schemes.hyperelliptic_curves.hyperelliptic_padic_field.HyperellipticCurve_padic_field method) curves_with_j_0() (in module sage.schemes.elliptic_curves.ell_finite_field) curves_with_j_0_char2() (in module sage.schemes.elliptic_curves.ell_finite_field) curves_with_j_0_char3() (in module sage.schemes.elliptic_curves.ell_finite_field) curves_with_j_1728() (in module sage.schemes.elliptic_curves.ell_finite_field) cyclic_subideal_p1() (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlg method) D data (sage.schemes.elliptic_curves.period_lattice_region.PeriodicRegion attribute) database_attributes() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) database_curve() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) DE() (sage.schemes.elliptic_curves.height.EllipticCurveCanonicalHeight method) deg_one_primes_iter() (in module sage.schemes.elliptic_curves.gal_reps_number_field) degree() (sage.schemes.elliptic_curves.hom.EllipticCurveHom method) (sage.schemes.elliptic_curves.hom_frobenius.EllipticCurveHom_frobenius method) (sage.schemes.elliptic_curves.hom_scalar.EllipticCurveHom_scalar method) (sage.schemes.hyperelliptic_curves.monsky_washnitzer.MonskyWashnitzerDifferentialRing method) (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialHyperellipticQuotientRing method) degree_over_H() (sage.schemes.elliptic_curves.heegner.RingClassField method) degree_over_K() (sage.schemes.elliptic_curves.heegner.RingClassField method) degree_over_Q() (sage.schemes.elliptic_curves.heegner.RingClassField method) deriv_at1() (sage.schemes.elliptic_curves.lseries_ell.Lseries_ell method) descend_to() (sage.schemes.elliptic_curves.ell_field.EllipticCurve_field method) diff() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialHyperellipticQuotientElement method) differential() (sage.schemes.elliptic_curves.formal_group.EllipticCurveFormalGroup method) differential_operator() (in module sage.schemes.hyperelliptic_curves.invariants) diffsymb() (in module sage.schemes.hyperelliptic_curves.invariants) diffxy() (in module sage.schemes.hyperelliptic_curves.invariants) dimension() (sage.schemes.hyperelliptic_curves.jacobian_generic.HyperellipticJacobian_generic method) (sage.schemes.hyperelliptic_curves.monsky_washnitzer.MonskyWashnitzerDifferentialRing method) discrete_log() (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_finite_field method) discriminant() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) (sage.schemes.elliptic_curves.heegner.HeegnerPoint method) (sage.schemes.elliptic_curves.heegner.HeegnerPoints_level_disc method) discriminant_of_K() (sage.schemes.elliptic_curves.heegner.RingClassField method) discriminant_valuation() (sage.schemes.elliptic_curves.ell_local_data.EllipticCurveLocalData method) discriminants() (sage.schemes.elliptic_curves.heegner.HeegnerPoints_level method) discriminants_with_bounded_class_number() (in module sage.schemes.elliptic_curves.cm) division_field() (sage.schemes.elliptic_curves.ell_field.EllipticCurve_field method) division_points() (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_field method) division_polynomial() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) division_polynomial_0() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) divisors_to_string() (in module sage.interfaces.genus2reduction) dokchitser() (sage.schemes.elliptic_curves.lseries_ell.Lseries_ell method) domain() (sage.schemes.elliptic_curves.heegner.GaloisAutomorphism method) (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlgEmbedding method) domain_conductor() (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlgEmbedding method) domain_gen() (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlgEmbedding method) Dp_valued_height() (sage.schemes.elliptic_curves.padic_lseries.pAdicLseriesSupersingular method) Dp_valued_regulator() (sage.schemes.elliptic_curves.padic_lseries.pAdicLseriesSupersingular method) Dp_valued_series() (sage.schemes.elliptic_curves.padic_lseries.pAdicLseriesSupersingular method) ds() (sage.schemes.elliptic_curves.period_lattice_region.PeriodicRegion method) dual() (sage.schemes.elliptic_curves.ell_curve_isogeny.EllipticCurveIsogeny method) (sage.schemes.elliptic_curves.hom.EllipticCurveHom method) (sage.schemes.elliptic_curves.hom_composite.EllipticCurveHom_composite method) (sage.schemes.elliptic_curves.hom_frobenius.EllipticCurveHom_frobenius method) (sage.schemes.elliptic_curves.hom_scalar.EllipticCurveHom_scalar method) (sage.schemes.elliptic_curves.hom_velusqrt.EllipticCurveHom_velusqrt method) (sage.schemes.elliptic_curves.weierstrass_morphism.WeierstrassIsomorphism method) E E2() (sage.schemes.elliptic_curves.ell_tate_curve.TateCurve method) e_log_RC() (sage.schemes.elliptic_curves.period_lattice.PeriodLattice_ell method) e_p() (sage.schemes.elliptic_curves.height.EllipticCurveCanonicalHeight method) egros_from_j() (in module sage.schemes.elliptic_curves.ell_egros) egros_from_j_0() (in module sage.schemes.elliptic_curves.ell_egros) egros_from_j_1728() (in module sage.schemes.elliptic_curves.ell_egros) egros_from_jlist() (in module sage.schemes.elliptic_curves.ell_egros) egros_get_j() (in module sage.schemes.elliptic_curves.ell_egros) ei() (sage.schemes.elliptic_curves.period_lattice.PeriodLattice_ell method) Element (sage.schemes.hyperelliptic_curves.monsky_washnitzer.MonskyWashnitzerDifferentialRing attribute) (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialCubicQuotientRing attribute) (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialHyperellipticQuotientRing attribute) ell() (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlg method) ell_heegner_discriminants() (in module sage.schemes.elliptic_curves.heegner) ell_heegner_discriminants_list() (in module sage.schemes.elliptic_curves.heegner) ell_heegner_point() (in module sage.schemes.elliptic_curves.heegner) elliptic_curve() (sage.schemes.elliptic_curves.ell_modular_symbols.ModularSymbol method) (sage.schemes.elliptic_curves.gal_reps.GaloisRepresentation method) (sage.schemes.elliptic_curves.gal_reps_number_field.GaloisRepresentation method) (sage.schemes.elliptic_curves.lseries_ell.Lseries_ell method) (sage.schemes.elliptic_curves.mod_sym_num.ModularSymbolNumerical method) (sage.schemes.elliptic_curves.padic_lseries.pAdicLseries method) elliptic_curve_congruence_graph() (in module sage.schemes.elliptic_curves.ell_rational_field) elliptic_exponential() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) (sage.schemes.elliptic_curves.period_lattice.PeriodLattice_ell method) elliptic_logarithm() (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_number_field method) (sage.schemes.elliptic_curves.period_lattice.PeriodLattice_ell method) EllipticCurve_field (class in sage.schemes.elliptic_curves.ell_field) EllipticCurve_finite_field (class in sage.schemes.elliptic_curves.ell_finite_field) EllipticCurve_from_c4c6() (in module sage.schemes.elliptic_curves.constructor) EllipticCurve_from_cubic() (in module sage.schemes.elliptic_curves.constructor) EllipticCurve_from_j() (in module sage.schemes.elliptic_curves.constructor) EllipticCurve_from_Weierstrass_polynomial() (in module sage.schemes.elliptic_curves.constructor) EllipticCurve_generic (class in sage.schemes.elliptic_curves.ell_generic) EllipticCurve_number_field (class in sage.schemes.elliptic_curves.ell_number_field) EllipticCurve_padic_field (class in sage.schemes.elliptic_curves.ell_padic_field) EllipticCurve_rational_field (class in sage.schemes.elliptic_curves.ell_rational_field) EllipticCurveCanonicalHeight (class in sage.schemes.elliptic_curves.height) EllipticCurveFactory (class in sage.schemes.elliptic_curves.constructor) EllipticCurveFormalGroup (class in sage.schemes.elliptic_curves.formal_group) EllipticCurveHom (class in sage.schemes.elliptic_curves.hom) EllipticCurveHom_composite (class in sage.schemes.elliptic_curves.hom_composite) EllipticCurveHom_frobenius (class in sage.schemes.elliptic_curves.hom_frobenius) EllipticCurveHom_scalar (class in sage.schemes.elliptic_curves.hom_scalar) EllipticCurveHom_velusqrt (class in sage.schemes.elliptic_curves.hom_velusqrt) EllipticCurveIsogeny (class in sage.schemes.elliptic_curves.ell_curve_isogeny) EllipticCurveLocalData (class in sage.schemes.elliptic_curves.ell_local_data) EllipticCurvePoint (class in sage.schemes.elliptic_curves.ell_point) EllipticCurvePoint_field (class in sage.schemes.elliptic_curves.ell_point) EllipticCurvePoint_finite_field (class in sage.schemes.elliptic_curves.ell_point) EllipticCurvePoint_number_field (class in sage.schemes.elliptic_curves.ell_point) EllipticCurves (class in sage.schemes.elliptic_curves.ec_database) EllipticCurves_with_good_reduction_outside_S() (in module sage.schemes.elliptic_curves.constructor) EllipticCurveSaturator (class in sage.schemes.elliptic_curves.saturation) EllipticCurveTorsionSubgroup (class in sage.schemes.elliptic_curves.ell_torsion) endomorphism_discriminant_from_class_number() (sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field method) eps() (in module sage.schemes.elliptic_curves.height) eval_modular_form() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) expand() (sage.schemes.elliptic_curves.period_lattice_region.PeriodicRegion method) extended_agm_iteration() (in module sage.schemes.elliptic_curves.period_lattice) extract_pow_y() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.MonskyWashnitzerDifferential method) (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialHyperellipticQuotientElement method) F factors() (sage.schemes.elliptic_curves.hom_composite.EllipticCurveHom_composite method) faltings_height() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) FastEllipticPolynomial (class in sage.schemes.elliptic_curves.hom_velusqrt) field() (sage.schemes.elliptic_curves.heegner.GaloisGroup method) fill_isogeny_matrix() (in module sage.schemes.elliptic_curves.ell_curve_isogeny) fill_ss_j_dict() (in module sage.schemes.elliptic_curves.ell_finite_field) find_char_zero_weier_point() (sage.schemes.hyperelliptic_curves.hyperelliptic_padic_field.HyperellipticCurve_padic_field method) find_post_isomorphism() (in module sage.schemes.elliptic_curves.hom) finite_endpoints() (sage.schemes.elliptic_curves.height.UnionOfIntervals method) fk_intervals() (sage.schemes.elliptic_curves.height.EllipticCurveCanonicalHeight method) formal() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) (sage.schemes.elliptic_curves.hom.EllipticCurveHom method) (sage.schemes.elliptic_curves.hom_composite.EllipticCurveHom_composite method) formal_group() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) Fricke_module() (in module sage.schemes.elliptic_curves.isogeny_small_degree) Fricke_polynomial() (in module sage.schemes.elliptic_curves.isogeny_small_degree) frob_basis_elements() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.MonskyWashnitzerDifferentialRing method) frob_invariant_differential() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.MonskyWashnitzerDifferentialRing method) frob_Q() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.MonskyWashnitzerDifferentialRing method) frobenius() (sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field method) (sage.schemes.elliptic_curves.ell_padic_field.EllipticCurve_padic_field method) (sage.schemes.elliptic_curves.padic_lseries.pAdicLseriesSupersingular method) (sage.schemes.hyperelliptic_curves.hyperelliptic_padic_field.HyperellipticCurve_padic_field method) frobenius_discriminant() (sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field method) frobenius_endomorphism() (sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field method) frobenius_expansion_by_newton() (in module sage.schemes.hyperelliptic_curves.monsky_washnitzer) frobenius_expansion_by_series() (in module sage.schemes.hyperelliptic_curves.monsky_washnitzer) Frobenius_filter() (in module sage.schemes.elliptic_curves.gal_reps_number_field) frobenius_isogeny() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) frobenius_matrix() (sage.schemes.hyperelliptic_curves.hyperelliptic_finite_field.HyperellipticCurve_finite_field method) frobenius_matrix_hypellfrob() (sage.schemes.hyperelliptic_curves.hyperelliptic_finite_field.HyperellipticCurve_finite_field method) frobenius_order() (sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field method) frobenius_polynomial() (sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field method) (sage.schemes.hyperelliptic_curves.hyperelliptic_finite_field.HyperellipticCurve_finite_field method) frobenius_polynomial_cardinalities() (sage.schemes.hyperelliptic_curves.hyperelliptic_finite_field.HyperellipticCurve_finite_field method) frobenius_polynomial_matrix() (sage.schemes.hyperelliptic_curves.hyperelliptic_finite_field.HyperellipticCurve_finite_field method) frobenius_polynomial_pari() (sage.schemes.hyperelliptic_curves.hyperelliptic_finite_field.HyperellipticCurve_finite_field method) from_factors() (sage.schemes.elliptic_curves.hom_composite.EllipticCurveHom_composite class method) full (sage.schemes.elliptic_curves.period_lattice_region.PeriodicRegion attribute) full_p_saturation() (sage.schemes.elliptic_curves.saturation.EllipticCurveSaturator method) G galois_group() (sage.schemes.elliptic_curves.heegner.RingClassField method) galois_group_over_hilbert_class_field() (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlg method) galois_group_over_quadratic_field() (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlg method) galois_orbit_over_K() (sage.schemes.elliptic_curves.heegner.HeegnerPointOnX0N method) galois_representation() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) GaloisAutomorphism (class in sage.schemes.elliptic_curves.heegner) GaloisAutomorphismComplexConjugation (class in sage.schemes.elliptic_curves.heegner) GaloisAutomorphismQuadraticForm (class in sage.schemes.elliptic_curves.heegner) GaloisGroup (class in sage.schemes.elliptic_curves.heegner) GaloisRepresentation (class in sage.schemes.elliptic_curves.gal_reps) (class in sage.schemes.elliptic_curves.gal_reps_number_field) gen() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) gens() (sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field method) (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) (sage.schemes.elliptic_curves.period_lattice.PeriodLattice_ell method) (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialCubicQuotientRing method) (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialHyperellipticQuotientRing method) gens_certain() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) gens_quadratic() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) genus() (sage.schemes.elliptic_curves.ell_field.EllipticCurve_field method) (sage.schemes.hyperelliptic_curves.hyperelliptic_generic.HyperellipticCurve_generic method) Genus2reduction (class in sage.interfaces.genus2reduction) geometric_endomorphism_algebra_is_field() (sage.schemes.hyperelliptic_curves.jacobian_generic.HyperellipticJacobian_generic method) geometric_endomorphism_ring_is_ZZ() (sage.schemes.hyperelliptic_curves.jacobian_generic.HyperellipticJacobian_generic method) get_boundary_point() (sage.schemes.hyperelliptic_curves.hyperelliptic_padic_field.HyperellipticCurve_padic_field method) global_integral_model() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) global_minimal_model() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) global_minimality_class() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) graph() (sage.schemes.elliptic_curves.isogeny_class.IsogenyClass_EC method) group_law() (sage.schemes.elliptic_curves.formal_group.EllipticCurveFormalGroup method) H has_additive_reduction() (sage.schemes.elliptic_curves.ell_local_data.EllipticCurveLocalData method) (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) has_bad_reduction() (sage.schemes.elliptic_curves.ell_local_data.EllipticCurveLocalData method) (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) has_cm() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) has_finite_order() (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_field method) (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_finite_field method) (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_number_field method) has_global_minimal_model() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) has_good_reduction() (sage.schemes.elliptic_curves.ell_local_data.EllipticCurveLocalData method) (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_number_field method) has_good_reduction_outside_S() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) has_infinite_order() (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_field method) (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_number_field method) has_multiplicative_reduction() (sage.schemes.elliptic_curves.ell_local_data.EllipticCurveLocalData method) (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) has_nonsplit_multiplicative_reduction() (sage.schemes.elliptic_curves.ell_local_data.EllipticCurveLocalData method) (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) has_odd_degree_model() (sage.schemes.hyperelliptic_curves.hyperelliptic_generic.HyperellipticCurve_generic method) has_rational_cm() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) has_split_multiplicative_reduction() (sage.schemes.elliptic_curves.ell_local_data.EllipticCurveLocalData method) (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) hasse_invariant() (sage.schemes.elliptic_curves.ell_field.EllipticCurve_field method) Hasse_Witt() (sage.schemes.hyperelliptic_curves.hyperelliptic_finite_field.HyperellipticCurve_finite_field method) heegner_conductors() (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlg method) heegner_discriminants() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlg method) heegner_discriminants_list() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) heegner_divisor() (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlg method) heegner_index() (in module sage.schemes.elliptic_curves.heegner) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) heegner_index_bound() (in module sage.schemes.elliptic_curves.heegner) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) heegner_point() (in module sage.schemes.elliptic_curves.heegner) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) (sage.schemes.elliptic_curves.heegner.KolyvaginCohomologyClass method) (sage.schemes.elliptic_curves.heegner.KolyvaginPoint method) heegner_point_height() (in module sage.schemes.elliptic_curves.heegner) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) heegner_point_on_X0N() (sage.schemes.elliptic_curves.heegner.HeegnerPointOnEllipticCurve method) heegner_points() (in module sage.schemes.elliptic_curves.heegner) heegner_sha_an() (in module sage.schemes.elliptic_curves.heegner) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) HeegnerPoint (class in sage.schemes.elliptic_curves.heegner) HeegnerPointOnEllipticCurve (class in sage.schemes.elliptic_curves.heegner) HeegnerPointOnX0N (class in sage.schemes.elliptic_curves.heegner) HeegnerPoints (class in sage.schemes.elliptic_curves.heegner) HeegnerPoints_level (class in sage.schemes.elliptic_curves.heegner) HeegnerPoints_level_disc (class in sage.schemes.elliptic_curves.heegner) HeegnerPoints_level_disc_cond (class in sage.schemes.elliptic_curves.heegner) HeegnerQuatAlg (class in sage.schemes.elliptic_curves.heegner) HeegnerQuatAlgEmbedding (class in sage.schemes.elliptic_curves.heegner) height() (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) height_above_floor() (sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field method) height_function() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) height_pairing_matrix() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) helper_matrix() (in module sage.schemes.hyperelliptic_curves.monsky_washnitzer) (sage.schemes.hyperelliptic_curves.monsky_washnitzer.MonskyWashnitzerDifferentialRing method) hilbert_class_polynomial() (in module sage.schemes.elliptic_curves.cm) hypellfrob() (in module sage.schemes.hyperelliptic_curves.hypellfrob) hyperelliptic_polynomials() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) (sage.schemes.hyperelliptic_curves.hyperelliptic_generic.HyperellipticCurve_generic method) HyperellipticCurve() (in module sage.schemes.hyperelliptic_curves.constructor) HyperellipticCurve_finite_field (class in sage.schemes.hyperelliptic_curves.hyperelliptic_finite_field) HyperellipticCurve_from_invariants() (in module sage.schemes.hyperelliptic_curves.mestre) HyperellipticCurve_g2 (class in sage.schemes.hyperelliptic_curves.hyperelliptic_g2) HyperellipticCurve_generic (class in sage.schemes.hyperelliptic_curves.hyperelliptic_generic) HyperellipticCurve_padic_field (class in sage.schemes.hyperelliptic_curves.hyperelliptic_padic_field) HyperellipticCurve_rational_field (class in sage.schemes.hyperelliptic_curves.hyperelliptic_rational_field) HyperellipticJacobian_g2 (class in sage.schemes.hyperelliptic_curves.jacobian_g2) HyperellipticJacobian_generic (class in sage.schemes.hyperelliptic_curves.jacobian_generic) I ideal() (sage.schemes.elliptic_curves.heegner.GaloisAutomorphismQuadraticForm method) identity_morphism() (in module sage.schemes.elliptic_curves.weierstrass_morphism) igusa_clebsch_invariants() (in module sage.schemes.hyperelliptic_curves.invariants) (sage.schemes.hyperelliptic_curves.hyperelliptic_g2.HyperellipticCurve_g2 method) igusa_to_clebsch() (in module sage.schemes.hyperelliptic_curves.invariants) image_classes() (sage.schemes.elliptic_curves.gal_reps.GaloisRepresentation method) image_type() (sage.schemes.elliptic_curves.gal_reps.GaloisRepresentation method) index() (sage.schemes.elliptic_curves.heegner.KolyvaginPoint method) (sage.schemes.elliptic_curves.isogeny_class.IsogenyClass_EC method) inf_max_abs() (in module sage.schemes.elliptic_curves.height) init() (in module sage.schemes.elliptic_curves.gp_simon) innermost_point() (sage.schemes.elliptic_curves.period_lattice_region.PeriodicRegion method) integral_model() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) integral_points() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) integral_points_with_bounded_mw_coeffs() (in module sage.schemes.elliptic_curves.ell_rational_field) integral_short_weierstrass_model() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) integral_x_coords_in_interval() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) integrate() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.MonskyWashnitzerDifferential method) intersection() (sage.schemes.elliptic_curves.height.UnionOfIntervals class method) interval_products() (in module sage.schemes.hyperelliptic_curves.hypellfrob) intervals() (sage.schemes.elliptic_curves.height.UnionOfIntervals method) invariant_differential() (sage.schemes.hyperelliptic_curves.hyperelliptic_generic.HyperellipticCurve_generic method) (sage.schemes.hyperelliptic_curves.monsky_washnitzer.MonskyWashnitzerDifferentialRing method) inverse() (sage.schemes.elliptic_curves.formal_group.EllipticCurveFormalGroup method) (sage.schemes.elliptic_curves.weierstrass_transform.WeierstrassTransformationWithInverse_class method) is_cm_j_invariant() (in module sage.schemes.elliptic_curves.cm) is_crystalline() (sage.schemes.elliptic_curves.gal_reps.GaloisRepresentation method) is_divisible_by() (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_field method) is_EllipticCurve() (in module sage.schemes.elliptic_curves.ell_generic) is_empty() (sage.schemes.elliptic_curves.height.UnionOfIntervals method) (sage.schemes.elliptic_curves.period_lattice_region.PeriodicRegion method) is_field() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialHyperellipticQuotientRing method) is_finite_order() (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_field method) is_global_integral_model() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) is_global_minimal_model() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) is_good() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) is_HCP() (in module sage.schemes.elliptic_curves.cm) is_HyperellipticCurve() (in module sage.schemes.hyperelliptic_curves.hyperelliptic_generic) is_identity() (sage.schemes.elliptic_curves.weierstrass_morphism.baseWI method) is_in_weierstrass_disc() (sage.schemes.hyperelliptic_curves.hyperelliptic_padic_field.HyperellipticCurve_padic_field method) is_inert() (in module sage.schemes.elliptic_curves.heegner) is_injective() (sage.schemes.elliptic_curves.hom.EllipticCurveHom method) (sage.schemes.elliptic_curves.hom_composite.EllipticCurveHom_composite method) (sage.schemes.elliptic_curves.hom_frobenius.EllipticCurveHom_frobenius method) (sage.schemes.elliptic_curves.hom_scalar.EllipticCurveHom_scalar method) is_integral() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) is_irreducible() (sage.schemes.elliptic_curves.gal_reps.GaloisRepresentation method) is_isogenous() (sage.schemes.elliptic_curves.ell_field.EllipticCurve_field method) (sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field method) (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) is_isomorphic() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) is_j_supersingular() (in module sage.schemes.elliptic_curves.ell_finite_field) is_kernel_polynomial() (in module sage.schemes.elliptic_curves.isogeny_small_degree) is_kolyvagin() (sage.schemes.elliptic_curves.heegner.GaloisGroup method) is_kolyvagin_conductor() (in module sage.schemes.elliptic_curves.heegner) is_local_integral_model() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) is_minimal() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) is_normalized() (sage.schemes.elliptic_curves.hom.EllipticCurveHom method) is_odd_degree() (sage.schemes.hyperelliptic_curves.hyperelliptic_g2.HyperellipticCurve_g2 method) is_on_curve() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) is_on_identity_component() (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_number_field method) is_ordinary() (sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) (sage.schemes.elliptic_curves.gal_reps.GaloisRepresentation method) (sage.schemes.elliptic_curves.padic_lseries.pAdicLseriesOrdinary method) (sage.schemes.elliptic_curves.padic_lseries.pAdicLseriesSupersingular method) is_p_integral() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) is_p_minimal() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) is_possible_j() (in module sage.schemes.elliptic_curves.ell_egros) is_potentially_crystalline() (sage.schemes.elliptic_curves.gal_reps.GaloisRepresentation method) is_potentially_semistable() (sage.schemes.elliptic_curves.gal_reps.GaloisRepresentation method) is_Q_curve() (in module sage.schemes.elliptic_curves.Qcurves) (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) is_quadratic_twist() (sage.schemes.elliptic_curves.ell_field.EllipticCurve_field method) is_quartic_twist() (sage.schemes.elliptic_curves.ell_field.EllipticCurve_field method) is_quasi_unipotent() (sage.schemes.elliptic_curves.gal_reps.GaloisRepresentation method) is_ramified() (in module sage.schemes.elliptic_curves.heegner) is_real() (sage.schemes.elliptic_curves.period_lattice.PeriodLattice_ell method) is_rectangular() (sage.schemes.elliptic_curves.period_lattice.PeriodLattice_ell method) is_reducible() (sage.schemes.elliptic_curves.gal_reps.GaloisRepresentation method) is_same_disc() (sage.schemes.hyperelliptic_curves.hyperelliptic_padic_field.HyperellipticCurve_padic_field method) is_semistable() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) (sage.schemes.elliptic_curves.gal_reps.GaloisRepresentation method) is_separable() (sage.schemes.elliptic_curves.ell_curve_isogeny.EllipticCurveIsogeny method) (sage.schemes.elliptic_curves.hom.EllipticCurveHom method) (sage.schemes.elliptic_curves.hom_composite.EllipticCurveHom_composite method) (sage.schemes.elliptic_curves.hom_frobenius.EllipticCurveHom_frobenius method) (sage.schemes.elliptic_curves.hom_scalar.EllipticCurveHom_scalar method) (sage.schemes.elliptic_curves.hom_velusqrt.EllipticCurveHom_velusqrt method) (sage.schemes.elliptic_curves.weierstrass_morphism.WeierstrassIsomorphism method) is_sextic_twist() (sage.schemes.elliptic_curves.ell_field.EllipticCurve_field method) is_singular() (sage.schemes.hyperelliptic_curves.hyperelliptic_generic.HyperellipticCurve_generic method) is_smooth() (sage.schemes.hyperelliptic_curves.hyperelliptic_generic.HyperellipticCurve_generic method) is_split() (in module sage.schemes.elliptic_curves.heegner) (sage.schemes.elliptic_curves.ell_tate_curve.TateCurve method) is_subfield() (sage.schemes.elliptic_curves.heegner.RingClassField method) is_supersingular() (sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) (sage.schemes.elliptic_curves.padic_lseries.pAdicLseriesOrdinary method) (sage.schemes.elliptic_curves.padic_lseries.pAdicLseriesSupersingular method) is_surjective() (sage.schemes.elliptic_curves.gal_reps.GaloisRepresentation method) (sage.schemes.elliptic_curves.gal_reps_number_field.GaloisRepresentation method) (sage.schemes.elliptic_curves.hom.EllipticCurveHom method) is_unipotent() (sage.schemes.elliptic_curves.gal_reps.GaloisRepresentation method) is_unramified() (sage.schemes.elliptic_curves.gal_reps.GaloisRepresentation method) is_weierstrass() (sage.schemes.hyperelliptic_curves.hyperelliptic_padic_field.HyperellipticCurve_padic_field method) is_x_coord() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) is_zero() (sage.schemes.elliptic_curves.hom.EllipticCurveHom method) isogenies() (sage.schemes.elliptic_curves.isogeny_class.IsogenyClass_EC method) isogenies_13_0() (in module sage.schemes.elliptic_curves.isogeny_small_degree) isogenies_13_1728() (in module sage.schemes.elliptic_curves.isogeny_small_degree) isogenies_2() (in module sage.schemes.elliptic_curves.isogeny_small_degree) isogenies_3() (in module sage.schemes.elliptic_curves.isogeny_small_degree) isogenies_5_0() (in module sage.schemes.elliptic_curves.isogeny_small_degree) isogenies_5_1728() (in module sage.schemes.elliptic_curves.isogeny_small_degree) isogenies_7_0() (in module sage.schemes.elliptic_curves.isogeny_small_degree) isogenies_7_1728() (in module sage.schemes.elliptic_curves.isogeny_small_degree) isogenies_prime_degree() (in module sage.schemes.elliptic_curves.isogeny_small_degree) (sage.schemes.elliptic_curves.ell_field.EllipticCurve_field method) (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) isogenies_prime_degree_general() (in module sage.schemes.elliptic_curves.isogeny_small_degree) isogenies_prime_degree_genus_0() (in module sage.schemes.elliptic_curves.isogeny_small_degree) isogenies_prime_degree_genus_plus_0() (in module sage.schemes.elliptic_curves.isogeny_small_degree) isogenies_prime_degree_genus_plus_0_j0() (in module sage.schemes.elliptic_curves.isogeny_small_degree) isogenies_prime_degree_genus_plus_0_j1728() (in module sage.schemes.elliptic_curves.isogeny_small_degree) isogenies_sporadic_Q() (in module sage.schemes.elliptic_curves.isogeny_small_degree) isogeny() (sage.schemes.elliptic_curves.ell_field.EllipticCurve_field method) isogeny_bound() (sage.schemes.elliptic_curves.gal_reps_number_field.GaloisRepresentation method) isogeny_class() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) isogeny_codomain() (sage.schemes.elliptic_curves.ell_field.EllipticCurve_field method) isogeny_codomain_from_kernel() (in module sage.schemes.elliptic_curves.ell_curve_isogeny) isogeny_degree() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) isogeny_degrees_cm() (in module sage.schemes.elliptic_curves.isogeny_class) isogeny_ell_graph() (sage.schemes.elliptic_curves.ell_field.EllipticCurve_field method) isogeny_graph() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) IsogenyClass_EC (class in sage.schemes.elliptic_curves.isogeny_class) IsogenyClass_EC_NumberField (class in sage.schemes.elliptic_curves.isogeny_class) IsogenyClass_EC_Rational (class in sage.schemes.elliptic_curves.isogeny_class) isomorphism_to() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) isomorphisms() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) J j_invariant() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) Jacobian() (in module sage.schemes.elliptic_curves.jacobian) jacobian() (sage.schemes.hyperelliptic_curves.hyperelliptic_g2.HyperellipticCurve_g2 method) (sage.schemes.hyperelliptic_curves.hyperelliptic_generic.HyperellipticCurve_generic method) Jacobian_of_curve() (in module sage.schemes.elliptic_curves.jacobian) Jacobian_of_equation() (in module sage.schemes.elliptic_curves.jacobian) JacobianHomset_divisor_classes (class in sage.schemes.hyperelliptic_curves.jacobian_homset) JacobianMorphism_divisor_class_field (class in sage.schemes.hyperelliptic_curves.jacobian_morphism) join() (sage.schemes.elliptic_curves.height.UnionOfIntervals static method) K kernel_polynomial() (sage.schemes.elliptic_curves.ell_curve_isogeny.EllipticCurveIsogeny method) (sage.schemes.elliptic_curves.hom.EllipticCurveHom method) (sage.schemes.elliptic_curves.hom_composite.EllipticCurveHom_composite method) (sage.schemes.elliptic_curves.hom_frobenius.EllipticCurveHom_frobenius method) (sage.schemes.elliptic_curves.hom_scalar.EllipticCurveHom_scalar method) (sage.schemes.elliptic_curves.hom_velusqrt.EllipticCurveHom_velusqrt method) (sage.schemes.elliptic_curves.weierstrass_morphism.WeierstrassIsomorphism method) kodaira_symbol() (sage.schemes.elliptic_curves.ell_local_data.EllipticCurveLocalData method) (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) kodaira_type() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) kodaira_type_old() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) KodairaSymbol() (in module sage.schemes.elliptic_curves.kodaira_symbol) KodairaSymbol_class (class in sage.schemes.elliptic_curves.kodaira_symbol) kolyvagin_cohomology_class() (sage.schemes.elliptic_curves.heegner.HeegnerPointOnEllipticCurve method) (sage.schemes.elliptic_curves.heegner.KolyvaginPoint method) kolyvagin_conductors() (sage.schemes.elliptic_curves.heegner.HeegnerPoints_level_disc method) kolyvagin_cyclic_subideals() (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlg method) kolyvagin_generator() (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlg method) kolyvagin_generators() (sage.schemes.elliptic_curves.heegner.GaloisGroup method) (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlg method) kolyvagin_point() (in module sage.schemes.elliptic_curves.heegner) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) (sage.schemes.elliptic_curves.heegner.HeegnerPointOnEllipticCurve method) (sage.schemes.elliptic_curves.heegner.KolyvaginCohomologyClass method) kolyvagin_point_on_curve() (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlg method) kolyvagin_reduction_data() (in module sage.schemes.elliptic_curves.heegner) kolyvagin_sigma_operator() (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlg method) KolyvaginCohomologyClass (class in sage.schemes.elliptic_curves.heegner) KolyvaginCohomologyClassEn (class in sage.schemes.elliptic_curves.heegner) KolyvaginPoint (class in sage.schemes.elliptic_curves.heegner) kummer_morphism() (sage.schemes.hyperelliptic_curves.hyperelliptic_g2.HyperellipticCurve_g2 method) kummer_surface() (sage.schemes.hyperelliptic_curves.jacobian_g2.HyperellipticJacobian_g2 method) KummerSurface (class in sage.schemes.hyperelliptic_curves.kummer_surface) L L1_vanishes() (sage.schemes.elliptic_curves.lseries_ell.Lseries_ell method) L_invariant() (sage.schemes.elliptic_curves.ell_tate_curve.TateCurve method) L_ratio() (sage.schemes.elliptic_curves.lseries_ell.Lseries_ell method) label() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) Lambda() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) largest_disc_with_class_number() (in module sage.schemes.elliptic_curves.cm) largest_fundamental_disc_with_class_number() (in module sage.schemes.elliptic_curves.cm) left_orders() (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlg method) level() (sage.schemes.elliptic_curves.heegner.HeegnerPoint method) (sage.schemes.elliptic_curves.heegner.HeegnerPoints method) (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlg method) lift() (in module sage.schemes.hyperelliptic_curves.monsky_washnitzer) (sage.schemes.elliptic_curves.ell_tate_curve.TateCurve method) lift_of_hilbert_class_field_galois_group() (sage.schemes.elliptic_curves.heegner.GaloisGroup method) lift_x() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) (sage.schemes.hyperelliptic_curves.hyperelliptic_generic.HyperellipticCurve_generic method) lll_reduce() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) lmfdb_page() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) local_analytic_interpolation() (sage.schemes.hyperelliptic_curves.hyperelliptic_padic_field.HyperellipticCurve_padic_field method) local_coord() (sage.schemes.hyperelliptic_curves.hyperelliptic_generic.HyperellipticCurve_generic method) local_coordinates_at_infinity() (sage.schemes.hyperelliptic_curves.hyperelliptic_generic.HyperellipticCurve_generic method) local_coordinates_at_nonweierstrass() (sage.schemes.hyperelliptic_curves.hyperelliptic_generic.HyperellipticCurve_generic method) local_coordinates_at_weierstrass() (sage.schemes.hyperelliptic_curves.hyperelliptic_generic.HyperellipticCurve_generic method) local_data() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) local_integral_model() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) local_minimal_model() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) log() (sage.schemes.elliptic_curves.formal_group.EllipticCurveFormalGroup method) lseries() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) (sage.schemes.hyperelliptic_curves.hyperelliptic_rational_field.HyperellipticCurve_rational_field method) Lseries_ell (class in sage.schemes.elliptic_curves.lseries_ell) lseries_gross_zagier() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) M make_monic() (in module sage.schemes.elliptic_curves.heegner) manin_constant() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) manin_symbol() (sage.schemes.elliptic_curves.mod_sym_num.ModularSymbolNumerical method) map_to_complex_numbers() (sage.schemes.elliptic_curves.heegner.HeegnerPointOnEllipticCurve method) (sage.schemes.elliptic_curves.modular_parametrization.ModularParameterization method) map_to_curve() (sage.schemes.elliptic_curves.heegner.HeegnerPointOnX0N method) matrix() (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlgEmbedding method) (sage.schemes.elliptic_curves.isogeny_class.IsogenyClass_EC method) matrix_of_frobenius() (in module sage.schemes.hyperelliptic_curves.monsky_washnitzer) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) (sage.schemes.hyperelliptic_curves.hyperelliptic_rational_field.HyperellipticCurve_rational_field method) matrix_of_frobenius_hyperelliptic() (in module sage.schemes.hyperelliptic_curves.monsky_washnitzer) matrix_on_subgroup() (sage.schemes.elliptic_curves.hom.EllipticCurveHom method) max_pow_y() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.MonskyWashnitzerDifferential method) (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialHyperellipticQuotientElement method) ME() (sage.schemes.elliptic_curves.height.EllipticCurveCanonicalHeight method) measure() (sage.schemes.elliptic_curves.padic_lseries.pAdicLseries method) Mestre_conic() (in module sage.schemes.hyperelliptic_curves.mestre) min() (sage.schemes.elliptic_curves.height.EllipticCurveCanonicalHeight method) min_gr() (sage.schemes.elliptic_curves.height.EllipticCurveCanonicalHeight method) min_on_disk() (in module sage.schemes.elliptic_curves.height) min_pow_y() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.MonskyWashnitzerDifferential method) (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialHyperellipticQuotientElement method) minimal_discriminant_ideal() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) minimal_model() (sage.schemes.elliptic_curves.ell_local_data.EllipticCurveLocalData method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) minimal_quadratic_twist() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) mod() (sage.schemes.elliptic_curves.heegner.KolyvaginPoint method) mod5family() (in module sage.schemes.elliptic_curves.mod5family) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) modp_dual_elliptic_curve_factor() (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlg method) modp_splitting_data() (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlg method) modp_splitting_map() (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlg method) modular_degree() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) modular_form() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) modular_parametrization() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) modular_symbol() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) (sage.schemes.elliptic_curves.padic_lseries.pAdicLseries method) modular_symbol_numerical() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) modular_symbol_space() (in module sage.schemes.elliptic_curves.ell_modular_symbols) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) ModularParameterization (class in sage.schemes.elliptic_curves.modular_parametrization) ModularSymbol (class in sage.schemes.elliptic_curves.ell_modular_symbols) ModularSymbolECLIB (class in sage.schemes.elliptic_curves.ell_modular_symbols) ModularSymbolNumerical (class in sage.schemes.elliptic_curves.mod_sym_num) ModularSymbolSage (class in sage.schemes.elliptic_curves.ell_modular_symbols) module sage.interfaces.genus2reduction sage.schemes.elliptic_curves.cm sage.schemes.elliptic_curves.constructor sage.schemes.elliptic_curves.descent_two_isogeny sage.schemes.elliptic_curves.ec_database sage.schemes.elliptic_curves.ell_curve_isogeny sage.schemes.elliptic_curves.ell_egros sage.schemes.elliptic_curves.ell_field sage.schemes.elliptic_curves.ell_finite_field sage.schemes.elliptic_curves.ell_generic sage.schemes.elliptic_curves.ell_local_data sage.schemes.elliptic_curves.ell_modular_symbols sage.schemes.elliptic_curves.ell_number_field sage.schemes.elliptic_curves.ell_padic_field sage.schemes.elliptic_curves.ell_point sage.schemes.elliptic_curves.ell_rational_field sage.schemes.elliptic_curves.ell_tate_curve sage.schemes.elliptic_curves.ell_torsion sage.schemes.elliptic_curves.ell_wp sage.schemes.elliptic_curves.formal_group sage.schemes.elliptic_curves.gal_reps sage.schemes.elliptic_curves.gal_reps_number_field sage.schemes.elliptic_curves.gp_simon sage.schemes.elliptic_curves.heegner sage.schemes.elliptic_curves.height sage.schemes.elliptic_curves.hom sage.schemes.elliptic_curves.hom_composite sage.schemes.elliptic_curves.hom_frobenius sage.schemes.elliptic_curves.hom_scalar sage.schemes.elliptic_curves.hom_velusqrt sage.schemes.elliptic_curves.isogeny_class sage.schemes.elliptic_curves.isogeny_small_degree sage.schemes.elliptic_curves.jacobian sage.schemes.elliptic_curves.kodaira_symbol sage.schemes.elliptic_curves.lseries_ell sage.schemes.elliptic_curves.mod5family sage.schemes.elliptic_curves.mod_sym_num sage.schemes.elliptic_curves.modular_parametrization sage.schemes.elliptic_curves.padic_lseries sage.schemes.elliptic_curves.period_lattice sage.schemes.elliptic_curves.period_lattice_region sage.schemes.elliptic_curves.Qcurves sage.schemes.elliptic_curves.saturation sage.schemes.elliptic_curves.sha_tate sage.schemes.elliptic_curves.weierstrass_morphism sage.schemes.elliptic_curves.weierstrass_transform sage.schemes.hyperelliptic_curves.constructor sage.schemes.hyperelliptic_curves.hypellfrob sage.schemes.hyperelliptic_curves.hyperelliptic_finite_field sage.schemes.hyperelliptic_curves.hyperelliptic_g2 sage.schemes.hyperelliptic_curves.hyperelliptic_generic sage.schemes.hyperelliptic_curves.hyperelliptic_padic_field sage.schemes.hyperelliptic_curves.hyperelliptic_rational_field sage.schemes.hyperelliptic_curves.invariants sage.schemes.hyperelliptic_curves.jacobian_g2 sage.schemes.hyperelliptic_curves.jacobian_generic sage.schemes.hyperelliptic_curves.jacobian_homset sage.schemes.hyperelliptic_curves.jacobian_morphism sage.schemes.hyperelliptic_curves.kummer_surface sage.schemes.hyperelliptic_curves.mestre sage.schemes.hyperelliptic_curves.monsky_washnitzer monomial() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialHyperellipticQuotientRing method) monomial_diff_coeffs() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialHyperellipticQuotientRing method) monomial_diff_coeffs_matrices() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialHyperellipticQuotientRing method) monsky_washnitzer() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialHyperellipticQuotientRing method) monsky_washnitzer_gens() (sage.schemes.hyperelliptic_curves.hyperelliptic_generic.HyperellipticCurve_generic method) MonskyWashnitzerDifferential (class in sage.schemes.hyperelliptic_curves.monsky_washnitzer) MonskyWashnitzerDifferentialRing (class in sage.schemes.hyperelliptic_curves.monsky_washnitzer) MonskyWashnitzerDifferentialRing_class (in module sage.schemes.hyperelliptic_curves.monsky_washnitzer) montgomery_model() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) mult_by_n() (sage.schemes.elliptic_curves.formal_group.EllipticCurveFormalGroup method) multiplication_by_m() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) multiplication_by_m_isogeny() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) mwrank() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) mwrank_curve() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) N n() (sage.schemes.elliptic_curves.heegner.KolyvaginCohomologyClass method) nearby_rational_poly() (in module sage.schemes.elliptic_curves.heegner) negation_morphism() (in module sage.schemes.elliptic_curves.weierstrass_morphism) newform() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) newton_sqrt() (sage.schemes.hyperelliptic_curves.hyperelliptic_padic_field.HyperellipticCurve_padic_field method) ngens() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) non_archimedean_local_height() (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_number_field method) non_minimal_primes() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) non_surjective() (sage.schemes.elliptic_curves.gal_reps.GaloisRepresentation method) (sage.schemes.elliptic_curves.gal_reps_number_field.GaloisRepresentation method) nonneg_region() (in module sage.schemes.elliptic_curves.height) normalise_periods() (in module sage.schemes.elliptic_curves.period_lattice) normalised_basis() (sage.schemes.elliptic_curves.period_lattice.PeriodLattice_ell method) Np() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) numerical_approx() (sage.schemes.elliptic_curves.heegner.HeegnerPointOnEllipticCurve method) (sage.schemes.elliptic_curves.heegner.KolyvaginPoint method) O odd_degree_model() (sage.schemes.hyperelliptic_curves.hyperelliptic_generic.HyperellipticCurve_generic method) omega() (sage.schemes.elliptic_curves.period_lattice.PeriodLattice_ell method) one() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialCubicQuotientRing method) (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialHyperellipticQuotientRing method) optimal_curve() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) optimal_embeddings() (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlg method) order() (sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field method) (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_field method) (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_finite_field method) (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_number_field method) (sage.schemes.elliptic_curves.heegner.GaloisAutomorphismComplexConjugation method) (sage.schemes.elliptic_curves.heegner.GaloisAutomorphismQuadraticForm method) order_of_vanishing() (sage.schemes.elliptic_curves.padic_lseries.pAdicLseries method) OrderClassNumber() (in module sage.schemes.elliptic_curves.cm) ordinary_primes() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) original_curve() (sage.schemes.elliptic_curves.ell_tate_curve.TateCurve method) P p1_element() (sage.schemes.elliptic_curves.heegner.GaloisAutomorphismQuadraticForm method) p_primary_bound() (sage.schemes.elliptic_curves.sha_tate.Sha method) p_primary_order() (sage.schemes.elliptic_curves.sha_tate.Sha method) p_projections() (in module sage.schemes.elliptic_curves.saturation) p_rank() (sage.schemes.hyperelliptic_curves.hyperelliptic_finite_field.HyperellipticCurve_finite_field method) p_saturation() (sage.schemes.elliptic_curves.saturation.EllipticCurveSaturator method) P_to_S() (sage.schemes.hyperelliptic_curves.hyperelliptic_padic_field.HyperellipticCurve_padic_field method) padic_E2() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) padic_elliptic_logarithm() (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_finite_field method) (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_number_field method) padic_height() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) (sage.schemes.elliptic_curves.ell_tate_curve.TateCurve method) padic_height_pairing_matrix() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) padic_height_via_multiply() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) padic_lseries() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) padic_regulator() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) (sage.schemes.elliptic_curves.ell_tate_curve.TateCurve method) padic_sigma() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) padic_sigma_truncated() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) pAdicLseries (class in sage.schemes.elliptic_curves.padic_lseries) pAdicLseriesOrdinary (class in sage.schemes.elliptic_curves.padic_lseries) pAdicLseriesSupersingular (class in sage.schemes.elliptic_curves.padic_lseries) parameter() (sage.schemes.elliptic_curves.ell_tate_curve.TateCurve method) parametrisation_onto_original_curve() (sage.schemes.elliptic_curves.ell_tate_curve.TateCurve method) parametrisation_onto_tate_curve() (sage.schemes.elliptic_curves.ell_tate_curve.TateCurve method) parent() (sage.schemes.elliptic_curves.heegner.GaloisAutomorphism method) pari_curve() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) pari_mincurve() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) period_lattice() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) PeriodicRegion (class in sage.schemes.elliptic_curves.period_lattice_region) PeriodLattice (class in sage.schemes.elliptic_curves.period_lattice) PeriodLattice_ell (class in sage.schemes.elliptic_curves.period_lattice) plot() (sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field method) (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_field method) (sage.schemes.elliptic_curves.heegner.HeegnerPointOnX0N method) (sage.schemes.elliptic_curves.heegner.HeegnerPoints_level_disc_cond method) (sage.schemes.elliptic_curves.heegner.KolyvaginPoint method) (sage.schemes.elliptic_curves.period_lattice_region.PeriodicRegion method) point() (sage.schemes.hyperelliptic_curves.jacobian_generic.HyperellipticJacobian_generic method) point_exact() (sage.schemes.elliptic_curves.heegner.HeegnerPointOnEllipticCurve method) (sage.schemes.elliptic_curves.heegner.KolyvaginPoint method) point_of_order() (in module sage.schemes.elliptic_curves.ell_field) point_search() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) points() (sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field method) (sage.schemes.elliptic_curves.ell_torsion.EllipticCurveTorsionSubgroup method) (sage.schemes.elliptic_curves.heegner.HeegnerPoints_level_disc_cond method) (sage.schemes.hyperelliptic_curves.hyperelliptic_finite_field.HyperellipticCurve_finite_field method) pollack_stevens_modular_symbol() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) poly_ring() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialCubicQuotientRing method) possible_isogeny_degrees() (in module sage.schemes.elliptic_curves.isogeny_class) post_rescaling() (sage.schemes.elliptic_curves.weierstrass_transform.WeierstrassTransformation method) power_series() (sage.schemes.elliptic_curves.modular_parametrization.ModularParameterization method) (sage.schemes.elliptic_curves.padic_lseries.pAdicLseriesOrdinary method) (sage.schemes.elliptic_curves.padic_lseries.pAdicLseriesSupersingular method) prime() (sage.schemes.elliptic_curves.ell_local_data.EllipticCurveLocalData method) (sage.schemes.elliptic_curves.ell_tate_curve.TateCurve method) (sage.schemes.elliptic_curves.padic_lseries.pAdicLseries method) (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialHyperellipticQuotientRing method) projective_point() (in module sage.schemes.elliptic_curves.constructor) prove_BSD() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) Psi() (in module sage.schemes.elliptic_curves.isogeny_small_degree) psi() (sage.schemes.elliptic_curves.height.EllipticCurveCanonicalHeight method) Psi2() (in module sage.schemes.elliptic_curves.isogeny_small_degree) Q Q() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.MonskyWashnitzerDifferentialRing method) (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialHyperellipticQuotientRing method) q_eigenform() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) q_expansion() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) qf_matrix() (sage.schemes.elliptic_curves.isogeny_class.IsogenyClass_EC method) quadratic_field() (sage.schemes.elliptic_curves.heegner.HeegnerPoint method) (sage.schemes.elliptic_curves.heegner.HeegnerPoints_level_disc method) (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlg method) (sage.schemes.elliptic_curves.heegner.RingClassField method) quadratic_form() (sage.schemes.elliptic_curves.heegner.GaloisAutomorphismQuadraticForm method) (sage.schemes.elliptic_curves.heegner.HeegnerPointOnEllipticCurve method) (sage.schemes.elliptic_curves.heegner.HeegnerPointOnX0N method) quadratic_order() (in module sage.schemes.elliptic_curves.heegner) (sage.schemes.elliptic_curves.heegner.HeegnerPoint method) quadratic_twist() (sage.schemes.elliptic_curves.ell_field.EllipticCurve_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) quartic_twist() (sage.schemes.elliptic_curves.ell_field.EllipticCurve_field method) quaternion_algebra() (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlg method) R ramified_primes() (sage.schemes.elliptic_curves.heegner.RingClassField method) random_element() (sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field method) random_point() (sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field method) rank() (sage.schemes.elliptic_curves.ec_database.EllipticCurves method) (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) rank_bound() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) rank_bounds() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) rat_term_CIF() (in module sage.schemes.elliptic_curves.height) rational_kolyvagin_divisor() (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlg method) rational_maps() (sage.schemes.elliptic_curves.ell_curve_isogeny.EllipticCurveIsogeny method) (sage.schemes.elliptic_curves.hom.EllipticCurveHom method) (sage.schemes.elliptic_curves.hom_composite.EllipticCurveHom_composite method) (sage.schemes.elliptic_curves.hom_frobenius.EllipticCurveHom_frobenius method) (sage.schemes.elliptic_curves.hom_scalar.EllipticCurveHom_scalar method) (sage.schemes.elliptic_curves.hom_velusqrt.EllipticCurveHom_velusqrt method) (sage.schemes.elliptic_curves.weierstrass_morphism.WeierstrassIsomorphism method) rational_points() (sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field method) (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.hyperelliptic_curves.hyperelliptic_generic.HyperellipticCurve_generic method) real_components() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) real_intersection_is_empty() (sage.schemes.elliptic_curves.height.EllipticCurveCanonicalHeight method) real_period() (sage.schemes.elliptic_curves.period_lattice.PeriodLattice_ell method) reduce() (sage.schemes.elliptic_curves.period_lattice.PeriodLattice_ell method) (sage.schemes.hyperelliptic_curves.monsky_washnitzer.MonskyWashnitzerDifferential method) reduce_all() (in module sage.schemes.hyperelliptic_curves.monsky_washnitzer) reduce_fast() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.MonskyWashnitzerDifferential method) reduce_mod() (sage.schemes.elliptic_curves.heegner.HeegnerPoints_level method) reduce_mod_q() (in module sage.schemes.elliptic_curves.saturation) reduce_neg_y() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.MonskyWashnitzerDifferential method) reduce_neg_y_fast() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.MonskyWashnitzerDifferential method) reduce_neg_y_faster() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.MonskyWashnitzerDifferential method) reduce_negative() (in module sage.schemes.hyperelliptic_curves.monsky_washnitzer) reduce_pos_y() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.MonskyWashnitzerDifferential method) reduce_pos_y_fast() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.MonskyWashnitzerDifferential method) reduce_positive() (in module sage.schemes.hyperelliptic_curves.monsky_washnitzer) reduce_tau() (in module sage.schemes.elliptic_curves.period_lattice) reduce_zero() (in module sage.schemes.hyperelliptic_curves.monsky_washnitzer) reduced_quadratic_form() (sage.schemes.elliptic_curves.heegner.HeegnerPointOnX0N method) reducible_primes() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.gal_reps.GaloisRepresentation method) (sage.schemes.elliptic_curves.gal_reps_number_field.GaloisRepresentation method) reducible_primes_Billerey() (in module sage.schemes.elliptic_curves.gal_reps_number_field) reducible_primes_naive() (in module sage.schemes.elliptic_curves.gal_reps_number_field) reduction() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) ReductionData (class in sage.interfaces.genus2reduction) refine() (sage.schemes.elliptic_curves.period_lattice_region.PeriodicRegion method) regulator() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) regulator_of_points() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) reorder() (sage.schemes.elliptic_curves.isogeny_class.IsogenyClass_EC method) residue_disc() (sage.schemes.hyperelliptic_curves.hyperelliptic_padic_field.HyperellipticCurve_padic_field method) right_ideals() (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlg method) ring_class_field() (sage.schemes.elliptic_curves.heegner.HeegnerPoint method) (sage.schemes.elliptic_curves.heegner.HeegnerPoints_level_disc_cond method) RingClassField (class in sage.schemes.elliptic_curves.heegner) root_number() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) rst_transform() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) S S() (sage.schemes.elliptic_curves.height.EllipticCurveCanonicalHeight method) S_integral_points() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) S_to_Q() (sage.schemes.hyperelliptic_curves.hyperelliptic_padic_field.HyperellipticCurve_padic_field method) sage.interfaces.genus2reduction module sage.schemes.elliptic_curves.cm module sage.schemes.elliptic_curves.constructor module sage.schemes.elliptic_curves.descent_two_isogeny module sage.schemes.elliptic_curves.ec_database module sage.schemes.elliptic_curves.ell_curve_isogeny module sage.schemes.elliptic_curves.ell_egros module sage.schemes.elliptic_curves.ell_field module sage.schemes.elliptic_curves.ell_finite_field module sage.schemes.elliptic_curves.ell_generic module sage.schemes.elliptic_curves.ell_local_data module sage.schemes.elliptic_curves.ell_modular_symbols module sage.schemes.elliptic_curves.ell_number_field module sage.schemes.elliptic_curves.ell_padic_field module sage.schemes.elliptic_curves.ell_point module sage.schemes.elliptic_curves.ell_rational_field module sage.schemes.elliptic_curves.ell_tate_curve module sage.schemes.elliptic_curves.ell_torsion module sage.schemes.elliptic_curves.ell_wp module sage.schemes.elliptic_curves.formal_group module sage.schemes.elliptic_curves.gal_reps module sage.schemes.elliptic_curves.gal_reps_number_field module sage.schemes.elliptic_curves.gp_simon module sage.schemes.elliptic_curves.heegner module sage.schemes.elliptic_curves.height module sage.schemes.elliptic_curves.hom module sage.schemes.elliptic_curves.hom_composite module sage.schemes.elliptic_curves.hom_frobenius module sage.schemes.elliptic_curves.hom_scalar module sage.schemes.elliptic_curves.hom_velusqrt module sage.schemes.elliptic_curves.isogeny_class module sage.schemes.elliptic_curves.isogeny_small_degree module sage.schemes.elliptic_curves.jacobian module sage.schemes.elliptic_curves.kodaira_symbol module sage.schemes.elliptic_curves.lseries_ell module sage.schemes.elliptic_curves.mod5family module sage.schemes.elliptic_curves.mod_sym_num module sage.schemes.elliptic_curves.modular_parametrization module sage.schemes.elliptic_curves.padic_lseries module sage.schemes.elliptic_curves.period_lattice module sage.schemes.elliptic_curves.period_lattice_region module sage.schemes.elliptic_curves.Qcurves module sage.schemes.elliptic_curves.saturation module sage.schemes.elliptic_curves.sha_tate module sage.schemes.elliptic_curves.weierstrass_morphism module sage.schemes.elliptic_curves.weierstrass_transform module sage.schemes.hyperelliptic_curves.constructor module sage.schemes.hyperelliptic_curves.hypellfrob module sage.schemes.hyperelliptic_curves.hyperelliptic_finite_field module sage.schemes.hyperelliptic_curves.hyperelliptic_g2 module sage.schemes.hyperelliptic_curves.hyperelliptic_generic module sage.schemes.hyperelliptic_curves.hyperelliptic_padic_field module sage.schemes.hyperelliptic_curves.hyperelliptic_rational_field module sage.schemes.hyperelliptic_curves.invariants module sage.schemes.hyperelliptic_curves.jacobian_g2 module sage.schemes.hyperelliptic_curves.jacobian_generic module sage.schemes.hyperelliptic_curves.jacobian_homset module sage.schemes.hyperelliptic_curves.jacobian_morphism module sage.schemes.hyperelliptic_curves.kummer_surface module sage.schemes.hyperelliptic_curves.mestre module sage.schemes.hyperelliptic_curves.monsky_washnitzer module satisfies_heegner_hypothesis() (in module sage.schemes.elliptic_curves.heegner) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) (sage.schemes.elliptic_curves.heegner.HeegnerQuatAlg method) satisfies_kolyvagin_hypothesis() (sage.schemes.elliptic_curves.heegner.HeegnerPointOnEllipticCurve method) (sage.schemes.elliptic_curves.heegner.HeegnerPoints_level_disc_cond method) (sage.schemes.elliptic_curves.heegner.KolyvaginPoint method) satisfies_weak_heegner_hypothesis() (in module sage.schemes.elliptic_curves.heegner) saturation() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) scalar_multiplication() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) scalar_multiply() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialCubicQuotientRingElement method) scale_curve() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) scaling_factor() (sage.schemes.elliptic_curves.ell_curve_isogeny.EllipticCurveIsogeny method) (sage.schemes.elliptic_curves.hom.EllipticCurveHom method) (sage.schemes.elliptic_curves.hom_composite.EllipticCurveHom_composite method) (sage.schemes.elliptic_curves.hom_frobenius.EllipticCurveHom_frobenius method) (sage.schemes.elliptic_curves.hom_scalar.EllipticCurveHom_scalar method) (sage.schemes.elliptic_curves.hom_velusqrt.EllipticCurveHom_velusqrt method) (sage.schemes.elliptic_curves.weierstrass_morphism.WeierstrassIsomorphism method) scheme() (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_field method) (sage.schemes.hyperelliptic_curves.jacobian_morphism.JacobianMorphism_divisor_class_field method) selmer_rank() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) series() (sage.schemes.elliptic_curves.padic_lseries.pAdicLseriesOrdinary method) (sage.schemes.elliptic_curves.padic_lseries.pAdicLseriesSupersingular method) set_order() (sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field method) (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_field method) sextic_twist() (sage.schemes.elliptic_curves.ell_field.EllipticCurve_field method) Sha (class in sage.schemes.elliptic_curves.sha_tate) sha() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) shift() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialCubicQuotientRingElement method) short_weierstrass_model() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) sigma() (sage.schemes.elliptic_curves.formal_group.EllipticCurveFormalGroup method) (sage.schemes.elliptic_curves.period_lattice.PeriodLattice_ell method) sign() (sage.schemes.elliptic_curves.ell_modular_symbols.ModularSymbol method) silverman_height_bound() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) simon_two_descent() (in module sage.schemes.elliptic_curves.gp_simon) (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) simplest_rational_poly() (in module sage.schemes.elliptic_curves.heegner) Sn() (sage.schemes.elliptic_curves.height.EllipticCurveCanonicalHeight method) solve_linear_differential_system() (in module sage.schemes.elliptic_curves.ell_wp) SpecialCubicQuotientRing (class in sage.schemes.hyperelliptic_curves.monsky_washnitzer) SpecialCubicQuotientRingElement (class in sage.schemes.hyperelliptic_curves.monsky_washnitzer) SpecialHyperellipticQuotientElement (class in sage.schemes.hyperelliptic_curves.monsky_washnitzer) SpecialHyperellipticQuotientRing (class in sage.schemes.hyperelliptic_curves.monsky_washnitzer) SpecialHyperellipticQuotientRing_class (in module sage.schemes.hyperelliptic_curves.monsky_washnitzer) square() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialCubicQuotientRingElement method) Step4Test() (in module sage.schemes.elliptic_curves.Qcurves) supersingular_j_polynomial() (in module sage.schemes.elliptic_curves.ell_finite_field) supersingular_primes() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) sympow() (sage.schemes.elliptic_curves.lseries_ell.Lseries_ell method) sympow_derivs() (sage.schemes.elliptic_curves.lseries_ell.Lseries_ell method) T tamagawa_exponent() (sage.schemes.elliptic_curves.ell_local_data.EllipticCurveLocalData method) (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) tamagawa_number() (sage.schemes.elliptic_curves.ell_local_data.EllipticCurveLocalData method) (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) tamagawa_number_old() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) tamagawa_numbers() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) tamagawa_product() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) tamagawa_product_bsd() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) tangent_at_smooth_point() (in module sage.schemes.elliptic_curves.constructor) tate_curve() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) tate_pairing() (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_field method) TateCurve (class in sage.schemes.elliptic_curves.ell_tate_curve) tau() (sage.schemes.elliptic_curves.heegner.HeegnerPointOnEllipticCurve method) (sage.schemes.elliptic_curves.heegner.HeegnerPointOnX0N method) (sage.schemes.elliptic_curves.height.EllipticCurveCanonicalHeight method) (sage.schemes.elliptic_curves.period_lattice.PeriodLattice_ell method) taylor_series() (sage.schemes.elliptic_curves.lseries_ell.Lseries_ell method) teichmuller() (sage.schemes.elliptic_curves.padic_lseries.pAdicLseries method) (sage.schemes.hyperelliptic_curves.hyperelliptic_padic_field.HyperellipticCurve_padic_field method) test_els() (in module sage.schemes.elliptic_curves.descent_two_isogeny) test_mu() (sage.schemes.elliptic_curves.height.EllipticCurveCanonicalHeight method) test_padic_square() (in module sage.schemes.elliptic_curves.descent_two_isogeny) test_qpls() (in module sage.schemes.elliptic_curves.descent_two_isogeny) test_valuation() (in module sage.schemes.elliptic_curves.descent_two_isogeny) three_selmer_rank() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) tiny_integrals() (sage.schemes.hyperelliptic_curves.hyperelliptic_padic_field.HyperellipticCurve_padic_field method) tiny_integrals_on_basis() (sage.schemes.hyperelliptic_curves.hyperelliptic_padic_field.HyperellipticCurve_padic_field method) torsion_basis() (sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field method) torsion_bound() (in module sage.schemes.elliptic_curves.ell_torsion) torsion_order() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) torsion_points() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) torsion_polynomial() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) torsion_subgroup() (sage.schemes.elliptic_curves.ell_number_field.EllipticCurve_number_field method) (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) trace() (sage.schemes.elliptic_curves.hom.EllipticCurveHom method) trace_of_frobenius() (sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field method) trace_to_real_numerical() (sage.schemes.elliptic_curves.heegner.KolyvaginPoint method) transportable_symbol() (sage.schemes.elliptic_curves.mod_sym_num.ModularSymbolNumerical method) transpose_list() (in module sage.schemes.hyperelliptic_curves.monsky_washnitzer) truncate_neg() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialHyperellipticQuotientElement method) tuple() (sage.schemes.elliptic_curves.weierstrass_morphism.baseWI method) twist_values() (sage.schemes.elliptic_curves.lseries_ell.Lseries_ell method) twist_zeros() (sage.schemes.elliptic_curves.lseries_ell.Lseries_ell method) twists() (sage.schemes.elliptic_curves.ell_finite_field.EllipticCurve_finite_field method) two_descent() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) two_descent_by_two_isogeny() (in module sage.schemes.elliptic_curves.descent_two_isogeny) two_descent_by_two_isogeny_work() (in module sage.schemes.elliptic_curves.descent_two_isogeny) two_descent_simon() (sage.schemes.elliptic_curves.ell_rational_field.EllipticCurve_rational_field method) two_division_polynomial() (sage.schemes.elliptic_curves.ell_generic.EllipticCurve_generic method) two_selmer_bound() (sage.schemes.elliptic_curves.sha_tate.Sha method) two_torsion_part() (in module sage.schemes.elliptic_curves.ell_curve_isogeny) two_torsion_rank() (sage.schemes.elliptic_curves.ell_field.EllipticCurve_field method) U ubs() (in module sage.schemes.hyperelliptic_curves.invariants) Ueberschiebung() (in module sage.schemes.hyperelliptic_curves.invariants) unfill_isogeny_matrix() (in module sage.schemes.elliptic_curves.ell_curve_isogeny) union() (sage.schemes.elliptic_curves.height.UnionOfIntervals class method) UnionOfIntervals (class in sage.schemes.elliptic_curves.height) V value_ring() (sage.schemes.hyperelliptic_curves.jacobian_homset.JacobianHomset_divisor_classes method) values_along_line() (sage.schemes.elliptic_curves.lseries_ell.Lseries_ell method) verify() (sage.schemes.elliptic_curves.period_lattice_region.PeriodicRegion method) W w() (sage.schemes.elliptic_curves.formal_group.EllipticCurveFormalGroup method) w1 (sage.schemes.elliptic_curves.period_lattice_region.PeriodicRegion attribute) w2 (sage.schemes.elliptic_curves.period_lattice_region.PeriodicRegion attribute) weierstrass_p() (in module sage.schemes.elliptic_curves.ell_wp) (sage.schemes.elliptic_curves.ell_field.EllipticCurve_field method) weierstrass_points() (sage.schemes.hyperelliptic_curves.hyperelliptic_padic_field.HyperellipticCurve_padic_field method) WeierstrassIsomorphism (class in sage.schemes.elliptic_curves.weierstrass_morphism) WeierstrassTransformation (class in sage.schemes.elliptic_curves.weierstrass_transform) WeierstrassTransformationWithInverse() (in module sage.schemes.elliptic_curves.weierstrass_transform) WeierstrassTransformationWithInverse_class (class in sage.schemes.elliptic_curves.weierstrass_transform) weil_pairing() (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_field method) wp_c() (sage.schemes.elliptic_curves.height.EllipticCurveCanonicalHeight method) wp_intervals() (sage.schemes.elliptic_curves.height.EllipticCurveCanonicalHeight method) wp_on_grid() (sage.schemes.elliptic_curves.height.EllipticCurveCanonicalHeight method) X x() (sage.schemes.elliptic_curves.formal_group.EllipticCurveFormalGroup method) (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialHyperellipticQuotientRing method) x_poly_exact() (sage.schemes.elliptic_curves.heegner.HeegnerPointOnEllipticCurve method) x_rational_map() (sage.schemes.elliptic_curves.ell_curve_isogeny.EllipticCurveIsogeny method) (sage.schemes.elliptic_curves.hom.EllipticCurveHom method) (sage.schemes.elliptic_curves.hom_composite.EllipticCurveHom_composite method) (sage.schemes.elliptic_curves.hom_frobenius.EllipticCurveHom_frobenius method) (sage.schemes.elliptic_curves.hom_scalar.EllipticCurveHom_scalar method) (sage.schemes.elliptic_curves.hom_velusqrt.EllipticCurveHom_velusqrt method) (sage.schemes.elliptic_curves.weierstrass_morphism.WeierstrassIsomorphism method) x_to_p() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.MonskyWashnitzerDifferentialRing method) xy() (sage.schemes.elliptic_curves.ell_point.EllipticCurvePoint_field method) Y y() (sage.schemes.elliptic_curves.formal_group.EllipticCurveFormalGroup method) (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialHyperellipticQuotientRing method) Z zero() (sage.schemes.hyperelliptic_curves.monsky_washnitzer.SpecialHyperellipticQuotientRing method) zero_sums() (sage.schemes.elliptic_curves.lseries_ell.Lseries_ell method) zeros() (sage.schemes.elliptic_curves.lseries_ell.Lseries_ell method) zeros_in_interval() (sage.schemes.elliptic_curves.lseries_ell.Lseries_ell method) zeta_function() (sage.schemes.hyperelliptic_curves.hyperelliptic_finite_field.HyperellipticCurve_finite_field method)