An elliptic curve $E$ over a field $k$ is a smooth projective curve of genus $1$ together with a distinguished $k$-rational point $O$.
The most commonly used model for elliptic curves is a Weierstrass model: a smooth plane cubic with the point $O$ as the unique point at infinity.
Knowl status:
- Review status: reviewed
- Last edited by John Jones on 2018-06-18 02:34:46
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- ag.abelian_surface
- ag.abelian_variety
- ag.cluster_picture
- ag.modcurve.x0
- ag.modcurve.x1
- dq.ec.reliability
- dq.ecnf.extent
- dq.ecnf.reliability
- ec.additive_reduction
- ec.analytic_sha_order
- ec.bad_reduction
- ec.bsdconjecture
- ec.canonical_height
- ec.complex_multiplication
- ec.conductor
- ec.congruent_number_curve
- ec.congruent_number_problem
- ec.discriminant
- ec.endomorphism
- ec.endomorphism_ring
- ec.galois_rep
- ec.galois_rep_elladic_image
- ec.galois_rep_modell_image
- ec.global_minimal_model
- ec.good_ordinary_reduction
- ec.good_reduction
- ec.good_supersingular_reduction
- ec.integral_model
- ec.invariants
- ec.isogeny
- ec.isogeny_class
- ec.isogeny_class_degree
- ec.isogeny_graph
- ec.isogeny_matrix
- ec.isomorphism
- ec.j_invariant
- ec.kodaira_symbol
- ec.local_data
- ec.local_minimal_discriminant
- ec.local_minimal_model
- ec.local_root_number
- ec.maximal_elladic_galois_rep
- ec.maximal_galois_rep
- ec.minimal_discriminant
- ec.mordell_weil_group
- ec.mordell_weil_theorem
- ec.multiplicative_reduction
- ec.mw_generators
- ec.nonsplit_multiplicative_reduction
- ec.obstruction_class
- ec.period
- ec.potential_good_reduction
- ec.q.3675.g1.bottom
- ec.q.37.a1.bottom
- ec.q.47775.be1.bottom
- ec.q.analytic_rank
- ec.q.analytic_sha_value
- ec.q.bsdconjecture
- ec.q.canonical_height
- ec.q.conductor
- ec.q.cremona_label
- ec.q.discriminant
- ec.q.endomorphism_ring
- ec.q.faltings_height
- ec.q.faltings_ratio
- ec.q.invariants
- ec.q.j_invariant
- ec.q.lmfdb_label
- ec.q.manin_constant
- ec.q.minimal_twist
- ec.q.modular_degree
- ec.q.modular_form
- ec.q.modular_parametrization
- ec.q.period_lattice
- ec.q.regulator
- ec.q.semistable
- ec.q.torsion_growth
- ec.q_curve
- ec.rank
- ec.reduction
- ec.reduction_type
- ec.regulator
- ec.ring
- ec.search_input
- ec.semi_global_minimal_model
- ec.semistable
- ec.simple_equation
- ec.split_multiplicative_reduction
- ec.tamagawa_number
- ec.torsion_order
- ec.twists
- ec.weierstrass_coeffs
- g2c.decomposition
- g2c.end_alg
- g2c.geom_end_alg
- g2c.hasse_weil_conjecture
- g2c.real_period
- hgm.A2.2_B1.1.top
- hgm.A3_B4.top
- mf.bianchi.2.0.4.1-16384.1-d.top
- mf.bianchi.2.0.7.1-10000.1-b.top
- mf.gl2.history.elliptic
- modcurve
- modcurve.contains_negative_one
- modcurve.level_structure
- modcurve.modular_cover
- modcurve.rational_points
- rcs.cande.lfunction
- rcs.rigor.ec
- rcs.rigor.ec.q
- rcs.rigor.lfunction.ec
- rcs.source.ec
- st_group.1.2.A.1.1a.bottom
- st_group.1.2.A.1.1a.top
- st_group.1.2.B.1.1a.bottom
- st_group.1.2.B.2.1a.bottom
- st_group.definition
- lmfdb/ecnf/ecnf_stats.py (lines 82-83)
- lmfdb/ecnf/main.py (line 167)
- lmfdb/elliptic_curves/__init__.py (line 7)
- lmfdb/elliptic_curves/__init__.py (line 14)
- lmfdb/elliptic_curves/web_ec.py (line 71)
- lmfdb/knowledge/knowl.py (line 207)
- lmfdb/templates/matches.html (line 41)
- 2018-06-18 02:34:46 by John Jones (Reviewed)