Elliptic Curve: other results

Results named in Tau Ceti's TauCeti.AlgebraicGeometry.EllipticCurve modules and in no roadmap's section, as Tau Ceti has them at commit ace60277.

The criterion behind the weak… to The weak Mordell–Weil theorem

• The criterion behind the weak Mordell–Weil theorem
• Deligne's theorem (WeierstrassCurve.IsIntegralModularForm.mem_adjoin)
• The factorisation theorem
• The factorisation theorem for isogenies (Silverman II.2.12)
• The Galois cocycle carried by that isomorphism
• The Hurwitz genus formula for y² = x³ - x over K(x), as a numerical identity
• The Jacobian criterion as two equalities, the form Nonsingular negates
• The kernel form of the factorisation theorem (Silverman III.4.11)
• Kraus's global criterion
• Kraus's local criterion
• The modified Szpiro conjecture implies Szpiro's conjecture, with the same constants
• The Mordell–Weil rank bound from the 2-Selmer group
• The Nagell–Lutz theorem
• Perfect local Tate duality for E[m]
• Suyama's exact ellipticity criterion
• Szpiro's conjecture for Frey curves
• Szpiro's conjecture implies asymptotic Fermat
• Szpiro's conjecture implies the abc conjecture with exponent 3 / 2
• Vieta's formula at a pair of parameters, cleared of the inverse of the cubic's leading coefficient
• The weak Mordell–Weil theorem

The Wronskian identity of an…

• The Wronskian identity of an isogeny

The dependency explorer needs JavaScript and its graph data.

Download the complete graph data.