Mordell curve

A Mordell curveMathworldPlanetmath is an elliptic curveMathworldPlanetmath E/K, for some field K, which admits a model by a Weierstrass equation of the form:



  1. 1.

    Let E1/:y2=x3+2, this is a Mordell curve with Mordell-Weil group E1() and generated by (-1,1).

  2. 2.

    Let E2/:y2=x3+109858299531561, then E2()/35. See here.

  3. 3.

    In general, a Mordell curve of the form y2=x3+n2 has torsion group isomorphicPlanetmathPlanetmathPlanetmath to /3 generated by (0,n).

  4. 4.

    Let E3/:y2=x3+496837487681 then this is a Mordell curve with E3()8. See here.

  5. 5. you can find a list of the minimal-known positive and negative k for Mordell curves of given rank, and the Mordell curves with maximum rank known (see BS-D conjecture).

Title Mordell curve
Canonical name MordellCurve
Date of creation 2013-03-22 13:49:57
Last modified on 2013-03-22 13:49:57
Owner alozano (2414)
Last modified by alozano (2414)
Numerical id 5
Author alozano (2414)
Entry type Definition
Classification msc 14H52
Related topic EllipticCurve
Related topic BirchAndSwinnertonDyerConjecture
Related topic ArithmeticOfEllipticCurves
Defines Mordell curve