Explicit Families Of Elliptic Curves With The Same Mod 6 Representation

Zexiang Chen

Explicit Families Of Elliptic Curves With The Same Mod 6 Representation

Number Theory 2014-05-27 v2

Authors: Zexiang Chen

Abstract

Let $E$ be an elliptic curve over $\mathbb{Q}$ . In this paper we study two certain modular curves which parameterize families of elliptic curves which are directly (resp. reverse) 6-congruent to $E$ together with the explicit parametrizations. The equations for the direct case has been worked out but the parametrization is only given for very few cases. In this paper we use a new method to obtain the equations for both direct and reverse cases together with full (and simpler) parametrizations.

Keywords

elliptic curves modular curves mod 6 representation 6-congruent explicit parametrization rational points

Cite

@article{arxiv.1403.7557,
  title  = {Explicit Families Of Elliptic Curves With The Same Mod 6 Representation},
  author = {Zexiang Chen},
  journal= {arXiv preprint arXiv:1403.7557},
  year   = {2014}
}

Related papers

View all related →