Explicit Families Of Elliptic Curves With The Same Mod 6 Representation

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.

References in corpus (2)

• The Hessian of a genus one curve
• On families of n-congruent elliptic curves