Symplectic criteria for elliptic curves, revisited

Alain Kraus, Nuno Freitas, Ignasi Sánchez-Rodríguez

Let $\ell$ and $p\ge 3$ be different primes. Let $E/{\mathbb{Q}}_{\ell }$ and $E^{\prime }/{\mathbb{Q}}_{\ell }$ be elliptic curves with isomorphic $p$-torsion. Assume that $E$ has potentially mult…