A conjecture of Watkins for quadratic twists

Jose A. Esparza-Lozano, Hector Pasten

Watkins conjectured that for an elliptic curve $E$ over $\mathbb{Q}$ of Mordell-Weil rank $r$, the modular degree of $E$ is divisible by $2^r$. If $E$ has non-trivial rational $2$-…