A conjecture of Watkins for quadratic twists

Esparza-Lozano, Jose; Pasten, Hector

doi:10.1090/proc/15376

A conjecture of Watkins for quadratic twists
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by Jose A. Esparza-Lozano and Hector Pasten PDF

Proc. Amer. Math. Soc. 149 (2021), 2381-2385 Request permission

Abstract:

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 $2$-torsion, we prove the conjecture for all the quadratic twists of $E$ by squarefree integers with sufficiently many prime factors.

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