A conjecture of Watkins for quadratic twists

2021/02/08 by Esparza-Lozano, Jose A., Pasten, Hector
#11G18 #FOS: Mathematics #Number Theory (math.NT) #Primary 11G05 #Secondary 11F11

paper · doi:10.48550/arxiv.2102.04185

Abstract

Watkins conjectured that for an elliptic curve E over 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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