A CONJECTURE OF WATKINS FOR QUADRATIC TWISTS
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Date
2021
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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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Keywords
Elliptic curve, rank, modularity