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arXiv · 1611.05671

On a special case of Watkins' conjecture

Matija Kazalicki·Daniel Kohen
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Abstract

Watkins' conjecture asserts that for a rational elliptic curve $E$ the degree of the modular parametrization is divisible by $2^r$, where $r$ is the rank of $E$. In this paper we prove that if the modular degree is odd then $E$ has rank $0$. Moreover, we prove that the conjecture holds for all rank two rational elliptic curves of prime conductor and positive discriminant.

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Matija Kazalicki, Daniel Kohen. 2016-11-17. On a special case of Watkins' conjecture. https://arxiv.org/abs/1611.05671

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