On a special case of Watkins' conjecture

2016/11/17 by Kazalicki, Matija, Kohen, Daniel
#11F67 #11G05 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1611.05671

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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