On a special case of Watkins' conjecture
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.
 Publication:

arXiv eprints
 Pub Date:
 November 2016
 arXiv:
 arXiv:1611.05671
 Bibcode:
 2016arXiv161105671K
 Keywords:

 Mathematics  Number Theory;
 11G05;
 11F67
 EPrint:
 6 pages