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 e-prints
- Pub Date:
- November 2016
- DOI:
- 10.48550/arXiv.1611.05671
- arXiv:
- arXiv:1611.05671
- Bibcode:
- 2016arXiv161105671K
- Keywords:
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- Mathematics - Number Theory;
- 11G05;
- 11F67
- E-Print:
- 6 pages