On a special case of Watkins’ conjecture-Reference-Cited by-同舟云学术

On a special case of Watkins’ conjecture

Published:2017-09-06 Issue:2 Volume:146 Page:541-545
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Kazalicki Matija,Kohen Daniel

Abstract

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

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2018-146-02/S0002-9939-2017-13759-9/S0002-9939-2017-13759-9.pdf

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