Elliptic Curves of Odd Modular Degree
Number Theory
2007-05-23 v1
Abstract
The modular degree m_E of an elliptic curve E/Q is the minimal degree of any surjective morphism X_0(N) -> E, where N is the conductor of E. We give a necessarily set of criteria for m_E to be odd. Specializing to N prime our results imply a conjecture of Mark Watkins. As a technical tool we also prove a certain multiplicity one result for p=2 that may be of independent interest.
Cite
@article{arxiv.math/0503359,
title = {Elliptic Curves of Odd Modular Degree},
author = {Frank Calegari and Matthew Emerton},
journal= {arXiv preprint arXiv:math/0503359},
year = {2007}
}