Elliptic Curves of Odd Modular Degree
Abstract
The modular degree mE of an elliptic curve E/Q is the minimal degree of any surjective morphism X0(N) -> E, where N is the conductor of E. We give a necessarily set of criteria for mE 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.
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