Elliptic Curves of Odd Modular Degree

Details Elliptic Curves of Odd Modular Degree Elliptic Curves of Odd Modular Degree

2005-03-17

arxiv.org/abs/math/0503359v1

Mathematics

Number Theory

Scientific paper

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.

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