Elliptic Curves of Odd Modular Degree

Frank Calegari; Matthew Emerton

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Elliptic Curves of Odd Modular Degree

Frank Calegari·Matthew Emerton

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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.

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Frank Calegari, Matthew Emerton. 2005-03-17. Elliptic Curves of Odd Modular Degree. https://arxiv.org/abs/math/0503359

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