Strongly modular models of Q-curves

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• Andrea Ferraguti (Cambridge)
• Tuesday 07 November 2017, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Beth Romano.

A strongly modular Q-curve is an elliptic curve over a number field whose L-function is a product of L-functions of classical weight 2 newforms. We address the problem of deciding when an elliptic curve has a strongly modular model, showing that this holds precisely when the curve has a model that is completely defined over an abelian number field. The proof relies on Galois cohomological methods. When the curve is defined over a quadratic or biquadratic field, we show how to find all of its strongly modular twists, using exclusively the arithmetic of the base field. This is joint work with Peter Bruin.

This talk is part of the Number Theory Seminar series.

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