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SUMMARY: Strongly modular models of Q-curves - Andrea Ferraguti (Cambridge
 )
DTSTART:20171107T143000Z
DTEND:20171107T153000Z
UID:TALK78891@talks.cam.ac.uk
CONTACT:Beth Romano
DESCRIPTION: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 n
 ewforms. We address the problem of deciding when an elliptic curve has a s
 trongly modular model\, showing that this holds precisely when the curve h
 as a model that is completely defined over an abelian number field. The pr
 oof relies on Galois cohomological methods. When the curve is defined over
  a quadratic or biquadratic field\, we show how to find all of its strongl
 y modular twists\, using exclusively the arithmetic of the base field. Thi
 s is joint work with Peter Bruin.
LOCATION:MR13
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