University of Cambridge > Talks.cam > Junior Algebra/Logic/Number Theory seminar > On the p-part of the Birch–Swinnerton-Dyer conjecture for elliptic curves with CM by the ring of integers of Q(√−3)

On the p-part of the Birch–Swinnerton-Dyer conjecture for elliptic curves with CM by the ring of integers of Q(√−3)

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  • UserYukako Kezuka University of Cambridge
  • ClockFriday 28 November 2014, 15:00-16:00
  • HouseCMS, MR4.

If you have a question about this talk, please contact Julian Brough.

We study an infinite family of quadratic and cubic twists of the elliptic curve E parametrised by the modular curve X0(27). There are two main results, both of which support the validity of the famous Birch– Swinnerton-Dyer conjecture. One of them concerns the 2-adic valuation of the algebraic part of the L-series of quadratic twists of E evaluated at 1, and the other concerns the 3-adic valuations of the L-series of cubic twists of E at 1. We check that the bounds obtained in the main results are precisely the bounds predicted by the conjecture, with equality holding when the Tate–Shafarevich groups of the curves are trivial.

This talk is part of the Junior Algebra/Logic/Number Theory seminar series.

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