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SUMMARY:On the p-part of the Birch–Swinnerton-Dyer conjecture for ellipt
 ic curves with CM by the ring of integers of Q(√−3) - Yukako Kezuka Un
 iversity of Cambridge
DTSTART:20141128T150000Z
DTEND:20141128T160000Z
UID:TALK56526@talks.cam.ac.uk
CONTACT:Julian Brough
DESCRIPTION:We study an infinite family of quadratic and cubic twists of t
 he elliptic curve E parametrised by the\nmodular curve X0(27). There are t
 wo main results\, both of which support the validity of the famous Birch
 –\nSwinnerton-Dyer conjecture. One of them concerns the 2-adic valuation
  of the algebraic part of the L-series\nof quadratic twists of E evaluated
  at 1\, and the other concerns the 3-adic valuations of the L-series of cu
 bic\ntwists of E at 1. We check that the bounds obtained in the main resul
 ts are precisely the bounds predicted\nby the conjecture\, with equality h
 olding when the Tate–Shafarevich groups of the curves are trivial.
LOCATION:CMS\, MR4
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