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SUMMARY:Eugenia Rosu (TU Darmstadt and University​ of Leiden)
DTSTART:20220606T110000Z
DTEND:20220606T120000Z
DTSTAMP:20260423T023055Z
UID:WarsawNT/44
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WarsawNT/44/
 ">Twists of elliptic curves with CM</a>\nby Eugenia Rosu (TU Darmstadt and
  University​ of Leiden) as part of Warsaw Number Theory Seminar\n\nLectu
 re held in IMPAN Warsaw\, ground floor\, room 6.\n\nAbstract\nWe consider 
 certain families of sextic twists of the elliptic curve $y^2=x^3+1$ that a
 re not defined over $\\mathbb{Q}$\, but over $\\mathbb{Q}[\\sqrt{-3}]$. We
  compute a formula that relates the central value of their L-functions $L(
 E\, 1)$ to the square of a trace of a modular function evaluated at a CM p
 oint. Assuming the Birch and Swinnerton-Dyer conjecture\, when the value a
 bove is non-zero\, we should recover the order of the Tate-Shafarevich gro
 up\, and we show that the value is indeed an integer square.\n
LOCATION:https://researchseminars.org/talk/WarsawNT/44/
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