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SUMMARY:Eugenia Rosu (Universität Regensburg)
DTSTART:20210521T134500Z
DTEND:20210521T144500Z
DTSTAMP:20260423T040005Z
UID:RSVP/14
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/RSVP/14/">Tw
 ists of elliptic curves with CM</a>\nby Eugenia Rosu (Universität Regensb
 urg) as part of Rendez-vous on special values and periods\n\n\nAbstract\nW
 e consider certain families of sextic twists $E_D$ of the elliptic curve $
 y^2=x^3+1$ that are not defined over $\\mathbb{Q}$\, but over $\\mathbb{Q}
 [\\sqrt{-3}]$.\n\nWe compute a formula that relates the $L$-value $L(E_D\,
  1)$ to the square of a trace of a modular function at a CM point. \nAssum
 ing the Birch and Swinnerton-Dyer conjecture\, when the value above is non
 -zero\, we should recover the order of the Tate-Shafarevich group\, and un
 der certain conditions we show that the value is indeed a square.\n
LOCATION:https://researchseminars.org/talk/RSVP/14/
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