The University of Arizona

L-functions of cubic twists of elliptic curves with CM

L-functions of cubic twists of elliptic curves with CM

Series: Algebra and Number Theory Seminar
Location: ENR2 S395
Presenter: Eugenia Rosu, U of A

We consider a twist of the elliptic curve y^2=x^3+1 such that the new elliptic curve is not defined over Q. We look at its cubic twists E_D and compute a formula that relates the central value L(E_D, 1) to the trace of a modular function at a CM point. Assuming the Birch and Swinnerton-Dyer conjecture, when the value of L(E_D, 1) is non-zero we should recover the order of the Tate-Shafarevich group using our formulas.

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