A Stickelberger index for the Tate-Shafarevich group revisited
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We obtain an algebraic description of the critical value of the L-series of an elliptic curve of rank zero over an abelian number field with conductor coprime to the one of the curve. We do this by construction of matching Stickelberger-ideals and computation of their indices. By inserting the result into the formula of the conjecture of Birch and Swinnerton-Dyer we can describe the order of the Tate-Shafarevich group by a number of algebraic expressions.
Mathematics Subject Classification (2000)11G05 11F11
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