Numerical evidence for the equivariant Birch and Swinnerton-Dyer conjecture (Part II)

Bley, Werner

doi:10.1090/S0025-5718-2012-02572-5

Numerical evidence for the equivariant Birch and Swinnerton-Dyer conjecture (Part II)
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Math. Comp. 81 (2012), 1681-1705 Request permission

Abstract:

We continue the study of the Equivariant Tamagawa Number Conjecture for the base change of an elliptic curve begun by the author in 2009. We recall that the methods developed there, apart from very special cases, cannot be applied to verify the $l$-part of the ETNC if $l$ divides the order of the group. In this note we focus on extensions of $l$-power degree ($l$ an odd prime) and describe methods for computing numerical evidence for ETNC${_l}$. For cyclic $l$-power extensions we also express the validity of ETNC${_l}$ in terms of explicit congruences.

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