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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnm164, 33 pages, doi:10.1093/imrn/rnm164 published on February 6, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

Equivariant Birch–Swinnerton–Dyer Conjecture for the Base Change of Elliptic Curves: An Example

Tejaswi Navilarekallu

Department of Mathematics, Indian Institute of Science, Bangalore 560012, India

Correspondence: Correspondence to be sent to: navilarekallu{at}gmail.com

Let E be an elliptic curve defined over Formula and let Formula be a finite Galois extension with Galois group G. The equivariant Birch–Swinnerton–Dyer conjecture for Formula viewed as a motive over Formula with coefficients in Formula relates the twisted L-values associated with E with the arithmetic invariants of the same. In this paper I prescribe an approach to verify this conjecture for a given data. Using this approach, we verify the conjecture for an elliptic curve of conductor 11 and an S3-extension of Formula .


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