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Proving the Birch and Swinnerton-Dyer conjecture for specific elliptic curves of analytic rank zero and one

Published online by Cambridge University Press:  01 November 2011

Robert L. Miller*
Warwick Mathematics Institute Zeeman Building, University of Warwick, Coventry CV4 7AL, United Kingdom The Mathematical Sciences Research Institute, 17 Gauss Way, Berkeley CA 94720-5070, USA


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We describe an algorithm to prove the Birch and Swinnerton-Dyer conjectural formula for any given elliptic curve defined over the rational numbers of analytic rank zero or one. With computer assistance we rigorously prove the formula for 16714 of the 16725 such curves of conductor less than 5000.

Research Article
Copyright © London Mathematical Society 2011


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