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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

Ranks of elliptic curves


Authors: Karl Rubin and Alice Silverberg
Journal: Bull. Amer. Math. Soc. 39 (2002), 455-474
MSC (2000): Primary 11G05; Secondary 11-02, 14G05, 11G40, 14H52
Published electronically: July 8, 2002
MathSciNet review: 1920278
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Abstract | References | Similar Articles | Additional Information

Abstract: This paper gives a general survey of ranks of elliptic curves over the field of rational numbers. The rank is a measure of the size of the set of rational points. The paper includes discussions of the Birch and Swinnerton-Dyer Conjecture, the Parity Conjecture, ranks in families of quadratic twists, and ways to search for elliptic curves of large rank.


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Additional Information

Karl Rubin
Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305
Email: rubin@math.stanford.edu

Alice Silverberg
Affiliation: Department of Mathematics, Ohio State University, Columbus, Ohio 43210
Email: silver@math.ohio-state.edu

DOI: http://dx.doi.org/10.1090/S0273-0979-02-00952-7
PII: S 0273-0979(02)00952-7
Received by editor(s): January 5, 2002
Received by editor(s) in revised form: February 1, 2002
Published electronically: July 8, 2002
Additional Notes: The authors thank the NSF (grants DMS-9800881 and DMS-9988869), the Alexander von Humboldt Foundation, and the Universität Erlangen-Nürnberg. Silverberg also thanks the NSA (grant MDA904-99-1-0007), MSRI, and AIM
Article copyright: © Copyright 2002 American Mathematical Society