Bulletin of the American Mathematical Society

Author(s): Karl Rubin; Alice Silverberg
Journal: Bull. Amer. Math. Soc. 39 (2002), 455-474.
MSC (2000): Primary 11G05; Secondary 11-02, 14G05, 11G40, 14H52
Posted: July 8, 2002
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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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Retrieve articles in Bulletin of the American Mathematical Society with MSC (2000): 11G05, 11-02, 14G05, 11G40, 14H52

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: 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 2002
Posted: 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
Copyright of article: Copyright 2002, American Mathematical Society

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