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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Ranks of elliptic curves
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by Karl Rubin and Alice Silverberg PDF
Bull. Amer. Math. Soc. 39 (2002), 455-474 Request permission


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
  • MR Author ID: 151435
  • Email:
  • Alice Silverberg
  • Affiliation: Department of Mathematics, Ohio State University, Columbus, Ohio 43210
  • MR Author ID: 213982
  • Email:
  • Received by editor(s): January 5, 2002
  • Received by editor(s) in revised form: February 20, 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
  • © Copyright 2002 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 39 (2002), 455-474
  • MSC (2000): Primary 11G05; Secondary 11-02, 14G05, 11G40, 14H52
  • DOI:
  • MathSciNet review: 1920278