Ranks of elliptic curves

Rubin, Karl; Silverberg, Alice

doi:10.1090/S0273-0979-02-00952-7

Ranks of elliptic curves
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Bull. Amer. Math. Soc. 39 (2002), 455-474 Request permission

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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