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Rank distribution in a family of cubic twists

Mark Watkins
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Abstract

In 1987, Zagier and Kramarz published a paper in which they presented evidence that a positive proportion of the even-signed cubic twists of the elliptic curve $x^3+y^3=1$ should have positive rank. We extend their data, showing that it is more likely that the proportion goes to zero.

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Mark Watkins. 2005-09-17. Rank distribution in a family of cubic twists. https://arxiv.org/abs/math/0412427

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