Rank distribution in a family of cubic twists

Details Rank distribution in a family of cubic twists Rank distribution in a family of cubic twists

2004-12-21

arxiv.org/abs/math/0412427v2

Mathematics

Number Theory

Scientific paper

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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