English

Rank distribution in a family of cubic twists

Number Theory 2007-05-23 v2

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 x3+y3=1x^3+y^3=1 should have positive rank. We extend their data, showing that it is more likely that the proportion goes to zero.

Keywords

Cite

@article{arxiv.math/0412427,
  title  = {Rank distribution in a family of cubic twists},
  author = {Mark Watkins},
  journal= {arXiv preprint arXiv:math/0412427},
  year   = {2007}
}