Rank distribution in a family of cubic twists

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.

References in corpus (1)

• Curves D y^2 = x^3 - x of odd analytic rank

Cited by in corpus (2)

• Vanishing of L-functions of elliptic curves over number fields
• Elliptic Curves x^3 + y^3 = k of High Rank