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 (2)

• On the frequency of vanishing of quadratic twists of modular L-functions
• Curves D y^2 = x^3 - x of odd analytic rank

Cited by in corpus (6)

• Variation in the number of points on elliptic curves and applications to excess rank
• Vanishing of L-functions of elliptic curves over number fields
• Determining Optimal Test Functions for Bounding the Average Rank in Families of $L$-Functions
• Investigations of Zeros Near the Central Point of Elliptic Curve L-Functions
• Elliptic Curves x^3 + y^3 = k of High Rank
• Some Results in the Theory of Low-lying Zeros: Determining the 1-level density, identifying the group symmetry and the arithmetic of moments of Satake parameters