Note on the rank of quadratic twists of Mordell equations

2005/09/30 by Chang, Sungkon
#14H52 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.math/0510001

Abstract

14H52 : Elliptic curves Let E be the elliptic curve given by a Mordell equation y²=x³-A where A is an integer. For certain A, we use Stoll's formula to compute a lower bound for the proportion of square-free integers D up to X such that the Mordell-Weil rank of the quadratic twist by D is less than 2k, for given non-negative k. We also compute an upper bound for a certain average rank of quadratic twists of E.

Related

• A note on rank zero quadratic twists of a Mordell curve
• Number of integral points on quadratic twists of elliptic curves
• Iwasawa theory and ranks of elliptic curves in quadratic twist families
• Average rank in families of quadratic twists: a geometric point of view
• Quadratic twists of elliptic curves and class numbers