Note on the rank of quadratic twists of Mordell equations

Details Note on the rank of quadratic twists of Mordell equations Note on the rank of quadratic twists of Mordell equations

2005-09-30

arxiv.org/abs/math/0510001v1

Mathematics

Number Theory

8 pages; accepted by J. Number Theory

Scientific paper

14H52 : Elliptic curves Let E be the elliptic curve given by a Mordell equation y^2=x^3-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.

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