Note on the rank of quadratic twists of Mordell equations
  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. 
Sungkon Chang