Lower Bounds on the Canonical Height of Non-Torsion Points on Mordell Curves

Le Boudec establishes a lower bound on the minimal canonical height of the non-torsion rational points of a natural density $1$ subset of the family of quadratic twists of the congruent number elliptic curve. We establish similar results for the sextic twist family of Mordell curves given by $y^2 = x^3+d$.