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Q: cubic twists of Mordell curve and their rank

debanjanaLet $a$ be a non-zero integer. Consider the elliptic curve $E_a/\mathbb{Q}$ given by the equation $$ E_a: y^2 = x^3 + a. $$ For a cube-free integer $D$, define the elliptic curves $E_{aD^2}/\mathbb{Q}$ and $E_{aD^4}/\mathbb{Q}$. These are cubic twists of the original elliptic curve. I would like ...


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