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cubic twists of Mordell curve and their rank

Let $a$ 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 $E_{aD^2}/\mathbb{Q}$...
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