09:24
5

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 $E_{aD^2}/\mathbb{Q}$ and $E_{aD^4}/\mathbb{Q}$. These are cubic twists of the original elliptic curve.
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