Tom A. Fisher
Abstract
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We compute equations for the families of elliptic curves $9$-congruent to a given elliptic curve. We use these to find infinitely many non-trivial pairs of $9$-congruent elliptic curves over ${\mathbb Q}$, i.e. pairs of non-isogenous elliptic curves over
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We compute equations for the families of elliptic curves $9$-congruent to a given elliptic curve. We use these to find infinitely many non-trivial pairs of $9$-congruent elliptic curves over ${\mathbb Q}$, i.e. pairs of non-isogenous elliptic curves over
Key concepts: Mathematics, Supersingular elliptic curve, Elliptic curve, Schoof's algorithm, Hessian form of an elliptic curve, Modular elliptic curve, Sato–Tate conjecture, Twists of curves