Constructing families of elliptic curves with prescribed mod 3 representation via Hessian and Cayleyan curves

Details Constructing families of elliptic curves with prescribed mod 3 representation via Hessian and Cayleyan curves Constructing families of elliptic curves with prescribed mod 3 representation via Hessian and Cayleyan curves

2011-12-29

arxiv.org/abs/1112.6317v1

Mathematics

Number Theory

Scientific paper

For a given elliptic curve $E_0$ defined over a number field $k$, we construct two families of elliptic curves whose mod 3 representations are isomorphic to that of $E_0$. The isomorphisms in the first family are symplectic, and those in the second family are anti-symplectic. Our construction is based on the notion of Hessian and Cayleyan curves in classical geometry.

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