Elliptic curves with a point of order 13 defined over cyclic cubic fields

Abstract

We show that there is essentially a unique elliptic curve $E$ defined over a cubic Galois extension $K$ of $\mathbb{Q}$ with a $K$-rational point of order 13 and such that $E$ is not defined over $\mathbb{Q}$.

6 pages

References in corpus (2)

• Independence of rational points on twists of a given curve
• Torsion of elliptic curves over cyclic cubic fields