On the small cyclic torsion of elliptic curves over cubic number fields

Research paper by Jian Wang

Indexed on: 22 Mar '17Published on: 22 Mar '17Published in: arXiv - Mathematics - Number Theory

Abstract

Let $E$ be an elliptic defined over a number field $K$. Then its Mordell-Weil group $E(K)$ is finitely generated: $E(K)\cong E(K)_{tor}\times\mathbb{Z}^r$. In this paper, we discuss the cyclic torsion subgroup of elliptic curves over cubic number fields. For $N=49,25,32,$ or $55,40,22,24$, we show that $\mathbb{Z}/N\mathbb{Z}$ is not a subgroup of $E(K)_{tor}$ for any elliptic curve $E$ over a cubic number field $K$.