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arXiv · 1703.07614

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

Jian Wang
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Abstract

Merel's result on the strong uniform boundedness conjecture made it meaningful to classify the torsion part of the Mordell-Weil groups of all elliptic curves defined over number fields of fixed degree $d$. In this paper, we discuss the cyclic torsion subgroup of elliptic curves over cubic number fields. For $N=49,40,25$ or $22$, 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 $K$.

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Jian Wang. 2017-03-22. On the small cyclic torsion of elliptic curves over cubic number fields. https://arxiv.org/abs/1703.07614

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