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arXiv · 1602.08934

Growth of torsion of elliptic curves with full 2-torsion over quadratic cyclotomic fields

Burton Newman
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Abstract

Let $K = \mathbb{Q}(\sqrt{-3})$ or $\mathbb{Q}(\sqrt{-1})$ and let $C_n$ denote the cyclic group of order $n$. We study how the torsion part of an elliptic curve over $K$ grows in a quadratic extension of $K$. In the case $E(K)[2] \approx C_2 \oplus C_2$ we determine how a given torsion structure can grow in a quadratic extension and the maximum number of quadratic extensions in which it grows. We also classify the torsion structures which occur as the quadratic twist of a given torsion structure.

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Burton Newman. 2016-02-29. Growth of torsion of elliptic curves with full 2-torsion over quadratic cyclotomic fields. https://arxiv.org/abs/1602.08934

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