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Non-cyclic Torsion of Elliptic Curves Over Imaginary Quadratic Fields of Class Number 1 (2111.11395v5)
Published 22 Nov 2021 in math.NT
Abstract: Let $K$ be a non-cylotomic imaginary quadratic field of class number 1 and $E/K$ is an elliptic curve with $E(K)[2]\simeq \mathbb{Z}/2\mathbb{Z} \oplus\mathbb{Z}/2\mathbb{Z}.$ In this article, we determine the torsion groups that can arise as $E(L)_{\text{tor}}$ where $L$ is a quadratic extension of $K.$
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