Growth of Odd Torsion Over Imaginary Quadratic Fields of Class Number 1

Abstract

Let $K$ be a non-cylotomic imaginary quadratic field of class number 1 and $E/K$ is an elliptic curve with $E(K)[2]\simeq {\mathbb{Z}}_1.$ We determine the odd-order torsion groups that can arise as $E(L{)}_{\text{tor}}$ where $L$ is a quadratic extension of $K.$

Magma computations added, minor fixes

References in corpus (1)

• Torsion of rational elliptic curves over quadratic fields