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Let K denote the quadratic field $\mathbb{Q}(\sqrt{d})$ where d=$-1$ or $-3$.Let E be an elliptic curve defined over K. In this paper, we analyze thetorsion subgroups of E in the maximal elementary abelian $2$-extension of $K$.

Torsion groups of elliptic curves over quadratic cyclotomic fields in elementary abelian 2-extensions