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

Abstract

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 the torsion subgroups of E in the maximal elementary abelian $2$-extension of $K$.

arXiv commentA major revision done, 35 pages

Cited by in corpus (1)

• Growth of torsion of elliptic curves with odd-order torsion over quadratic cyclotomic fields