Torsion of elliptic curves with rational $j$-invariant over the maximal elementary abelian 2-extension of $\mathbb{Q}$

Abstract

In this paper, we classify the possible torsion subgroup structures of elliptic curves defined over the compositum of all quadratic extensions of the rational number field, whose $j$-invariant is a rational number not equal to 0 or 1728.

22 pages, 2 tables, to be published in Tohoku Mathematical Journal