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

TL;DR

This paper classifies the torsion subgroup structures of elliptic curves with rational j-invariant over the maximal elementary abelian 2-extension of , focusing on those with j 0 not equal to 0 or 1728.

Contribution

It provides a complete classification of torsion subgroups for elliptic curves with rational j-invariant over a specific infinite extension of , extending prior results.

Findings

Identifies all possible torsion subgroup structures in the given setting.

Shows restrictions on torsion subgroups based on the j-invariant.

Provides explicit descriptions of torsion configurations.

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.