Torsion of elliptic curves over quadratic cyclotomic fields

TL;DR

This paper investigates the possible torsion groups of elliptic curves defined over quadratic cyclotomic fields, specifically over  and 3, expanding understanding of elliptic curve torsion structures in these fields.

Contribution

It classifies the torsion subgroups of elliptic curves over  and 3, providing new insights into their structure over these quadratic cyclotomic fields.

Findings

Complete classification of torsion groups over  and 3

Identification of new torsion structures specific to these fields

Extension of known results from nd  to these quadratic fields

Abstract

In this paper we study the possible torsions of elliptic curves over $\mathbb Q(i)$ and $\mathbb Q(\sqrt {-3})$.