Thue equations and torsion groups of elliptic curves

TL;DR

This paper introduces a novel way to identify rational torsion subgroups of elliptic curves with points of order greater than 4 by linking them to solutions of Thue equations.

Contribution

It provides a new characterization of torsion subgroups of elliptic curves using solutions to systems of Thue equations for points of order greater than 4.

Findings

Characterization of torsion subgroups via Thue equations

Connection between elliptic curve torsion points and Diophantine equations

New method for analyzing elliptic curve torsion structures

Abstract

A new characterization of rational torsion subgroups of elliptic curves is found, for points of order greater than 4, through the existence of solution for systems of Thue equations.