Computing the rational torsion of an elliptic curve using Tate normal form

Description

It is a classical result (apparently due to Tate) that all elliptic curves with a torsion point of order n (4 ≤ n ≤ 10, or n = 12) lie in a oneparameter family. However, this fact does not appear to have been used ever for computing the torsion of an elliptic curve. We present here a extremely down–to–earth algorithm using the existence of such a family.

Abstract

Junta de Andalucía

Additional details