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

I. García; M. A. Olalla Acosta; J. M. Tornero

paper

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

arXiv:math/0011066

Abstract

It is a classical result (apparently due to Tate) that all elliptic curves with a torsion point of order n ( $4 \leq n \leq 10$ , or n = 12) lie in a one-parameter 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.

14 pages