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

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

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

Algebraic Geometry 2016-08-15 v1

Authors: I. García , M. A. Olalla Acosta , J. M. Tornero

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.

Keywords

elliptic curves rational points on curves algebraic curves

Cite

@article{arxiv.math/0011066,
  title  = {Computing the rational torsion of an elliptic curve using Tate normal form},
  author = {I. García and M. A. Olalla Acosta and J. M. Tornero},
  journal= {arXiv preprint arXiv:math/0011066},
  year   = {2016}
}

Comments

14 pages

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