✦ LIBER ✦
Computing the Rational Torsion of an Elliptic Curve Using Tate Normal Form
✍ Scribed by Irene Garcı́a-Selfa; Miguel A. Olalla; José M. Tornero
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 137 KB
- Volume
- 96
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
✦ Synopsis
It is a classical result (apparently due to Tate) that all elliptic curves with a torsion point of order n ð44n410; or n ¼ 12Þ 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 an extremely down-to-earth algorithm using the existence of such a family.