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

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

2000-11-10

arxiv.org/abs/math/0011066v1

J. Number Theory 96, 76-88 (2002)

Mathematics

Algebraic Geometry

14 pages

Scientific paper

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.

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