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

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

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