Abstract
It is a classical result (apparently due to Tate) that all elliptic curves with a torsion point of order n (4⩽ n ⩽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 an extremely down-to-earth algorithm using the existence of such a family.
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