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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

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✦ 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.