Pure Mathematics
Preprint 1, 2004
Author(s):
T. S. Gustavsen, K. Ranestad
Title:
An AGM-type elliptic curve point counting
algorithm in characteristic three
Abstract:
Given an ordinary elliptic curve on Hesse form over a finite field of
characteristic three, we give a sequence of elliptic curves which leads to
an effective construction of the canonical lift, and obtain an algorithm for
computing the number of points. Our methods are based on the study of an
explicitly and naturally given 3-isogeny between elliptic curves on Hesse
form.
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