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An AGM-type elliptic curve point counting algorithm in characteristic three
Authors: Trond Stølen Gustavsen, Kristian RanestadAbstract:
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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