A Simple Point Counting Algorithm for Hessian Elliptic Curves in Characteristic Three

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.