Computing the number of points of an elliptic curve defined over a large finite field of characteristic 2 is one of the most tricky part of the development of an elliptic curve cryptosystem. A few years ago, Satoh proposed a new algorithm based on the computation of the canonical p-adic lifting of the curve. We will first recall some basics and the general lines of Satoh's algorithm. Based on an idea of Mestre, we will then explain how the Arithmetic-Geometric Mean can be used to speed-up the computations and provides an easy extension to the case of genus 2 curves.