We describe an algorithm, AGM-X
0(N), for point counting on elliptic curves of small characteristic p using p-adic lifts of their invariants associated to modular curves X
0(N). The algorithm generalizes the contruction of Satoh [10], SST [11], and Mestre [9]. We describe this method and give details
of its implementation for characteristics 2, 3, 5, 7, and 13.
Keywords Elliptic curve cryptography - modular curves - point counting