We describe the algorithms that are needed for an efficient
implementation of Schoof's method for computing the number of points
on en elliptic curve over a finite field. We try to unify the ideas of
Atkin and Elkies. In particular, we describe the computation of
equations for <I>X0(l)</I>, <I>l</I> a prime number, as well as the
efficient computation of factors of the division polynomials of an
elliptic curve.