The heart of Schoof's algorithm for computing the cardinality <I>m</I> of an
elliptic curve over a finite field is the computation of <I>m</I> modulo
small primes <I>l</I>. Elkies and Atkin have designed practical
improvements to the basic algorithm, that make use of ``good'' primes
<I>l</I>. We show how to use powers of good primes in an efficient way.
This is done by computing isogenies between curves over the ground
field. We investigate the properties of the ``isogeny cycles'' that
appear.