The heart of Schoof's algorithm for computing the cardinality $m$ of an
elliptic curve over a finite field is the computation of $m$ modulo
small primes $\ell$. Elkies and Atkin have designed practical
improvements to the basic algorithm, that make use of ``good'' primes
$\ell$. 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.