The efficient implementation of Schoof's algorithm for computing the
cardinality of elliptic curves over finite fields requires the
computation of isogenies between elliptic curves. We make a survey of
algorithms used for accomplishing this task. When the characteristic
of the field is large, Weierstrass's <I>P</I> functions can be used. When
the characteristic of the field is small, we now have three algorithms
at our disposal, two due to Couveignes and one to the first author. We
treat the same example using these three algorithms and make some
comparisons between them.