  We use class field theory to search for curves with many rational points over
small finite fields. By going through abelian covers of curves of small genus
we find a number of new curves. In particular, we settle the question of how
many points a curve over GF(2) of genus 17 can have, by finding one with 18
points. The search is aided by computer; in some cases it is exhaustive for
this type of curve of genus up to 50.
