  We present a construction of expander graphs obtained from Cayley graphs of
narrow ray class groups, whose eigenvalue bounds follow from the Generalized
Riemann Hypothesis. Our result implies that the Cayley graph of (Z/qZ)* with
respect to small prime generators is an expander. As another application, we
show that the graph of small prime degree isogenies between ordinary elliptic
curves achieves non-negligible eigenvalue separation, and explain the
relationship between the expansion properties of these graphs and the security
of the elliptic curve discrete logarithm problem.
