  Given a prime power q, for every pair of positive integers m and n with m
dividing the GCD of n and q-1, we construct a modular curve over F_q that
parametrizes elliptic curves over F_q along with F_q-defined points P and Q of
order m and n, respectively, with P and (n/m)Q having a given Weil pairing.
Using these curves, we estimate the number of elliptic curves over F_q that
have a given integer N dividing the number of their F_q-defined points.
