2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62478Given 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.18 pages, LaTeX. This is a preprint version from 1992Number TheoryAlgebraic Geometry11G20 (Primary) 14G15, 14H52 (Secondary)text