On the group orders of elliptic curves over finite fields
Abstract
Description
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.
18 pages, LaTeX. This is a preprint version from 1992
18 pages, LaTeX. This is a preprint version from 1992