Everett W. Howe: On the group orders of elliptic curves over finite fields, Compositio Math. 85 (1993) 229–247, MR 94a:11089, Zbl 0793.14023.

The paper is available online here. (There is also a preprint version.)

In this paper I use modular curves to provide an estimate for the probability that a given integer divides the order of the group of points on a ‘randomly chosen’ elliptic curve over a finite field.