The frequency with which N divides the order of an elliptic curve has important applications for both the elliptic curve factoring algorithm and for cryptosystems based on elliptic curves. Work of Everett Howe provides a good estimate of this number, with a bound on the error. The talk will cover this article, touching on modular curves, elliptic curves, and a variety of other topics. It should be relatively self-contained and accessible to most students.