Abstract
In this paper we propose new methods for selecting elliptic curves suited for the factorization of a composite number p^2q. The elliptic curves are selected from the curves which are parametrized by Atkin and Morain's method or Suyama's method. We show that, with our methods, it is possible to select the elliptic curves whose orders are divisible by 24, 32 or 64 over F_q. We also show that, with a computer search, these curves exist with sufficiently large probability.
