Genus 2 Curves with Complex Multiplication

The main goal of this paper is to give a bound on the denominators of Igusa class polynomials for genus 2 curves. Our motivation is from cryptography via the use of genus 2 curves with a prescribed number of points, and from class invariants with a view towards class field theory and Stark’s conjectures. All known methods for constructing such curves rely on complex multiplication and the calculat...