Let Q D be the set of moduli points on Siegel's modular threefold whose corresponding principally polarized abelian surfaces have quaternionic multiplication by a maximal order O in an indefinite quaternion algebra of discriminant D over Q such that the Rosati involution coincides with a positive involution of the form α → µ −1 αµ on O for some µ ∈ O with µ 2 + D = 0. In this paper, we first give a formula for the number of irreducible components in Q D , strengthening an earlier result of Rotger. Then for each irreducible component of genus 0, we determine its rational parameterization in terms of a Hauptmodul of the associated Shimura curve.