Abstract
One can define class invariants for a quartic primitive CM field K as special values of certain Siegel (or Hilbert) modular functions at CM points corresponding to K. Such constructions were given by de Shalit-Goren and Lauter. We provide explicit bounds on the primes appearing in the denominators of these algebraic numbers. This allows us, in particular, to construct S-units in certain abelian extensions of a reflex field of K, where S is effectively determined by K, and to bound the primes appearing in the denominators of the Igusa class polynomials arising in the construction of genus 2 curves with CM, as conjectured by Lauter.
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