For fixed non-CM α, only finitely many CM j satisfy that j-α is an algebraic unit, with explicit bounds given.
In: Journal reine angewandte Math 419 (1991), pp
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Integrality properties in the Moduli Space of Elliptic Curves: CM Case
For fixed non-CM α, only finitely many CM j satisfy that j-α is an algebraic unit, with explicit bounds given.