Singular Moduli that are Algebraic Units

Abstract

We prove that only finitely many $j$-invariants of elliptic curves with complex multiplication are algebraic units. A rephrased and generalized version of this result resembles Siegel's Theorem on integral points of algebraic curves.

9 pages

Cited by in corpus (9)

• Bad reduction of genus $2$ curves with CM jacobian varieties
• p-Adic distribution of CM points and Hecke orbits. II: Linnik equidistribution on the supersingular locus
• On singular moduli that are S-units
• There are at most finitely many singular moduli that are S-units
• Bound the difference of two singular moduli
• Multiplicative independence of modular functions
• Effective bounds on differences of singular moduli that are S-units
• Separating singular moduli and the primitive element problem
• No singular modulus is a unit