Singular Units and Isogenies Between CM Elliptic Curves

Abstract

In this note, we will apply the results of Gross-Zagier, Gross-Kohnen-Zagier and their generalizations to give a short proof that the differences of singular moduli are not units. As a consequence, we obtain a result on isogenies between reductions of CM elliptic curves.

arXiv commentFinal version. To appear in Compositio Math

References in corpus (1)

• On singular moduli for arbitrary discriminants

Cited by in corpus (4)

• There are at most finitely many singular moduli that are S-units
• Trinomials, singular moduli and Riffaut's conjecture
• Effective bounds on differences of singular moduli that are S-units
• No singular modulus is a unit