Vol. 9, No. 7, 2015

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Singular moduli that are algebraic units

Philipp Habegger

Vol. 9 (2015), No. 7, 1515–1524
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.

Keywords
elliptic curves, complex multiplication, heights
Mathematical Subject Classification 2010
Primary: 11G18
Secondary: 11G50, 11J86, 14G35, 14G40
Milestones
Received: 19 March 2014
Revised: 30 May 2015
Accepted: 15 July 2015
Published: 22 September 2015
Authors
Philipp Habegger
Departement Mathematik und Informatik
Universität Basel
Spiegelgasse 1
CH-4051 Basel
Switzerland