The Ramanujan Journal

, Volume 5, Issue 3, pp 311–317 | Cite as

Heights of CM Points on Complex Affine Curves

  • Florian Breuer


In this note we show that, assuming the generalized Riemann hypothesis for quadratic imaginary fields, an irreducible algebraic curve in ℂŋ is modular if and only if it contains a CM point of sufficiently large height. This is an effective version of a theorem of Edixhoven.

complex multiplication elliptic curves modular curves heights 


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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Florian Breuer
    • 1
  1. 1.UMR MathematiquesUniversite Denis DiderotParis 7France

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