The Ramanujan Journal

, Volume 22, Issue 3, pp 293–313 | Cite as

An explicit height bound for the classical modular polynomial

  • Reinier Bröker
  • Andrew V. SutherlandEmail author


For a prime l, let Φ l be the classical modular polynomial, and let h l ) denote its logarithmic height. By specializing a theorem of Cohen, we prove that \(h(\Phi_{l})\le 6l\log l+16l+14\sqrt{l}\log l\). As a corollary, we find that h l )≤6llog l+18l also holds. A table of h l ) values is provided for l≤3600.


Modular polynomials Height bounds j-function 

Mathematics Subject Classification (2000)



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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Brown UniversityProvidenceUSA
  2. 2.Massachusetts Institute of TechnologyCambridgeUSA

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