Class Invariants by the CRT Method

  • Andreas Enge
  • Andrew V. Sutherland
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6197)


We adapt the CRT approach for computing Hilbert class polynomials to handle a wide range of class invariants. For suitable discriminants D, this improves its performance by a large constant factor, more than 200 in the most favourable circumstances. This has enabled record-breaking constructions of elliptic curves via the CM method, including examples with |D| > 1015.


Elliptic Curve Elliptic Curf Modular Function Endomorphism Ring Chinese Remainder Theorem 
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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Andreas Enge
    • 1
  • Andrew V. Sutherland
    • 2
  1. 1.INRIA Bordeaux–Sud-OuestFrance
  2. 2.Massachusetts Institute of TechnologyCambridgeUSA

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