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Class Invariants by the CRT Method

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

Abstract

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.

Keywords

Elliptic Curve Elliptic Curf Modular Function Endomorphism Ring Chinese Remainder Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© 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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