Class Invariants by the CRT Method

  • Andreas Enge
  • Andrew V. Sutherland
Conference paper

DOI: 10.1007/978-3-642-14518-6_14

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6197)
Cite this paper as:
Enge A., Sutherland A.V. (2010) Class Invariants by the CRT Method. In: Hanrot G., Morain F., Thomé E. (eds) Algorithmic Number Theory. ANTS 2010. Lecture Notes in Computer Science, vol 6197. Springer, Berlin, Heidelberg


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.


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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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