Class invariants by the CRT method

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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. © 2010 Springer-Verlag Berlin Heidelberg.




Enge, A., & Sutherland, A. V. (2010). Class invariants by the CRT method. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6197 LNCS, pp. 142–156).

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