Class invariants by the CRT method

Details Class invariants by the CRT method Class invariants by the CRT method

2010-01-19

arxiv.org/abs/1001.3394v2

Algorithmic Number Theory 9th International Symposium (ANTS IX), LNCS 6197, pp. 142-156, Springer, 2010

Mathematics

Number Theory

15 pages, final version, to appear in ANTS IX (Algorithmic Number Theory Symposium, 2010)

Scientific paper

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|>10^15.

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