Class invariants by the CRT method
Number Theory
2013-02-05 v2
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|>10^15.
Cite
@article{arxiv.1001.3394,
title = {Class invariants by the CRT method},
author = {Andreas Enge and Andrew V. Sutherland},
journal= {arXiv preprint arXiv:1001.3394},
year = {2013}
}
Comments
15 pages, final version, to appear in ANTS IX (Algorithmic Number Theory Symposium, 2010)