English

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.

Keywords

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)

R2 v1 2026-06-21T14:36:46.992Z