Class invariants by the CRT method

TL;DR

This paper adapts the CRT method to efficiently compute a broad class of class invariants, significantly enhancing performance and enabling record-breaking elliptic curve constructions with large discriminants.

Contribution

It introduces an improved CRT-based approach for computing class invariants applicable to various discriminants, leading to substantial performance gains.

Findings

Performance improved by over 200 times in optimal cases

Enabled construction of elliptic curves with discriminants larger than 10^15

Achieved record-breaking elliptic curve constructions

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.