Introduction

The CM software implements the construction of ring class fields of imaginary quadratic number fields and of elliptic curves with complex multiplication via floating point approximations. It consists of libraries that can be called from within a C program and of executable command line applications. For the implemented algorithms, see A. Enge, The complexity of class polynomial computation via floating point approximations, Mathematics of Computation 78 (266), 2009, pp. 1089–1107.

The software is written by Andreas Enge and is distributed under the Gnu General Public License, either version 2 of the licence, or (at your option) any later version.

News

Version 0.2, "Blindhühnchen", released in February 2012, comes with the following new features:

Features
- new class invariants: multiple eta quotients with -imultieta
- double eta quotients with both primes >100
- new parameter choice for double eta quotients yielding smaller class polynomials
- slightly lower height bounds for double eta quotients
Bug fixes
- printing of field and curve cardinality even without parameter -v
- Weber polynomials work again (activated by -iweber)
- class polynomials for D=-4 and D=-16 work (no curve is constructed)
Dependencies
- factorisation of class polynomials is done by pari instead of ntl

Olds

The initial release of version 0.1 "Apfelkraut" was made in November 2009.