mwrank and related programs for elliptic curves
over Q
by J. E. Cremona, University of Warwick, U.K.
Updated 2008-07-20 [Changelog]
mwrank
mwrank is a program written in C++ for computing
Mordell-Weil groups of elliptic curves over Q via 2-descent.
It is available as source code (under GPL) or as a binary executable
(for linux-intel only).
News: From November 2007 mwrank has formed part of the eclib package
which is included in Sage. It may also become available as a Debian
package thanks to sterling work by Tim Abbott. The easiest way to
install and run mwrank is to install Sage (which also of course gives
you much much more). I will also update the mwrank distribution when
I can. [Last done: 2010-11-11] Full source code for eclib is
available from google
code.
To build mwrank from the source code you must
have Shoup's NTL
library installed on your computer, as well as gmp which each of these uses. The
only systems and compilers on which mwrank is developed and tested are
linux + gcc (currently up to gcc 4.2). It is also very strongly recommended to
have the PARI library installed, as it is used for integer factorization.
For other systems, mwrank is available
within SAGE.
- mwrank-2010-11-11.tgz:
source code (gzipped tar file, around 384k).
The source tarball now has the format mwrank-YYYY-MM-DD.tgz: the date
is the date on which the distribution was last updated. One day I
may start to use version numbers.
- ftp
directory for binaries of mwrank and programs listed below
- Other information files for mwrank:
Other C/C++ programs
These are available as executable binaries in the
ftp
directory and in the source
code distribution.
- conductor: computes conductor of input curves
- tate: computes conductor and local reduction data of input curves
- torsion: computes torsion subgroup of input curves
- indep: tests points for independence
- findinf: search for points on a curve, followed by
saturation. One can also input known points so this can be used to
saturate a known set of points.
- allisog: computes curves isogenous to input curves
- twist: computes quadratic twists of input curves
- ratpoint: search for points on a quartic
y2=g(x) (viewed as a 2-cover of its Jacobian)
after testing for local solubility. Points found are mapped to the
Jacobian via the 2-covering map. This is intended mainly for further
processing of quartics output by mwrank.
Various Magma
programs, many of which are now redundant having been incorporated
into recent Magma releases.
Various GP
scripts for elliptic curves including Heegner points.
