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, and is soon also to be 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). But I will also update the mwrank distribution when I can.

To build mwrank from the source code you must have either Shoup's NTL library or the LiDIA 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).

For other systems, mwrank is available within SAGE.
  1. mwrank-2008-07-20.tgz: source code (gzipped tar file, around 350k).
    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.
  2. ftp directory for binaries of mwrank and programs listed below
  3. 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.
  1. conductor: computes conductor of input curves
  2. tate: computes conductor and local reduction data of input curves
  3. torsion: computes torsion subgroup of input curves
  4. indep: tests points for independence
  5. 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.
  6. allisog: computes curves isogenous to input curves
  7. twist: computes quadratic twists of input curves
  8. 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.

Magma programs

Various Magma programs, many of which are now redundant having been incorporated into recent Magma releases.

Pari/GP programs

Various GP scripts for elliptic curves including Heegner points.

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