README file for programs mwrank, findinf, ratpoint

There are three main programs in this distribution, called mwrank,
findinf and ratpoint.  The first two work on elliptic curves over Q
given by Weierstrass equations with standard coefficients
[a1,a2,a3,a4,a6].  If the input curve is non-minimal or non-standard
(where standard means a1,a3 in {0,1} and a2 in {-1,0,1}) the input
curve is replaced by a standard minimal model, and points found are
transferred back to the original input model.  The programs tell you
when the model is changed.

In all cases there are 2 possible input formats for curves:

[a1,a2,a3,a4,a6]
a1 a2 a3 a4 a6

So if the first character read is '[' it expects a single non-space
delimiter between coefficients and one at the end; otherwise it
expects 5 integers separated by space.  If the input is invalid the
programs stop, so you can use 0 0 0 0 0 to end the input stream.


findinf searches for points on the curves up to a given bound on the
logarithmic height, using sieving.  One can opt for either seeing all
points as they are found (verbose=1) or nothing until a final report
(verbose=0); also, if verbose=1 then one can opt for a simple list of
the points found, with no post-processing, or a full processing of the
points to find linear dependencies between them using the height
pairing.  The "regulator" output is just the regulator of the subgroup
of points found.  Currently the sieve is based on Michael Stoll's
programme (which originated with a program of Elkies, with
developments by Stoll and Colin Stahlke).  Added in Jan 2005: the
subgroup of points found is (by default) automatically saturated at
the end.

mwrank is described more fully in the file mwrank.info.  Briefly,
mwrank does a 2-descent to determine the rank and gives points
covering the cosets of 2E(Q) in E(Q); it then goes on to complete to a
Mordell-Weil basis via a sieve-based saturation process after
determining an upper bound for the index.

ratpoint works with quartics g(x) with integer coefficients,
g(x)=a*x^4+b*x^3+c*x^2+d*x+e.  It finds the Jacobian E of the curve
C:y^2=g(x), searches C for rational points and maps any point found to
E using the 2-covering map.  Current version quits as soon as one
point on C is found.

Other programs: tmrank is a version of mwrank designed for testing
with the input file tmrank.in.  Each line of tmrank.in contains a
curve and its correct rank, and tmrank uses mwrank to compute the rank
and checks the result.

	        tate: Runs Tate's algorithm, outputs detail of
             	        reduction types etc.
		conductor: just output conductor
		torsion: outputs number (and optionally structure) of
             	        torsion points
		allisog: find the complete isogeny class of the input
             	        curve by computing a succession of isogenies
             	        of prime degree.  WARNING: this is unreliable
             	        and causes lots of warning messages if run in
             	        standard precision.  With higher precision
             	        (under LiDIA) it is reliable, though a lot
             	        slower.   I also have a Pari/GP program to do
             	        the same thing, available on request.

These four can be run interactively (by entering "tty" for the input
filename at the prompt) or in batch mode by entering the filename.
The file should contain a list of curves in the standard format, with
[0,0,0,0,0] to terminate cleanly.

	       twist: computes quadratic twists of a given curve,
	       giving their minimal models etc.  Interactive.
	       
	       indep: tests whether given points on a curve are
	       independent, using 2-descent NOT heights.  Test with 
	       "indep < e23".

Systems supported: only linux binaries are now provided.

*(0) Old versions for Sun (Solaris 7) are in sun/.
*(1) Old versions for SGI (IRIX  5.3) are in sgi/.
*(2) Versions for DOS/Wondiws are in dos/.
*Versions for Linux-Intel are in linux-intel/.
*(3) Versions for Linux-alpha are in linux-alpha/.
*(4) Versions for DEC alpha (OSF) are in alpha/.

(1) I don't have access to a newer SGI, and this one only has
    gcc-2.3.3, so this version is OLD.

(2) Has some very OLD versions, which really should not be used
(suffix .exe.old).  Also zip files containing recent versions for
DOS/WOndows, kindly provided by Tom Womack.  I no longer do any
programming on DOS or Windows machines, so please contact Tom at
tom@womack.net for any queries regarding these, which are built from
the latest source files as of May 2000.

(3,4) I no longer have access to any alpha machines, so these are OLD.

Sources: mwrank.tar.gz is a gzipper tar file of the distribution.  It
requires pre-installation of either LiDIA or NTL.  The NTL version is
generally faster.  Both NTL and LiDIA version may be used with or
without multiprecision floating point (see mwrank.info for more
details).


							John Cremona

							 6/2/95
						updated	 7/8/95
						updated	12/1/98
						updated	20/4/00
						updated	16/8/00
						updated	 5/7/01
						updated	 7/1/05
						updated	10/5/05

						john.cremona@nottingham.ac.uk