bash-2.05$ ./rankdist/mwrank -b 15 -c 15 -p 200
Program mwrank: uses 2-descent (via 2-isogeny if possible) to
determine the rank of an elliptic curve E over Q, and list a
set of points which generate E(Q) modulo 2E(Q).
and finally search for further points on the curve.
For more details see the file mwrank.doc.
For details of algorithms see the author's book.

Please acknowledge use of this program in published work, 
and send problems to John.Cremona@nottingham.ac.uk.

Version compiled on May 23 2001 at 22:19:04 by GCC egcs-2.91.60 19981201 (egcs-1.1.1 release)
using base arithmetic option LiDIA (LiDIA bigints and multiprecision floating point)
Using LiDIA multiprecision floating point with 200 decimal places.
Enter curve: [0, 0, 0, -29929, 0]

Curve [0,0,0,-29929,0] :        3 points of order 2:
[173 : 0 : 1], [-173 : 0 : 1], [0 : 0 : 1]
Using 2-isogenous curve [0,0,0,-329219,-72488038]
-------------------------------------------------------
First step, determining Selmer group
-------------------------------------------------------
-------------------------------------------------------
Rank <= 1
-------------------------------------------------------
Second step, determining E(Q)/phi(E'(Q)) and E'(Q)/phi'(E(Q))
-------------------------------------------------------
1. E(Q)/phi(E'(Q))
-------------------------------------------------------
First stage (no second descent yet)...
(-1,0,519,0,-59858):  no rational point found (hlim=6)
(-2,0,519,0,-29929):  no rational point found (hlim=6)
(173,0,519,0,346):  no rational point found (hlim=6)
(346,0,519,0,173):  no rational point found (hlim=6)
After first descent, this component of the rank
  has lower bound 0
       and upper bound 1
       (difference =   1)
Second descent will attempt to reduce this
Second stage (using second descent)...
d1=-1: 
 (x:y:z) = (69084044403:294726092360550044038:3728226965)
      Curve E         Point [-17793355366667311225971299918685 : -20360870451358918327824797419314 : 51821147995950007613689182125], height = 49.57410802089807960742348253992646079395327765330480530983638170552951546113319820195170990027158677973765666363091249563160218762162680600635005375005982904085512891035472351621276862593339751872314
Second descent successfully found rational point for d1=-1

-------------------------------------------------------
2. E'(Q)/phi'(E(Q))
-------------------------------------------------------
This component of the rank is 0

-------------------------------------------------------
Summary of results:
-------------------------------------------------------
     rank(E) = 1
     #E(Q)/2E(Q) = 8

Information on III(E/Q):
 #III(E/Q)[phi']    = 1
  #III(E/Q)[2]       = 1

Information on III(E'/Q):
 #phi'(III(E/Q)[2]) = 1
  #III(E'/Q)[phi]    = 1
  #III(E'/Q)[2]      = 1

-------------------------------------------------------

List of points on E = [0,0,0,-29929,0]:

I.  Points on E mod phi(E')
Point [-8828296763367959908803071411060 : -20360870451358918327824797419314 : 51821147995950007613689182125], height = 49.57410802089807960742348253992646079395327765330480530983638170552951546113319820195170990027158677973765666363091249563160218762162680600635005375005982904085512891035472351621276862593339751872314

II.  Points on phi(E') mod 2E
--none (modulo 2-torsion).

-------------------------------------------------------
Computing full set of 2 coset representatives for
2E(Q) in E(Q) (modulo torsion), and sorting into height order....done.

Rank = 1
Height Constant = 9.63211876239872566429767175577580928802490234375

Max height = 49.57410802089807960742348253992646079395327765330480530983638170552951546113319820195170990027158677973765666363091249563160218762162680600635005375005982904085512891035472351621276862593339751872314
Bound on naive height of extra generators = 15.140352986942956731789169815767638265130822083006089478870709078392168384570355355772412211141287419970850740403434721736844687513514089556261117083339981004539458767817191501801418736214821946524793
Only searching up to height 15
After point search, rank of points found is 1

Generator 1 is [-8828296763367959908803071411060 : -20360870451358918327824797419314 : 51821147995950007613689182125]; height 49.57410802089807960742348253992646079395327765330480530983638170552951546113319820195170990027158677973765666363091249563160218762162680600635005375005982904085512891035472351621276862593339751872314

The rank has been determined unconditionally.
The basis given is for a subgroup of full rank of the Mordell-Weil group
 (modulo torsion), possibly of index greater than 1.
Regulator (of this subgroup) = 49.57410802089807960742348253992646079395327765330480530983638170552951546113319820195170990027158677973765666363091249563160218762162680600635005375005982904085512891035472351621276862593339751872314

 (3841.91 seconds)

Enter curve: [0,0,0,0,0]

bash-2.05$ gcl
GCL (GNU Common Lisp)  Version(2.4.0) Sat Sep 22 19:14:39 JST 2001
Licensed under GNU Library General Public License
Contains Enhancements by W. Schelter

>(load "congr.lisp")

Loading congr.lisp
Finished loading congr.lisp
T

>(tri -8828296763367959908803071411060/51821147995950007613689182125 -20360870451358918327824797419314/51821147995950007613689182125 173)

((418416739097462232963/181421867613059954270
  62771966194118744177420/418416739097462232963
  11389552969201600543101928087171460571651881/75909946247628040203029119534348866602010)
 173 0)

>(bye)
bash-2.05$