bash-2.05a$ mwrank3
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 Feb 11 2003 at 17:40:15 by GCC 3.2.1
using base arithmetic option LiDIA_ALL (LiDIA bigints and multiprecision floating point)
Using LiDIA multiprecision floating point with 15 decimal places.
Enter curve: [0,0,0,-9,9]

Curve [0,0,0,-9,9] :    No points of order 2
Basic pair: I=27, J=-243
disc=19683
2-adic index bound = 2
2-adic index = 2
Two (I,J) pairs
Looking for quartics with I = 27, J = -243
Looking for Type 2 quartics:
Trying positive a from 1 up to 1 (square a first...)
(1,-1,-3,2,1)   --trivial
Trying positive a from 1 up to 1 (...then non-square a)
Finished looking for Type 2 quartics.
Looking for Type 1 quartics:
Trying positive a from 1 up to 1 (square a first...)
Trying positive a from 1 up to 1 (...then non-square a)
Finished looking for Type 1 quartics.
Looking for quartics with I = 432, J = -15552
Looking for Type 2 quartics:
Trying positive a from 1 up to 6 (square a first...)
Trying positive a from 1 up to 6 (...then non-square a)
Trying negative a from -1 down to -1
Finished looking for Type 2 quartics.
Looking for Type 1 quartics:
Trying positive a from 1 up to 7 (square a first...)
(1,0,-6,8,33)   --nontrivial...(x:y:z) = (1 : 1 : 0)
Point = [1 : 1 : 1]
        height = 0.387624594904276
Rank of B=im(eps) increases to 1 (The previous point is on the egg)
Exiting search for Type 1 quartics after finding one which is globally soluble.
Mordell rank contribution from B=im(eps) = 1
Selmer  rank contribution from B=im(eps) = 1
Sha     rank contribution from B=im(eps) = 0
Mordell rank contribution from A=ker(eps) = 0
Selmer  rank contribution from A=ker(eps) = 0
Sha     rank contribution from A=ker(eps) = 0
Rank = 1
Points generating E(Q)/2E(Q):
Point [1 : 1 : 1], height = 0.387624594904276
After descent, rank of points found is 1

Generator 1 is [1 : 1 : 1]; height 0.387624594904276

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) = 0.387624594904276

 (3 seconds)
Enter curve: [0,0,0,0,0]

bash-2.05a$