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,-9,81]

Curve [0,0,0,-9,81] :        No points of order 2
Basic pair: I=27, J=-2187
disc=-4704237
2-adic index bound = 2
2-adic index = 2
Two (I,J) pairs
Looking for quartics with I = 27, J = -2187
Looking for Type 3 quartics:
Trying positive a from 1 up to 3 (square a first...)
(1,-1,0,9,0)  --trivial
(1,-1,6,5,-2)  --nontrivial...(x:y:z) = (1 : 1 : 0)
Point = [-30 : 63 : 8]
      height = 2.33771265006877
Rank of B=im(eps) increases to 1
(1,2,-9,9,0)   --trivial
(1,2,9,9,0)    --trivial
Trying positive a from 1 up to 3 (...then non-square a)
(3,1,3,6,1)     --trivial
Trying negative a from -1 down to -2
Finished looking for Type 3 quartics.
Looking for quartics with I = 432, J = -139968
Looking for Type 3 quartics:
Trying positive a from 1 up to 15 (square a first...)
(1,0,-54,216,-207)     --nontrivial...(x:y:z) = (1 : 1 : 0)
Point = [9 : 27 : 1]
        height = 0.912532500970101
Doubling global 2-adic index to 2
global 2-adic index is equal to local index
so we abort the search for large quartics
Rank of B=im(eps) increases to 2
Exiting search for large quartics after finding enough globally soluble ones.
Mordell rank contribution from B=im(eps) = 2
Selmer  rank contribution from B=im(eps) = 2
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 = 2
Points generating E(Q)/2E(Q):
Point [9 : 27 : 1], height = 0.912532500970101
Point [-30 : 63 : 8], height = 2.33771265006877
After descent, rank of points found is 2

Generator 1 is [9 : 27 : 1]; height 0.912532500970101
Generator 2 is [-30 : 63 : 8]; height 2.33771265006877

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) = 0.18794827330682

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

bash-2.05a$