trying to use qflllgram on the height matrix of elliptic curve points sometimes gives odd results

[American Citizen <website.reader3@gmail.com>]

Hello everyone:

I have a certain rank=4 Z2xZ6 curve, from an isogenous Z12 rank 4 curve 
discovered by Tom Fisher in 2008, which I am currently using to analyze 
certain points on the curve, but these points are compositions of the 
Mordell-Weil basis points which are known.

The basic idea is this

h = ellheightmatrix(E,[p[1], p[2], p[3], p[4], q]);

mattranspose( qflllgram(h) )

Which normally will produce a matrix like such

[1 -1 0 0 1]

[1  0 0 0 0]

[0  1 0 0 0]

[0  0 1 0 0]

[0  0 0 1 0]

where the first row [ 1 -1 0 0 1 ] actually gives the composition of 
point q as the addition and/or subtraction of the known Mordell Weil 
basis points p[1], p[2], p[3], p[4] for this curve. Rows 2-5 actually 
inform us that they are the Mordell-Weil basis points and are unique. In 
the example given, then q = P1 - P2.

But sometimes the matrix does NOT come out right, and occasionally the 
gp pari program hangs up and then starts to add to the heap requesting 
gigabytes of ram stuck on apparently trying to do the qflllgram factoring.

Questions:

Is qflllgram(ellheightmatrix(e,pts)) the right way to discover the 
points composition of the unknown point q and the MW basis p1-4 ?

Should I be using a different matrix factoring command? If so, which one?

Why is qflllgram hanging up on certain unknown points q? I actually went 
to precision 500, but the qflllgram step failed to resolve and kept 
asking for more memory.

I would like to have all my output be like above, if possible.

Attached is the input file and the results file from my run until the 
hangup occurred. I flagged the strange results with an asterisk *.

Thanks for taking a look at this.

Randall

default precision: 57

point:1

[1 -1 0 0 1]

[1  0 0 0 0]

[0  1 0 0 0]

[0  0 1 0 0]

[0  0 0 1 0]

point:2

[-1 0 0 0 1]

[ 1 0 0 0 0]

[ 0 1 0 0 0]

[ 0 0 1 0 0]

[ 0 0 0 1 0]

point:3

[0 -1 1 -1 1]

[1  0 0  0 0]

[0  1 0  0 0]

[0  0 1  0 0]

[0  0 0  1 0]

point:4

[0 -1 1 0 1]

[1  0 0 0 0]

[0  1 0 0 0]

[0  0 1 0 0]

[0  0 0 1 0]

point:5

[-1 0 0 1 1]

[ 0 0 0 1 1]

[-1 1 0 1 1]

[ 0 0 1 0 0]

[-1 0 0 2 1]

point:6

[0 0 1 -1 1]

[1 0 0  0 0]

[0 1 0  0 0]

[0 0 1  0 0]

[0 0 0  1 0]

point:7

[1 -1 1 -1 1]

[1  0 0  0 0]

[0  1 0  0 0]

[0  0 1  0 0]

[0  0 0  1 0]

point:8

[1 -1 1 -1 1]

[1  0 0  0 0]

[0  1 0  0 0]

[0  0 1  0 0]

[0  0 0  1 0]

point:9 *

[-1 0 0 0  1]

[ 0 0 0 0  1]

[-1 1 0 0  1]

[ 1 0 1 0 -1]

[-1 0 0 1  1]

point:10 *

[-2 1 0 0 1]

[ 1 0 0 0 0]

[ 0 1 0 0 0]

[ 0 0 1 0 0]

[ 0 0 0 1 0]

point:11 *

[-1 0 0 1 1]

[ 0 0 0 1 1]

[ 0 1 0 0 0]

[ 0 0 1 0 0]

[ 0 0 0 1 0]

point:12

[1 0 -1 0 1]

[1 0  0 0 0]

[0 1  0 0 0]

[0 0  1 0 0]

[0 0  0 1 0]

point:13 *

[ 1 0 0  1  1]

[ 0 0 0 -1 -1]

[16 1 0 16 16]

[ 8 0 1  8  8]

[ 0 0 0  1  0]

point:14 *

[0 1 0 1 1]

[1 0 0 0 0]

[0 1 0 0 0]

[0 2 1 2 2]

[0 0 0 1 0]

point:15 *

[0 0 1 0 1]

[1 0 2 0 2]

[0 1 6 0 6]

[0 0 1 0 0]

[0 0 4 1 4]

point:16 Hangs up and starts asking for huge chunks of system RAM

Attachment: 303.gp
Description: application/gnuplot