Question on completeness of the qfminin() command on finding all vectors for a given positive definite symmetric matrix

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

To all:

Let e be a congruent number elliptic curve for n = 34

(1)   E = [0,0,0,-1156,0]

GP-Pari ellrank(E) command gives a basis for the Mordell-Weil points

(2)   p = [[-16,120],[-2,48]]

We will work with the qfminim() command and try to obtain all points on 
the curve using p, of a certain height or less.

% h = ellheightmatrix(ellinit(E),p);

    [ 3.0186699169749291099095663298294266022 
0.69722458204458762681298145257071547465]
h =
    [0.69722458204458762681298145257071547465 
2.5129601807581821684984906098707155252]

% M = qfminim(h,13,,2)[3]

[ 0  0 -1 -1 -1 -1 -2 -2]

[-1 -2  0 -1  1  2  1  0]

However when I actually used this to find all rational points < height 
13, I found 18 points which were missing from the 49 which qfminim() 
gave + torsion points.

The torsion points for E are [[-34, 0], [34, 0], [0, 0]].  The curve is 
Z2 x Z2. The 4th point is the infinite point, of course.

Cafefull investigation of the elliptic curve points shows that M seems 
to be missing some vectors.

[ 0  0 -1 -1 -1 -1 -2 -2]           [ 1 0 2 ]
                           MISSING:
[-1 -2  0 -1  1  2  1  0]           [ 1 2 0 ]

I obtained only 49 points, but there are actually 67 points of height < 
13 for curve E. I had to decompose these points as combinations of the 
basis, to uncover what was missing here.

Questions:

1. should I negate the columns of M and append them to M?  ( I am 
guessing that the columns need to be unique) It is obvious that the 
heights stay the same if we negate a column.

2. What about if M > 2 rows here, do the same, negate all columns of 
n-rows for a basis of n-points?

3. Does qfminin exhaustively find all the vectors? or is just a partial 
answer given as occurred in this case?

This did take me 2-3 hours to troubleshoot.

- Randall