The Lattice MxA4^2
An entry from the Catalogue of Lattices, which is a joint project of
Gabriele Nebe, RWTH Aachen University
(nebe@math.rwth-aachen.de)
and
Neil J. A. Sloane
(njasloane@gmail.com)
Last modified Fri Jul 18 13:11:34 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
KISSING_NUMBER
GRAM
DIVISORS (elementary divisors)
MINIMAL_NORM
HERMITE_NUMBER
HERMITIAN_GROUP_ORDER
HERMITIAN_GROUP_GENERATORS
HERMITIAN_STRUCTURE
PROPERTIES
REFERENCES
NOTES
LAST_LINE
-
NAME
MxA4^2
-
DIMENSION
32
-
KISSING_NUMBER
480
-
GRAM
32 0
4
0 4
0 0 4
-2 2 2 4
-5 1 3 5 38
-1 -5 1 -3 0 38
-3 -1 -5 -1 0 0 38
0 -2 -4 -5 -19 19 19 38
-3 1 3 3 18 4 2 -5 18
-1 -3 -1 -3 -4 18 2 11 0 18
-3 1 -3 1 -2 -2 18 11 0 0 18
0 0 -4 -3 -13 7 7 18 -9 9 9 18
-9 1 1 6 28 0 2 -13 14 2 6 -4 40
-1 -9 1 -4 0 28 0 13 -2 14 -2 4 0 40
-1 -1 -9 -4 -2 0 28 15 -6 2 14 12 0 0 40
3 -5 -5 -9 -15 15 13 28 -10 10 2 14 -20 20 20 40
2 2 0 0 -5 -11 -7 -7 -1 -5 -5 -4 -6 -12 -6 -6 8
-2 2 0 2 11 -5 -1 -5 5 -1 1 0 12 -6 0 -6 0 8
0 0 2 2 7 1 -5 -11 5 -1 -1 -6 6 0 -6 -12 0 0 8
-2 0 0 2 12 0 6 -5 5 -1 5 -1 12 0 6 -6 -4 4 4 8
2 2 2 1 -2 -8 -4 -5 -1 -5 -3 -3 -7 -11 -7 -5 4 0 0 -2 8
-2 2 0 1 8 -2 0 -3 5 -1 1 -1 11 -7 1 -5 0 4 0 2 0 8
-2 0 2 3 4 0 -2 -7 3 -1 -1 -5 7 -1 -7 -13 0 0 4 2 0 0 8
-3 1 -1 2 7 1 5 -2 4 0 4 -1 12 -2 6 -7 -2 2 2 4 -4 4 4 8
1 1 1 1 -1 -11 -3 -8 -5 -7 -1 -2 -2 -6 -2 -4 2 0 0 0 4 0 0 -2 8
-1 1 1 1 11 -1 -3 -6 7 -5 -1 -6 6 -2 -2 -4 0 2 2 2 0 4 0 2 0 8
-1 -1 1 1 3 3 -1 -6 1 1 -5 -6 2 2 -2 -4 0 -2 2 0 0 0 4 2 0 0 8
-2 0 0 1 9 5 5 -1 7 1 1 -5 6 2 2 -2 -2 0 2 2 -2 2 2 4 -4 4 4 8
0 -2 0 0 0 -4 -6 -5 -4 -4 -2 -2 0 4 -2 0 0 0 0 0 0 -2 0 -2 2 0 0 -2 8
2 0 2 0 4 0 0 1 4 -4 -2 -4 -4 0 -2 2 0 0 0 0 2 0 -2 -2 0 2 -2 0 0 8
0 -2 0 -2 6 0 0 -5 2 2 -4 -4 2 2 0 2 0 0 0 0 0 2 0 0 0 2 2 2 0 0 8
0 0 2 0 5 -1 5 0 6 0 0 -4 0 -2 -2 0 0 0 0 0 2 2 0 0 0 2 0 2 -4 4 4 8
-
DIVISORS (elementary divisors)
2^16
-
MINIMAL_NORM
4
-
HERMITE_NUMBER
2.83
-
HERMITIAN_GROUP_ORDER
2^8*3^3*5^2
-
HERMITIAN_GROUP_GENERATORS
7
32 32
1 -1 -1 1 0 -1 -1 1 1 -1 -1 1 0 0 0 0 -1 -1 0 1 0 0 0 0 0 -1 0 1 0 -1 0 1
1 0 0 1 1 -1 0 1 1 0 0 1 0 0 0 0 0 -1 1 -1 0 0 0 0 0 0 1 -1 0 0 1 -1
0 0 1 -1 0 0 0 -1 0 0 1 -1 0 0 0 0 -1 0 -1 -1 0 0 0 0 -1 0 0 -1 -1 0 0 -1
0 0 1 0 0 0 1 -1 0 0 1 0 0 0 0 0 -1 1 1 -3 0 0 0 0 -1 1 1 -2 -1 1 1 -2
-3 0 1 -3 -2 0 1 -3 0 -3 0 1 0 0 0 0 -6 4 2 -5 0 0 0 0 -3 1 1 -1 -3 1 1 -1
2 -2 -2 1 2 -1 -2 1 2 0 1 -1 0 0 0 0 -1 -4 -3 1 0 0 0 0 -1 -2 0 -1 -1 -2 0 -1
-1 3 0 -3 -1 3 1 -3 -3 2 2 -5 0 0 0 0 2 1 -5 3 0 0 0 0 0 0 -3 1 0 0 -3 1
2 1 0 -1 2 1 0 0 -1 3 3 -4 0 0 0 0 3 -2 -4 1 0 0 0 0 0 0 -1 -2 0 0 -1 -2
-1 1 0 -2 -1 1 0 -2 0 0 1 -2 0 0 0 0 -1 1 -2 0 0 0 0 0 -1 0 -1 0 -1 0 -1 0
1 -1 -2 2 1 -1 -2 2 1 1 -1 0 0 0 0 0 1 -3 -2 4 0 0 0 0 1 -2 -1 2 1 -2 -1 2
1 1 0 0 1 1 0 0 -1 2 2 -2 0 0 0 0 3 -1 -2 2 0 0 0 0 1 0 -1 0 1 0 -1 0
2 -1 -1 2 2 -1 -1 2 1 1 0 1 0 0 0 0 2 -3 -1 2 0 0 0 0 1 -1 0 0 1 -1 0 0
-1 1 1 -1 -1 1 1 -1 -1 0 0 0 1 0 0 0 0 2 1 -1 0 0 0 0 0 1 0 0 0 1 0 0
-1 0 0 -1 -1 0 0 -1 0 -1 0 0 0 1 0 0 -2 1 0 -1 0 0 0 0 -1 0 0 0 -1 0 0 0
0 0 -1 1 0 0 -1 1 0 0 -1 0 0 0 1 0 1 -1 -1 3 0 0 0 0 1 -1 -1 2 1 -1 -1 2
0 0 -1 0 0 0 -1 0 0 0 0 -1 0 0 0 1 0 -1 -2 2 0 0 0 0 0 -1 -1 1 0 -1 -1 1
0 0 0 1 0 0 0 1 0 0 -1 1 0 0 0 0 2 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1
-1 0 1 -1 -1 0 1 -1 0 -1 0 1 0 0 0 0 -2 3 2 -3 0 0 0 0 -1 1 1 -1 -1 1 1 -1
0 -1 -1 1 0 -1 -1 1 1 -1 -1 1 0 0 0 0 -1 -1 1 1 0 0 0 0 0 -1 0 1 0 -1 0 1
-1 0 0 -1 -1 0 0 -1 0 -1 0 0 0 0 0 0 -2 1 0 0 0 0 0 0 -1 0 0 0 -1 0 0 0
0 0 0 -1 0 0 0 -1 0 0 1 -1 0 0 0 0 -1 0 -1 -1 1 0 0 0 -1 0 0 -1 -1 0 0 -1
1 0 -1 1 1 0 -1 1 0 1 0 -1 0 0 0 0 2 -2 -2 3 0 1 0 0 1 -1 -1 1 1 -1 -1 1
0 1 1 -1 0 1 1 -1 -1 1 1 -1 0 0 0 0 1 1 0 -1 0 0 1 0 0 1 0 -1 0 1 0 -1
1 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 2 -1 0 1 0 0 0 1 1 0 0 0 1 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
-2 1 2 -2 -2 1 2 -2 -1 -1 0 1 0 0 0 0 -2 4 3 -4 0 0 0 0 -1 2 1 -1 0 2 1 -1
-1 0 0 -2 -1 0 0 -2 0 -1 1 -1 0 0 0 0 -3 1 -1 -2 0 0 0 0 -2 0 0 -1 -2 1 0 -1
-1 1 -1 0 -1 1 -1 0 -1 0 -1 -1 0 0 0 0 1 0 -2 4 0 0 0 0 1 -1 -2 3 1 -1 -1 3
0 1 -1 -1 0 1 -1 -1 -1 1 1 -3 0 0 0 0 1 -1 -4 3 0 0 0 0 0 -1 -2 1 0 -1 -2 2
32 32
0 -1 0 0 0 -1 0 0 0 -1 -1 1 0 0 0 0 -2 0 1 -1 0 0 0 0 -1 0 0 0 -1 0 0 0
1 0 0 0 1 0 0 0 1 -1 0 1 0 0 0 0 0 -1 0 -1 0 0 0 0 0 -1 0 0 0 -1 0 0
-1 1 1 -2 -1 1 1 -2 0 0 0 -1 0 0 0 0 -1 1 -1 -1 0 0 0 0 0 0 -1 0 0 0 -1 0
0 1 1 -1 0 1 1 -1 0 0 1 -1 0 0 0 0 0 1 0 -2 0 0 0 0 0 0 0 -1 0 0 0 -1
5 -6 0 6 2 -2 1 1 3 -2 1 4 2 -3 -1 5 -5 2 10 -13 1 -3 2 3 -1 2 5 -5 -1 0 2 -4
0 5 6 -6 0 3 2 -3 -3 4 5 -6 -1 1 4 -3 1 5 -3 -7 -2 3 5 -7 -2 4 0 -5 2 1 -2 0
-6 0 5 -6 -3 1 3 -3 -3 -2 1 0 -2 -2 0 -1 -8 11 6 -9 -5 0 1 -3 -3 3 2 -1 -2 4 3 -4
-6 6 6 -7 -2 3 2 -2 -5 3 2 -4 -4 2 3 -5 3 8 -2 0 -5 5 3 -7 0 3 -2 1 2 2 0 1
2 0 3 -2 2 2 2 -2 0 1 4 -3 0 0 1 1 0 3 1 -9 2 0 2 1 -1 2 1 -6 0 -1 -1 -3
-1 5 1 -4 -2 4 0 -2 -2 4 1 -5 -2 1 2 -3 5 1 -8 7 -3 4 3 -5 3 0 -5 4 5 -1 -4 5
-3 2 4 -2 0 0 2 2 -3 2 2 -1 -1 -1 -1 1 2 6 6 -3 -2 -1 1 1 1 4 3 -2 0 4 4 -5
-1 3 0 1 0 0 -2 4 -1 3 -1 0 -2 1 0 -2 8 -2 -3 11 -3 2 0 -1 5 -1 -2 6 4 0 1 3
2 1 -1 4 1 0 -2 7 2 3 -2 1 -2 1 1 -2 8 0 2 6 -2 2 0 0 9 -2 -1 7 7 -3 0 4
-4 1 3 -2 -5 -1 5 -3 -2 0 -1 3 0 -1 -1 0 -8 10 8 -10 -2 -2 0 0 -4 8 6 -5 -1 7 4 -4
2 -5 -3 6 2 -7 -6 7 5 -4 -2 7 0 1 -1 0 -2 -6 2 6 2 -2 -4 4 -1 -5 4 3 -3 -1 6 -2
-3 -2 -1 0 -5 -2 0 -4 1 -5 -3 6 1 0 -1 0 -8 2 0 0 0 -2 -2 0 -6 1 2 1 -4 3 3 0
2 -1 -3 2 2 0 -2 1 1 0 0 -1 0 1 0 0 3 -5 -4 5 2 1 -1 1 1 -3 -2 1 0 -3 -2 2
2 -1 -1 4 1 0 -1 3 1 1 -1 1 -1 0 0 0 4 -1 1 3 -1 1 0 1 4 -1 -1 3 3 -2 0 2
2 -1 1 0 2 -1 1 1 0 1 2 -1 1 -1 -1 2 -1 0 3 -5 2 -2 0 3 -1 2 3 -5 -1 1 1 -4
1 -2 1 2 1 -2 0 3 1 0 0 2 0 -1 -1 1 -1 1 5 -3 0 -2 -1 3 1 1 3 -1 0 1 3 -3
0 0 0 -2 0 2 0 -3 -1 0 1 -3 1 -1 0 1 0 -2 -4 1 0 0 1 -1 -1 -1 -3 0 -1 -1 -3 1
2 0 -2 2 1 0 -3 3 2 0 -2 1 0 1 1 -1 5 -4 -3 7 0 1 0 -1 4 -4 -3 6 3 -4 -2 5
0 2 2 -2 2 1 1 1 -1 3 2 -3 -1 0 1 -1 2 1 1 -3 -1 1 1 -1 2 1 0 -2 2 0 -1 -1
2 0 0 2 3 -2 -2 5 2 1 0 1 -1 1 1 -1 3 -2 2 1 0 1 0 0 3 -2 1 1 2 -2 1 0
-1 -2 -2 1 -2 -1 0 -1 1 -3 -3 3 2 -2 -2 2 -5 -1 2 0 0 -3 -2 2 -1 -1 0 2 -2 1 1 0
3 -3 -1 3 2 -2 -1 1 3 -2 0 3 2 0 0 2 -1 -3 2 -4 3 -2 0 2 -1 -1 2 -2 -2 -1 1 -2
0 1 0 -3 -1 2 0 -3 0 0 1 -3 0 0 2 -2 -3 1 -4 -2 -1 1 1 -4 -1 -1 -2 0 0 -1 -3 2
1 0 2 -2 1 1 1 -2 0 0 3 -2 0 0 2 0 -2 3 1 -8 0 1 3 -3 -2 1 1 -4 -1 0 -1 -2
0 -1 -2 3 -1 -2 -1 2 1 -1 -2 3 1 1 -1 0 1 -2 1 4 2 -2 -3 3 0 0 2 1 -1 1 2 0
0 -2 1 1 1 -2 1 0 0 -1 1 1 0 0 -1 2 -3 2 5 -6 2 -1 0 3 -3 2 3 -5 -3 1 2 -4
1 -2 -2 1 -1 0 -1 -2 1 -2 -1 1 2 -1 0 2 -3 -2 -1 0 1 -1 1 -1 -2 -1 -1 1 -1 -1 -2 2
-1 -1 1 -2 -1 1 2 -4 -1 -1 1 -1 1 -2 -1 3 -5 3 2 -6 0 -1 2 0 -3 2 0 -3 -2 1 -1 -2
32 32
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 1 1 -1 0 1 1 -1 -1 0 0 0 0 0 0 0 1 2 0 0 -1 0 1 -1 0 1 0 0 0 1 0 0
-1 0 0 -1 -1 1 0 -1 0 -1 0 0 0 0 0 0 -2 1 0 0 0 0 0 -1 -1 0 0 0 -1 0 0 0
0 0 -1 1 0 0 0 1 0 0 -1 0 0 0 0 0 2 -2 -1 4 -1 1 0 -1 1 -1 -1 2 1 -1 -1 2
0 0 -1 0 0 0 -1 1 0 0 0 -1 0 0 0 0 0 -2 -2 3 0 1 0 -1 0 -1 -1 1 0 -1 -1 1
-1 2 1 -3 -1 2 1 -3 -1 1 2 -3 0 0 0 0 0 1 -4 1 0 1 2 -2 -1 1 -1 -1 -1 1 -1 -1
0 0 -2 1 0 0 -2 1 0 1 -1 -1 0 0 0 0 2 -4 -3 7 -1 2 0 -2 1 -2 -2 3 1 -2 -2 3
1 1 0 1 1 1 0 1 -1 2 1 -1 0 0 0 0 5 -2 -2 3 -1 1 1 0 2 0 -1 1 2 0 -1 1
2 -1 -2 3 2 -1 -2 3 1 1 -1 1 0 0 0 0 3 -5 -1 4 0 1 -1 1 2 -2 -1 2 2 -2 -1 2
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 -1 0 0 0 -1 0 0 1 -1 0 0 0 0 -1 0 -1 -1 1 0 0 0 -1 0 0 -1 -1 0 0 -1
1 0 -1 1 1 0 -1 1 0 1 0 -1 0 0 0 0 2 -2 -2 3 0 1 0 0 1 -1 -1 1 1 -1 -1 1
0 1 1 -1 0 1 1 -1 -1 1 1 -1 0 0 0 0 1 1 0 -1 0 0 1 0 0 1 0 -1 0 1 0 -1
1 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 2 -1 0 1 0 0 0 1 1 0 0 0 1 0 0 0
0 0 0 1 0 0 0 1 0 0 -1 1 0 0 0 0 2 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1
-1 0 1 -1 -1 0 1 -1 0 -1 0 1 0 0 0 0 -2 3 2 -3 0 0 0 0 -1 1 1 -1 -1 1 1 -1
0 -1 -1 1 0 -1 -1 1 1 -1 -1 1 0 0 0 0 -1 -1 1 1 0 0 0 0 0 -1 0 1 0 -1 0 1
-1 0 0 -1 -1 0 0 -1 0 -1 0 0 0 0 0 0 -2 1 0 0 0 0 0 0 -1 0 0 0 -1 0 0 0
1 -1 0 2 1 -1 0 2 1 0 -1 2 0 0 0 0 1 0 3 -2 0 -1 -1 2 2 0 1 0 1 0 1 0
-1 1 2 -2 -1 1 2 -2 -1 0 1 0 0 0 0 0 -1 4 1 -4 0 -1 1 0 -1 3 1 -2 -1 2 1 -2
-1 -1 0 0 -1 -1 0 0 1 -2 -1 2 0 0 0 0 -3 2 3 -2 0 -1 -1 0 -1 0 2 0 -1 0 1 0
-2 1 1 -2 -2 1 1 -2 -1 -1 0 0 0 0 0 0 -1 3 0 0 -1 0 1 -2 -1 1 0 1 -1 1 0 0
0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 2 2 -3 0 -1 0 1 0 1 1 -1 1 1 1 -1
-1 1 1 -2 -1 1 1 -2 -1 0 1 -1 0 0 0 0 -1 2 -1 -1 0 0 1 -1 -1 1 0 -1 -1 2 0 -1
-1 0 0 0 -1 0 0 0 0 -1 -1 1 0 0 0 0 0 1 1 1 -1 0 0 -1 0 0 0 1 0 0 1 1
-1 1 0 -1 -1 1 0 -1 -1 0 0 -1 0 0 0 0 1 0 -2 3 -1 1 1 -2 0 0 -1 1 0 0 -1 2
32 32
1 -1 -1 1 0 -1 -1 1 1 -1 -1 1 0 0 0 0 -1 -1 0 1 0 0 0 0 0 -1 0 1 0 -1 0 1
1 0 0 1 1 -1 0 1 1 0 0 1 0 0 0 0 0 -1 1 -1 0 0 0 0 0 0 1 -1 0 0 1 -1
0 0 1 -1 0 0 0 -1 0 0 1 -1 0 0 0 0 -1 0 -1 -1 0 0 0 0 -1 0 0 -1 -1 0 0 -1
0 0 1 0 0 0 1 -1 0 0 1 0 0 0 0 0 -1 1 1 -3 0 0 0 0 -1 1 1 -2 -1 1 1 -2
-1 3 0 -3 -3 3 1 -4 0 0 2 -2 0 0 0 0 -1 4 -2 -1 0 0 0 0 0 1 0 0 0 1 0 0
0 -1 -3 3 0 -2 -3 2 0 2 0 -2 0 0 0 0 -1 -3 -3 5 0 0 0 0 -1 0 0 0 -1 0 0 0
3 0 -1 3 2 1 -2 2 -2 2 2 -2 0 0 0 0 6 -3 -4 7 0 0 0 0 1 -1 -1 2 1 -1 -1 2
3 -3 -3 5 3 -2 -3 3 0 2 0 0 0 0 0 0 3 -6 -4 6 0 0 0 0 0 -1 -1 1 0 -1 -1 1
-1 1 0 -2 -1 1 0 -2 0 0 1 -2 0 0 0 0 -1 1 -2 0 0 0 0 0 -1 0 -1 0 -1 0 -1 0
1 -1 -2 2 1 -1 -2 2 1 1 -1 0 0 0 0 0 1 -3 -2 4 0 0 0 0 1 -2 -1 2 1 -2 -1 2
1 1 0 0 1 1 0 0 -1 2 2 -2 0 0 0 0 3 -1 -2 2 0 0 0 0 1 0 -1 0 1 0 -1 0
2 -1 -1 2 2 -1 -1 2 1 1 0 1 0 0 0 0 2 -3 -1 2 0 0 0 0 1 -1 0 0 1 -1 0 0
0 3 0 -3 -2 4 2 -4 0 1 1 -2 1 0 0 0 2 2 -3 0 0 0 0 0 2 0 -2 1 2 0 -2 1
0 0 -3 3 -2 0 -2 0 0 1 -1 0 0 1 0 0 1 -1 -3 6 0 0 0 0 1 0 -1 3 1 0 -1 3
3 0 0 3 2 0 -2 4 0 1 1 0 0 0 1 0 5 -2 0 4 0 0 0 0 2 -1 1 1 2 -1 1 1
3 -3 -3 6 2 -2 -4 4 1 0 -1 2 0 0 0 1 3 -5 -2 7 0 0 0 0 1 -2 0 3 1 -2 0 3
-1 0 1 -1 0 0 1 0 0 -1 -1 1 0 0 0 0 0 1 2 -2 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 -1 -1 1 1 -2 1 -1 0 1 0 0 0 0 -1 2 0 -2 0 0 0 0 0 0 0 0 0 0 0 0
-1 1 0 -1 -1 0 0 0 0 0 0 -1 0 0 0 0 -1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 -1 -1 1 0 -1 0 0 1 -1 0 0 0 0 0 1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0
0 -1 1 -1 1 -1 0 0 0 -1 1 0 0 0 0 0 -2 0 1 -3 1 0 0 0 -2 0 1 -2 -2 0 1 -2
1 1 0 -1 1 1 0 0 0 1 1 -2 0 0 0 0 2 -1 -2 1 0 1 0 0 1 -1 -1 0 1 -1 -1 0
-2 2 2 -3 -1 1 2 -2 -2 1 1 -2 0 0 0 0 -1 3 1 -3 0 0 1 0 -1 2 0 -2 -1 2 0 -2
0 2 1 -1 0 1 1 0 -1 2 1 -2 0 0 0 0 2 1 0 0 0 0 0 1 1 1 0 -1 1 1 0 -1
1 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 0 1 -1 0 0 0 0 1 0 1 -1 0 0 1 -1
-1 2 1 -2 -1 1 1 -1 -1 1 1 -2 0 0 0 0 0 2 0 -1 0 0 0 0 0 2 0 -1 0 1 0 -1
-1 0 1 0 0 -1 0 1 -1 0 0 0 0 0 0 0 -1 1 2 -1 0 0 0 0 -1 1 2 -1 -1 1 1 -1
-1 1 0 0 -1 0 0 0 -1 1 0 -1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0
-2 0 1 -2 -2 1 2 -3 0 -2 -1 2 0 0 0 0 -3 3 2 -4 0 0 0 0 -1 1 0 0 0 1 0 0
1 -1 -1 0 0 0 -1 -1 1 -1 1 0 0 0 0 0 -1 -1 -2 0 0 0 0 0 -1 -1 0 0 -1 0 0 0
-1 2 0 -2 -1 2 0 -1 -1 0 0 -2 0 0 0 0 1 1 -2 2 0 0 0 0 1 -1 -2 2 1 -1 -1 2
1 1 0 -1 1 1 -1 0 -1 1 2 -3 0 0 0 0 2 -1 -3 2 0 0 0 0 0 -1 -1 0 0 -1 -1 1
32 32
-1 0 1 -1 0 0 1 -1 -1 0 0 0 0 0 0 0 -1 1 1 -2 0 0 0 0 -1 1 0 -1 -1 1 0 -1
0 0 0 -1 0 1 0 -1 0 -1 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 -1 -1 1 0 -1 -1 1
-1 1 0 -1 -1 1 1 -1 0 0 -1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 -1 1 1 0 -1 1
0 1 0 -1 0 1 0 0 0 0 0 -1 0 0 0 0 1 0 -1 1 0 0 0 0 1 -1 -1 1 1 -1 -1 1
7 1 -4 4 5 1 -3 4 3 3 0 0 0 0 0 0 10 -10 -6 9 0 1 0 0 6 -5 -3 4 7 -6 -4 6
-1 3 0 4 -2 2 1 2 -3 3 0 0 0 0 0 0 7 4 3 3 -1 0 0 0 4 3 1 2 4 3 2 2
5 -5 2 6 4 -5 0 6 3 -3 0 6 0 0 0 0 -4 1 11 -11 1 -1 -1 2 -2 1 7 -6 -2 0 7 -6
0 -5 -1 8 -1 -4 -1 5 0 -3 -3 6 0 0 0 0 -3 4 10 -3 0 -1 -1 1 -1 2 5 0 -2 2 6 -1
3 -1 -2 3 3 0 -1 3 3 0 -1 3 0 0 0 0 5 -4 1 1 0 0 -1 1 4 -3 0 2 4 -3 -1 3
0 1 1 1 -2 2 2 -1 -2 2 2 -1 0 0 0 0 2 6 2 -3 0 -1 0 1 1 4 2 -2 1 3 2 -1
1 -2 1 1 1 -3 0 3 1 -3 0 3 0 0 0 0 -5 3 8 -7 1 -1 -1 1 -3 1 5 -4 -2 0 4 -3
-1 -1 1 1 -2 -1 0 1 -2 -1 0 1 0 0 0 0 -2 5 4 -1 0 -1 0 0 -2 3 3 -1 -2 2 3 -1
6 2 -2 2 4 2 -2 4 0 5 3 -4 -1 0 0 0 11 -5 -5 8 -1 2 1 0 5 -2 -1 1 7 -5 -4 5
-2 4 0 2 -4 2 2 0 -4 3 -1 -2 0 -1 0 0 2 6 3 2 -3 0 1 -2 2 4 0 1 4 3 1 3
4 -4 2 6 4 -6 -2 8 2 -1 -1 6 0 0 -1 0 0 -3 8 -2 1 -2 -3 4 -1 1 6 -3 -1 0 7 -5
0 -4 -2 8 -2 -4 -2 4 1 -2 -5 6 0 0 0 -1 -3 0 5 3 -1 -1 -2 0 0 1 2 3 -1 1 5 1
-1 -1 0 -2 0 0 0 -2 1 -1 0 0 0 0 0 0 -2 -1 -2 -1 0 0 0 0 -1 -1 -1 0 -2 0 -1 -1
3 -1 -2 2 2 0 -2 2 1 1 0 0 0 0 0 0 4 -4 -3 5 0 0 0 0 2 -2 -1 2 2 -3 -2 3
-1 3 2 -4 0 2 2 -2 -1 1 2 -2 0 0 0 0 1 2 0 -3 0 0 0 0 0 1 0 -2 1 1 -1 -1
2 1 1 0 2 0 0 2 0 1 1 0 0 0 0 0 3 -1 1 0 0 0 0 0 1 0 1 -1 2 -1 0 0
-1 -1 0 -2 0 0 0 -2 1 -1 0 0 0 0 0 0 -3 -1 -2 -1 1 0 0 0 -1 -1 -1 0 -2 0 -1 -1
3 -1 -2 2 2 0 -2 2 1 1 0 0 0 0 0 0 4 -5 -3 5 0 1 0 0 2 -2 -1 2 2 -3 -2 3
-1 3 2 -4 0 2 2 -2 -1 1 2 -2 0 0 0 0 1 2 -1 -3 0 0 1 0 0 1 0 -2 1 1 -1 -1
2 1 1 0 2 0 0 2 0 1 1 0 0 0 0 0 3 -1 1 -1 0 0 0 1 1 0 1 -1 2 -1 0 0
-2 1 1 -4 -2 1 1 -4 -1 -1 0 -2 0 0 0 0 -4 1 -3 0 0 1 1 -2 -3 0 -2 0 -2 0 -2 0
2 -1 -3 2 2 -1 -3 2 3 -1 -2 2 0 0 0 0 2 -7 -3 6 0 1 -1 0 2 -5 -2 4 2 -4 -2 4
0 3 1 -2 0 3 1 -2 -1 3 2 -4 0 0 0 0 4 -1 -5 2 0 1 1 0 2 0 -3 0 2 0 -2 0
3 0 -1 2 3 0 -1 2 2 1 1 0 0 0 0 0 3 -4 -1 0 1 0 -1 2 2 -2 0 -1 2 -2 0 0
0 1 -1 0 1 -1 -2 2 0 2 0 -2 0 0 0 0 2 -4 -3 6 0 0 0 0 1 -1 -1 1 1 -1 -1 1
0 -1 -1 2 1 -1 0 2 0 0 -2 2 0 0 0 0 1 -1 3 0 0 0 0 0 1 0 0 1 1 0 0 1
2 -1 -1 2 1 -1 0 0 2 0 0 2 0 0 0 0 -1 -2 0 -2 0 0 0 0 0 0 1 -1 0 0 1 -1
1 -2 -1 2 0 -1 1 0 2 -2 -2 4 0 0 0 0 -3 1 4 -5 0 0 0 0 0 0 1 0 0 0 1 0
32 32
2 1 -1 1 2 0 -2 2 1 1 0 -1 -1 2 2 -2 4 -3 -3 3 0 3 1 -2 2 -3 -2 2 2 -3 -2 3
-1 1 0 1 0 0 0 2 0 1 -1 1 -2 1 0 -2 3 1 0 3 -2 1 -1 0 3 0 0 2 2 0 1 1
2 -2 0 3 2 -2 0 2 1 0 1 1 0 0 -1 2 0 0 4 -3 2 -1 -1 4 -1 1 3 -4 -1 0 2 -3
0 -2 -1 3 0 -2 0 2 1 -1 -1 3 0 0 -2 1 0 0 3 1 1 -2 -3 4 0 1 3 -1 -1 1 3 -2
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-
PROPERTIES
Modular=1
UnimodularHermitian=1
-
REFERENCES
Bachoc, Nebe: Classification of two genera of 32-dimensional lattices
over the Hurwitz order
-
NOTES
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe