The Lattice overlattice(A2xA11)
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 13:08:41 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DET
TYPE
GRAM
EIGENVALUES
DIVISORS
MINIMAL_NORM
MINVECS
KISSING_NUMBER
HERMITE_NUMBER
GROUP_ORDER
GROUP_NAME
GROUP_GENERATORS
PROPERTIES
REFERENCES
NOTES
LAST_LINE
-
NAME
overlattice(A2xA11)
-
DIMENSION
22
-
DET
3^11
-
TYPE
-
GRAM
22 0
4
-2 4
-2 2 4
-2 2 2 4
-2 2 2 2 4
-2 1 1 1 1 4
1 1 0 0 0 1 4
-2 0 0 0 0 1 -1 4
-1 -1 1 -1 -1 -1 -1 2 6
-2 2 2 2 2 1 0 0 -1 4
1 1 1 -1 -1 1 1 0 -1 -1 6
-2 0 2 0 2 1 -1 2 1 2 -1 6
-2 2 0 2 0 1 0 2 -1 2 -1 0 6
-2 2 0 0 2 1 0 2 -1 2 -1 2 2 6
1 -1 -2 0 -2 1 0 -1 -2 0 -1 -2 1 -1 6
1 1 1 -1 0 1 1 0 0 -1 4 0 -1 0 -2 6
1 1 1 0 -1 1 1 -2 -2 1 2 -1 0 -1 2 1 6
-1 -1 0 1 -1 -1 -1 2 3 -1 -1 0 1 -1 -1 -1 -3 6
-1 -1 1 -1 1 2 -1 0 0 1 0 2 -1 0 0 0 1 -2 6
-1 -1 1 -1 -1 -1 -1 2 4 -1 0 2 0 -1 -2 0 -2 3 0 6
-1 -1 1 -1 1 2 -1 0 0 0 0 2 -2 0 0 0 1 -2 4 0 6
1 -2 -2 0 0 -2 -2 0 -1 0 -3 0 0 0 1 -3 -1 0 0 -1 0 6
-
EIGENVALUES
-
DIVISORS
3^11
-
MINIMAL_NORM
4
-
MINVECS
-
KISSING_NUMBER
2*198
-
HERMITE_NUMBER
-
GROUP_ORDER
2^12 * 3^6 * 5^2 * 7 * 11
-
GROUP_NAME
A11 otimes A2
-
GROUP_GENERATORS
5
22 22
8 6 5 -6 -2 7 -4 6 -5 3 -6 -3 -3 -3 -3 -2 -1 1 -1 1 -1 -1
-6 -5 -5 6 2 -5 3 -6 5 -3 6 3 3 3 2 1 1 -1 1 -1 1 1
-7 -6 -7 8 3 -7 4 -8 7 -4 8 4 4 4 3 1 1 -1 1 -1 2 1
-8 -7 -7 8 3 -7 4 -8 7 -4 8 4 4 4 3 1 1 -2 1 -1 1 1
-7 -6 -5 6 2 -6 4 -6 5 -3 6 3 3 3 2 1 1 -1 1 -1 1 1
-8 -6 -7 7 3 -7 4 -7 6 -3 7 4 3 3 3 2 1 -1 1 -1 1 1
0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 1 -1 -1 0 0 2 -2 1 -2 -1 -1 -1 0 1 0 0 0 1 0 0
4 4 6 -6 -2 3 -2 7 -6 3 -6 -4 -3 -3 -1 0 -1 1 -1 1 0 -1
-6 -5 -5 6 2 -6 3 -6 5 -3 6 3 3 3 2 1 1 -1 1 -1 1 1
0 0 -3 3 0 0 0 -3 2 -1 2 2 1 1 0 0 0 0 0 0 1 0
-3 -2 -2 2 1 -3 2 -2 2 -1 2 1 1 1 1 1 1 0 0 0 1 1
-2 -1 -2 3 0 -2 1 -2 2 -1 2 1 1 1 1 1 0 -1 1 0 0 1
-2 -1 -1 1 0 -2 1 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0
1 0 0 -1 1 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0
0 0 -2 2 0 0 0 -1 1 0 1 1 0 0 0 0 0 0 0 0 1 0
-4 -3 -7 6 3 -4 2 -7 6 -3 7 4 3 3 2 0 1 0 1 -1 1 1
4 3 4 -4 -2 3 -2 5 -4 3 -5 -3 -2 -2 -1 0 -1 0 -1 1 0 -1
-5 -3 -4 4 1 -5 3 -5 4 -2 5 3 2 2 2 1 0 0 1 -1 1 1
4 4 5 -5 -2 4 -2 4 -4 2 -5 -3 -2 -2 -1 0 -1 1 -1 1 0 0
-6 -5 -6 6 3 -6 4 -7 6 -3 7 4 3 3 3 1 1 0 1 -1 1 1
2 1 1 -1 -1 2 -1 1 -1 1 -1 -1 -1 0 -1 -1 0 0 0 1 -1 0
22 22
-1 0 -2 1 0 0 0 -1 1 0 1 1 0 0 0 0 0 0 0 0 0 0
1 0 0 0 1 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
1 1 1 0 -1 0 0 1 -1 0 -1 0 -1 0 0 0 0 0 0 0 0 0
1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-6 -5 -5 6 2 -6 3 -6 5 -3 6 3 3 3 2 1 1 -1 1 -1 1 1
-8 -6 -7 7 3 -7 4 -7 6 -3 7 4 3 3 3 2 1 -1 1 -1 1 1
0 -1 1 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0
1 0 2 -2 0 1 0 1 -1 0 -1 -1 0 0 0 0 0 1 0 0 0 0
1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 -2 -2 2 1 -1 0 -2 2 -1 2 1 1 1 0 0 0 -1 0 0 0 0
1 0 0 0 0 0 0 1 0 1 0 -1 0 0 0 0 0 0 0 0 0 0
0 -1 0 1 0 0 0 -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 1 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0
-6 -5 -6 7 2 -5 3 -7 6 -3 7 4 3 3 2 0 1 -1 1 -1 1 1
0 0 -1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0
0 0 -2 2 0 -1 0 -1 1 0 1 1 0 0 0 0 0 0 1 0 0 0
-1 -1 1 0 0 -1 1 0 0 -1 0 0 0 1 1 0 0 0 0 0 0 0
-1 -1 0 0 0 -1 0 -1 0 0 1 0 1 0 0 0 0 0 0 0 0 0
0 -1 2 -2 0 1 0 1 -1 0 -1 -1 0 0 0 0 0 0 0 0 -1 0
-1 -1 -1 0 1 -1 0 -1 1 0 1 0 1 0 0 0 1 0 0 0 0 0
5 5 6 -6 -3 5 -3 6 -5 3 -6 -3 -3 -3 -2 -1 -1 1 -1 0 -1 -1
22 22
0 0 1 -1 0 0 0 2 -1 1 -1 -1 -1 -1 0 0 0 0 0 0 0 0
0 1 0 0 -1 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 -1 0 0 0 0 0 0 0 0 0 0 0 0
0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-1 -1 -1 1 1 -1 0 -2 1 -1 2 1 1 1 1 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 -1 0 0 0 0 0 0
0 0 0 0 0 0 0 -1 0 -1 0 1 1 0 0 0 0 0 0 0 0 0
-1 -1 -1 2 0 -1 1 -2 1 -2 1 1 1 1 0 0 0 0 1 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 2 -2 0 1 -1 1 -1 0 -1 -1 0 -1 0 0 0 0 -1 0 0 0
1 1 2 -1 0 0 0 1 -1 -1 -1 0 0 0 0 0 0 0 0 0 0 0
0 1 -1 1 -1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
0 1 0 0 -1 0 0 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0
-3 -2 -1 0 1 -2 1 0 0 1 1 0 0 0 1 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0 0 -1 0 0 0 0 1 0 0 0 0 0 0 0
1 2 1 -2 0 1 -1 2 -1 1 -1 -1 -1 -1 0 0 0 1 0 0 0 0
-1 -1 -2 2 0 -1 1 -2 1 -1 1 1 1 1 0 0 0 0 0 0 1 0
2 1 1 0 0 1 -1 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0
-1 -1 0 1 0 0 1 -2 1 -2 1 1 1 1 0 0 0 0 0 0 0 1
0 -1 -1 1 2 -1 0 -2 2 -1 2 1 1 1 1 0 0 0 0 0 0 0
3 2 0 -1 0 2 -1 2 -1 2 -2 -1 -1 -1 -1 0 0 0 0 1 0 0
22 22
-1 -1 0 0 1 -1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0
1 2 2 -2 -2 1 0 2 -2 1 -2 -1 -1 -1 -1 0 -1 0 0 0 0 0
0 1 2 -2 -1 1 0 2 -2 0 -2 -1 -1 -1 -1 0 0 0 0 0 -1 0
1 2 1 -2 -1 1 0 2 -2 1 -2 -1 -1 -1 -1 0 0 1 0 0 0 0
0 0 1 -2 0 1 0 1 -1 1 -1 -1 0 -1 -1 0 0 0 -1 0 0 0
1 0 0 0 0 1 0 0 0 0 0 0 0 0 -1 -1 0 0 0 0 0 0
0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 -1 1 0 1 0 -3 2 -1 2 1 1 1 0 -1 0 0 0 0 0 1
3 3 2 -2 -1 3 -2 2 -1 0 -2 -1 -1 -1 -1 -1 0 0 0 0 -1 0
-1 0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 4 -3 -2 2 -1 2 -3 0 -3 -1 -1 -1 -1 0 -1 0 0 0 -1 0
2 1 3 -3 0 3 -1 2 -2 1 -2 -2 -1 -1 -1 -1 0 0 -1 1 -1 0
-3 -1 -4 4 0 -3 2 -4 3 -1 4 2 1 2 1 0 0 0 1 0 1 1
-5 -4 -4 4 2 -4 3 -6 5 -2 6 3 3 2 2 0 0 -1 0 -1 1 1
0 -1 -4 5 1 -2 1 -3 3 -1 3 2 1 2 1 0 0 0 1 0 1 0
1 1 4 -4 -1 2 -1 3 -3 1 -3 -2 -1 -2 -1 0 -1 0 0 0 -1 0
-3 -2 -2 3 0 -3 2 -1 1 -1 1 1 0 1 1 1 0 -1 1 0 0 0
3 3 2 -3 -1 3 -2 2 -2 1 -2 -1 -1 -1 -1 -1 0 1 0 0 -1 0
-2 -3 -2 3 1 -2 1 -2 2 -1 2 1 1 1 0 0 1 -1 0 0 0 0
3 3 2 -2 -1 3 -2 2 -2 0 -2 -1 -1 -1 -1 -1 0 0 0 1 -1 0
-2 -3 -2 3 1 -1 1 -2 2 -1 2 1 1 1 0 0 1 -1 0 0 0 0
-3 -3 -4 4 2 -3 2 -4 4 -1 4 2 2 2 2 1 1 0 0 0 1 1
22 22
1 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 1 1 0 -1 0 0 1 -1 0 -1 0 -1 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 1 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 1 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 1 0 0 -1 0 0 1 0 0 -1 0 -1 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 1 0 0 -1 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 1 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 -1 0 0 1 0 0 -1 1 0 1 0 1 1 0 0 0 0 0 0 0 0
0 -1 0 0 1 0 0 -1 1 0 1 0 1 0 1 0 0 0 0 0 0 0
0 1 0 0 -1 0 0 1 -1 0 -1 0 -1 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 1 0 0 0 0 0
-1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0
-1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0
0 1 0 0 -1 0 0 1 -1 0 -1 0 -1 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 1 0
0 -1 0 0 1 0 0 -1 1 0 1 0 1 0 0 0 0 0 0 0 0 1
-
PROPERTIES
MODULAR = 3
-
REFERENCES
-
NOTES
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe