The Lattice 6QF.6.c
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 13:08:51 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
MINIMAL_NORM
DET
KISSING_NUMBER
GRAM
GROUP_ORDER
PROPERTIES
NOTES
REFERENCES
MAGMA
LAST_LINE
-
NAME
6QF.6.c
-
DIMENSION
6
-
MINIMAL_NORM
4
-
DET
1331
-
KISSING_NUMBER
6
-
GRAM
6 6
4 0 0 -2 -1 2
0 4 0 -1 2 2
0 0 4 -2 2 -1
-2 -1 -2 5 -1 -1
-1 2 2 -1 5 0
2 2 -1 -1 0 5
-
GROUP_ORDER
48
-
PROPERTIES
INTEGRAL=1
MODULAR=11
-
NOTES
In good genus.
There is just one other extremal lattice in this genus, namely
[ 4 0 0 2 -2 1]
[ 0 4 0 1 -2 -2]
[ 0 0 4 2 -1 2]
[ 2 1 2 5 -2 1]
[ -2 -2 -1 -2 5 0]
[ 1 -2 2 1 0 5]
-
REFERENCES
E. M. Rains and N. J. A. Sloane,
The Shadow Theory of Modular and Unimodular Lattices,
J. Number Theory, 73 (1998), pp. 359-389;
http://neilsloane.com/doc/shad.pdf or shad.ps
-
MAGMA
L6 := LatticeWithGram(6, [
4, 0, 0, -2, -1, 2,
0, 4, 0, -1, 2, 2,
0, 0, 4, -2, 2, -1,
-2, -1, -2, 5, -1, -1,
-1, 2, 2, -1, 5, 0,
2, 2, -1, -1, 0, 5]);
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe