The Lattice dim12modular5Group57600
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 Thu Oct 27 15:22:45 CEST 2016
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME"> NAME
DIM"> DIM
GRAM"> GRAM
DET"> DET
GROUP_ORDER"> GROUP_ORDER
GROUP_GENERATORS"> GROUP_GENERATORS
PROPERTIES"> PROPERTIES
MINIMAL_NORM"> MINIMAL_NORM
KISSING_NUMBER"> KISSING_NUMBER
NOTES"> NOTES
REFERENCES"> REFERENCES
LAST_LINE"> LAST_LINE
-
NAME
dim12modular5Group57600
-
DIM
12
-
GRAM
12 12
5 1 -1 2 2 1 2 1 2 -2 -2 2
1 4 -2 2 1 1 0 1 2 1 0 0
-1 -2 5 -3 -2 1 -1 1 -3 0 1 -1
2 2 -3 5 2 -1 2 -1 2 0 0 1
2 1 -2 2 4 -1 0 1 2 -1 0 1
1 1 1 -1 -1 4 0 2 -1 -1 0 -1
2 0 -1 2 0 0 4 0 0 0 -1 0
1 1 1 -1 1 2 0 4 -1 0 0 -1
2 2 -3 2 2 -1 0 -1 5 0 -2 1
-2 1 0 0 -1 -1 0 0 0 4 0 -2
-2 0 1 0 0 0 -1 0 -2 0 4 0
2 0 -1 1 1 -1 0 -1 1 -2 0 4
-
DET
5^6
-
GROUP_ORDER
2^8 * 3^2 * 5^2
-
GROUP_GENERATORS
[-1 0 0 0 0 1 0 0 0 0 0 1]
[ 0 0 0 0 -1 -1 0 1 0 -1 0 0]
[ 0 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 -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 -1 0 0 0 0 0]
[ 0 1 0 0 -1 -1 0 0 0 -1 0 0]
[ 0 0 0 0 0 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 -1 0 0 0 -1 0 -1]
[ 0 0 0 0 0 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 1 0 0 0 0 0 0]
[-1 0 0 0 0 0 0 0 0 0 -1 1]
[ 0 -1 -1 1 -1 0 -1 1 0 0 0 0]
[ 0 0 1 0 0 0 0 0 0 0 0 0]
[ 0 -1 -1 0 0 0 0 0 0 0 0 0]
[ 0 0 -1 -1 0 0 0 0 0 0 0 0]
[-2 0 1 1 1 1 0 0 0 0 -1 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 0 -1 0 -1 0 0 0 0 0 0 0]
[ 2 0 -1 0 -1 -1 -1 0 -1 0 1 -1]
[ 0 -1 0 0 1 1 0 0 0 1 0 0]
[ 0 0 0 0 0 0 0 0 0 0 -1 0]
[ 0 -1 0 1 0 1 -1 0 0 1 0 0]
[ 2 0 0 0 -1 -1 -1 0 0 0 1 -1]
[-1 0 0 0 0 1 1 0 0 0 0 1]
[ 1 0 0 0 0 0 -1 0 0 0 0 -1]
[ 0 -1 0 1 -1 0 -1 1 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 -1 0 1 -1 0 0 1 1 0 1 0]
[ 1 0 0 0 -1 -1 -1 0 0 0 0 -1]
[ 2 0 -1 -1 -1 -1 0 0 0 0 1 -1]
[ 0 0 0 0 0 0 0 0 0 -1 0 0]
[ 0 0 0 1 0 0 -1 0 -1 0 -1 0]
-
PROPERTIES
INTEGRAL=1
MODULAR=5
-
MINIMAL_NORM
4
-
KISSING_NUMBER
60
-
NOTES
Odd extremal 5-modular lattice
-
REFERENCES
Xiaolu Hou, Frédérique Oggier, "Modular lattices from a variation of Construction A over number fields", arXiv:1604.01583.
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe