The Lattice N(2A12)
An entry from the Catalogue of Lattices, which is a joint project of
Gabriele Nebe, RWTH Aachen University
(nebe@math.rwthaachen.de)
and
Neil J. A. Sloane
(njasloane@gmail.com)
Last modified Fri Jul 18 13:20:38 CEST 2014
INDEX FILE 
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DETERMINANT
MINIMAL_NORM
KISSING_NUMBER
DENSITY
HERMITE_NUMBER
GROUP_ORDER
GRAM
BASIS
ROOT_SYSTEM
NOTES
LAST_LINE

NAME
N(2A12)

DIMENSION
24

DETERMINANT
1

MINIMAL_NORM
2

KISSING_NUMBER
312

DENSITY
.596E07

HERMITE_NUMBER
2

GROUP_ORDER
2^22 * 3^10 * 5^4 * 7^2 * 11^2 * 13^2

GRAM
24 0
2
1 2
1 1 2
1 1 1 2
1 1 1 1 2
0 0 1 0 0 2
0 0 1 0 0 1 2
0 0 1 0 0 1 1 2
0 0 0 0 0 0 0 0 2
0 0 0 0 0 0 0 0 1 2
0 0 0 0 0 0 0 0 1 0 2
0 0 0 0 0 0 0 0 1 0 1 2
0 0 0 0 0 0 0 0 1 0 1 1 2
0 0 0 0 0 0 0 0 1 0 1 1 1 2
0 0 0 0 0 0 0 0 1 0 1 1 1 1 2
0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 2
0 0 1 0 0 1 1 1 0 1 1 1 1 1 0 1 4
1 0 0 0 1 1 1 0 1 0 1 1 1 1 1 1 0 4
1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 2 4
1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 1 2 3 4
1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 3 0 0 0 4
1 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 2 0 0 0 3 4
1 1 1 1 1 0 0 0 1 1 1 0 1 1 0 1 1 1 1 1 0 1 4
1 1 1 1 1 0 0 0 0 1 1 0 1 1 0 1 2 1 2 2 1 0 2 4

BASIS
24 26
.000000000000E+00 .100000000000E+01 .000000000000E+00
.100000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .100000000000E+01
.100000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.100000000000E+01 .100000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.100000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .100000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.100000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .100000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .100000000000E+01 .100000000000E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .100000000000E+01 .000000000000E+00
.100000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .100000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .100000000000E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .100000000000E+01 .100000000000E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .100000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .100000000000E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .100000000000E+01
.100000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .100000000000E+01
.000000000000E+00 .100000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .100000000000E+01
.000000000000E+00 .000000000000E+00 .100000000000E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .100000000000E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.100000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .100000000000E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .100000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .100000000000E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.100000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00
.846153846154E+00 .153846153846E+00 .153846153846E+00
.153846153846E+00 .846153846154E+00 .153846153846E+00
.153846153846E+00 .153846153846E+00 .153846153846E+00
.153846153846E+00 .153846153846E+00 .153846153846E+00
.153846153846E+00 .769230769231E+00 .769230769231E+00
.230769230769E+00 .230769230769E+00 .230769230769E+00
.230769230769E+00 .769230769231E+00 .230769230769E+00
.230769230769E+00 .230769230769E+00 .230769230769E+00
.230769230769E+00 .230769230769E+00
.384615384615E+00 .615384615385E+00 .384615384615E+00
.384615384615E+00 .384615384615E+00 .615384615385E+00
.615384615385E+00 .384615384615E+00 .384615384615E+00
.384615384615E+00 .615384615385E+00 .384615384615E+00
.615384615385E+00 .769230769231E01 .923076923077E+00
.769230769231E01 .769230769231E01 .769230769231E01
.769230769231E01 .769230769231E01 .769230769231E01
.769230769231E01 .769230769231E01 .769230769231E01
.769230769231E01 .769230769231E01
.230769230769E+00 .230769230769E+00 .230769230769E+00
.769230769231E+00 .769230769231E+00 .230769230769E+00
.230769230769E+00 .230769230769E+00 .230769230769E+00
.769230769231E+00 .230769230769E+00 .230769230769E+00
.230769230769E+00 .846153846154E+00 .846153846154E+00
.153846153846E+00 .153846153846E+00 .153846153846E+00
.153846153846E+00 .153846153846E+00 .153846153846E+00
.153846153846E+00 .153846153846E+00 .153846153846E+00
.153846153846E+00 .153846153846E+00
.230769230769E+00 .230769230769E+00 .230769230769E+00
.769230769231E+00 .769230769231E+00 .230769230769E+00
.230769230769E+00 .769230769231E+00 .230769230769E+00
.230769230769E+00 .230769230769E+00 .230769230769E+00
.230769230769E+00 .846153846154E+00 .846153846154E+00
.153846153846E+00 .153846153846E+00 .153846153846E+00
.153846153846E+00 .153846153846E+00 .153846153846E+00
.153846153846E+00 .153846153846E+00 .153846153846E+00
.153846153846E+00 .153846153846E+00
.153846153846E+00 .153846153846E+00 .153846153846E+00
.846153846154E+00 .846153846154E+00 .153846153846E+00
.153846153846E+00 .153846153846E+00 .153846153846E+00
.153846153846E+00 .153846153846E+00 .153846153846E+00
.153846153846E+00 .769230769231E+00 .769230769231E+00
.230769230769E+00 .230769230769E+00 .230769230769E+00
.230769230769E+00 .769230769231E+00 .230769230769E+00
.230769230769E+00 .230769230769E+00 .230769230769E+00
.230769230769E+00 .230769230769E+00
.153846153846E+00 .153846153846E+00 .153846153846E+00
.846153846154E+00 .846153846154E+00 .153846153846E+00
.153846153846E+00 .153846153846E+00 .153846153846E+00
.153846153846E+00 .153846153846E+00 .153846153846E+00
.153846153846E+00 .769230769231E+00 .769230769231E+00
.230769230769E+00 .230769230769E+00 .230769230769E+00
.230769230769E+00 .230769230769E+00 .230769230769E+00
.230769230769E+00 .769230769231E+00 .230769230769E+00
.230769230769E+00 .230769230769E+00
.769230769231E01 .769230769231E01 .769230769231E01
.923076923077E+00 .769230769231E01 .769230769231E01
.769230769231E01 .769230769231E01 .769230769231E01
.769230769231E01 .769230769231E01 .769230769231E01
.769230769231E01 .384615384615E+00 .615384615385E+00
.384615384615E+00 .615384615385E+00 .384615384615E+00
.384615384615E+00 .615384615385E+00 .615384615385E+00
.384615384615E+00 .384615384615E+00 .615384615385E+00
.384615384615E+00 .384615384615E+00
.769230769231E01 .769230769231E01 .769230769231E01
.923076923077E+00 .769230769231E01 .769230769231E01
.769230769231E01 .769230769231E01 .769230769231E01
.769230769231E01 .769230769231E01 .769230769231E01
.769230769231E01 .615384615385E+00 .615384615385E+00
.384615384615E+00 .615384615385E+00 .384615384615E+00
.384615384615E+00 .615384615385E+00 .384615384615E+00
.384615384615E+00 .384615384615E+00 .384615384615E+00
.615384615385E+00 .384615384615E+00

ROOT_SYSTEM
2A12

NOTES
One of the 24 even unimodular lattices in dimension 24 (the Niemeier lattices)

LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe