The Lattice L_24.2
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 13:17:58 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
GRAM
DIVISORS
MINIMAL_NORM
KISSING_NUMBER
HERMITE_NUMBER
GROUP_ORDER
GROUP_NAME
GROUP_GENERATORS
PROPERTIES
REFERENCES
NOTES
LAST_LINE
-
NAME
L_24.2
-
DIMENSION
24
-
GRAM
24 0
6
2 6
2 3 6
0 2 0 6
2 3 3 0 6
3 2 3 -1 2 6
0 0 0 0 0 0 6
0 -1 1 0 -1 1 2 6
2 3 3 0 3 3 -2 -1 6
0 -1 1 1 -1 1 -1 3 0 6
2 3 3 0 3 2 1 -1 3 -2 6
2 1 -1 1 1 0 -1 -2 0 -2 1 6
3 2 2 0 3 3 0 0 3 -1 2 0 6
3 1 1 1 1 3 0 1 2 1 1 -1 3 6
0 1 0 0 1 -1 2 -2 1 -3 2 0 2 -1 6
3 2 3 1 2 3 0 0 2 0 2 -1 3 3 0 6
1 -1 -2 -1 -1 1 1 0 -1 0 -1 0 0 1 0 -1 6
1 -1 -1 -2 -1 1 -2 -2 0 -2 -1 1 0 1 -1 2 0 6
1 -1 0 0 -1 0 -1 1 0 1 -1 1 1 1 0 0 -3 1 6
1 1 0 -2 0 2 -2 -2 2 -1 1 2 0 0 -1 -1 0 2 1 6
1 0 0 -1 0 0 0 -2 0 -3 1 1 1 -1 1 1 0 3 0 1 6
-2 0 1 0 0 -1 -2 2 0 1 -1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 6
0 2 2 -1 1 2 -2 -1 3 -1 1 -2 2 0 1 2 -1 1 -1 2 1 0 6
1 2 3 0 2 2 -1 -1 3 -1 2 -1 1 2 0 3 -3 2 1 2 0 0 3 6
-
DIVISORS
3^12
-
MINIMAL_NORM
6
-
KISSING_NUMBER
26208
-
HERMITE_NUMBER
3.46410
-
GROUP_ORDER
2^5 * 3^2 * 7 * 13
-
GROUP_NAME
SL_2(13) o SL_2(3)
-
GROUP_GENERATORS
3
24 24
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 0 3 5 3 1 -6 6 -1 -4 0 -7 0 -2 4 -3 -3 7 -3 4 -3 -5 -5 -4
1 0 3 4 3 2 -10 9 -2 -5 -3 -7 -2 0 8 0 -5 4 -6 7 -1 -6 -8 -4
-1 0 -2 -3 -2 0 3 -4 1 2 -1 4 0 2 -2 2 0 -5 1 -2 2 3 2 2
1 1 6 7 5 3 -16 15 -4 -7 -3 -12 -1 -2 12 -3 -7 10 -9 10 -3 -11 -13 -6
1 0 4 6 4 2 -9 9 -2 -5 -1 -9 -1 -2 7 -2 -4 8 -5 7 -3 -7 -8 -5
1 0 2 3 2 2 -7 6 -2 -3 -1 -5 0 -1 5 -1 -3 3 -4 4 -1 -4 -6 -2
2 -1 2 4 2 1 -2 2 0 -2 1 -5 0 -2 1 -3 -1 5 -1 2 -2 -2 -2 -3
1 0 2 3 2 1 -5 5 -1 -3 -1 -5 -1 -1 4 -1 -3 4 -3 4 -2 -4 -4 -3
0 0 0 -1 0 1 -2 1 0 -1 -2 0 -2 2 2 2 -2 -2 -2 2 1 0 -2 -1
1 0 2 3 2 0 -3 3 -1 -2 0 -4 0 -1 2 -2 -1 4 -1 2 -2 -3 -2 -2
-1 1 -1 -1 0 0 0 0 0 1 0 1 0 0 0 0 1 -1 1 -1 1 0 0 2
1 0 6 7 5 3 -15 14 -4 -7 -3 -12 -1 -2 12 -2 -7 9 -9 11 -3 -10 -13 -6
0 0 3 3 2 2 -8 7 -2 -4 -2 -6 -1 0 6 0 -4 3 -5 6 -1 -5 -7 -3
1 -1 1 2 1 -1 2 -1 0 0 2 -1 1 -2 -2 -2 1 3 2 -1 -2 0 2 -1
0 0 1 1 0 1 -4 3 -1 -2 -2 -2 0 0 3 1 -2 0 -3 3 0 -2 -4 0
0 0 1 2 1 -1 2 -1 0 1 3 -1 1 -2 -2 -2 2 4 2 -1 -2 0 2 -1
-1 0 -2 -2 -2 -1 5 -4 1 2 1 4 1 0 -4 1 3 -3 3 -3 1 3 4 3
0 0 0 -1 0 2 -4 3 -1 -2 -3 -1 -2 2 4 2 -3 -3 -3 3 2 -1 -4 0
-1 1 -2 -3 -1 0 1 -1 0 1 -1 3 -1 2 0 2 0 -4 0 -1 2 1 1 2
-1 0 -2 -3 -2 0 3 -3 0 2 -1 5 0 2 -1 2 1 -5 1 -2 2 3 3 3
2 -1 3 6 3 -1 1 1 1 -2 3 -6 1 -4 -2 -5 1 9 2 1 -4 -2 1 -5
0 -1 -2 -2 -2 -2 8 -7 2 3 2 5 1 0 -6 0 3 -2 4 -5 0 4 7 2
0 0 -1 -1 -1 0 0 0 0 0 -1 1 0 1 0 1 -1 -2 -1 0 1 0 0 1
24 24
-2 -1 -9 -12 -8 -3 21 -21 5 10 2 19 1 5 -16 5 8 -17 11 -15 6 15 18 10
0 -1 -3 -3 -2 -1 9 -9 2 3 2 6 0 1 -7 1 4 -5 6 -6 1 6 8 3
0 -1 -4 -4 -3 -2 12 -11 3 5 3 8 1 1 -9 0 5 -5 7 -8 1 7 10 4
0 -1 -4 -4 -3 -2 12 -11 3 5 3 8 1 0 -9 1 5 -5 7 -8 1 8 10 4
0 -1 -2 -2 -2 -1 7 -7 2 2 2 4 1 0 -6 0 3 -3 5 -5 0 4 6 2
-2 0 -6 -8 -5 -1 10 -11 2 6 0 12 0 4 -7 4 4 -12 5 -8 5 8 9 7
0 0 1 1 0 0 1 -1 0 1 1 0 1 -1 -1 -2 1 2 1 -1 -1 0 1 0
-2 1 -3 -6 -3 0 1 -2 0 3 -3 7 -1 4 1 5 0 -9 -1 -1 4 3 1 4
0 -1 -3 -3 -2 -1 8 -8 2 3 2 5 0 1 -6 1 3 -4 5 -5 1 5 7 2
-1 1 -4 -5 -3 0 4 -4 1 3 -1 6 0 2 -2 3 1 -7 1 -3 3 4 3 4
0 -1 0 0 0 0 2 -2 0 1 1 1 0 1 -1 -1 0 0 1 -1 0 1 2 0
-1 -1 -4 -5 -3 -1 8 -8 2 4 0 8 0 2 -6 3 3 -8 4 -6 3 6 7 5
-1 -1 -4 -5 -4 -2 12 -12 3 5 2 9 1 2 -9 2 5 -7 7 -8 2 8 10 4
-2 0 -5 -8 -5 -1 9 -10 2 5 -1 11 0 4 -6 5 3 -12 4 -6 5 8 7 6
1 -1 2 3 1 -1 3 -2 1 0 3 -2 1 -2 -3 -4 2 6 3 -2 -3 0 3 -2
0 -1 -4 -5 -4 -2 12 -12 3 5 2 9 1 2 -9 1 4 -7 6 -8 2 8 10 4
-2 1 -2 -4 -3 0 1 -2 0 2 -1 5 0 2 -1 3 1 -6 0 -2 3 2 1 4
0 0 -1 -2 -1 0 0 -1 0 0 -2 2 -1 2 0 2 -1 -4 -1 0 2 1 0 1
0 -1 -2 -2 -1 -1 6 -5 2 2 0 4 0 1 -4 1 2 -3 3 -3 1 4 5 1
0 0 1 2 2 1 -4 4 -1 -2 -1 -3 -1 0 3 0 -2 2 -2 3 0 -3 -3 -2
1 -1 0 1 0 0 2 -2 0 0 1 0 0 0 -2 -1 0 1 1 -1 -1 1 2 -1
-1 1 0 -2 0 1 -6 5 -1 -2 -4 0 -3 3 6 4 -3 -4 -4 4 2 -2 -5 0
1 0 2 3 2 0 -3 3 -1 -2 1 -4 0 -1 2 -2 -1 5 -1 2 -2 -3 -2 -3
1 -1 -1 0 0 -2 7 -6 2 2 3 2 1 -1 -6 -2 3 1 5 -4 -1 3 6 0
24 24
0 0 0 1 0 -1 2 -1 0 1 2 0 1 -1 -2 -2 1 2 1 -1 -1 0 2 0
-1 -1 -6 -7 -5 -2 13 -13 3 6 2 11 1 2 -10 3 5 -10 7 -9 3 9 11 6
0 0 -1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 -2 -3 -2 0 4 -4 1 1 0 3 0 1 -3 1 1 -4 2 -3 1 3 3 2
-1 0 -3 -4 -3 -1 5 -5 1 3 0 6 0 2 -3 3 2 -6 2 -3 2 4 4 3
0 0 -1 -1 -1 -1 2 -2 1 1 1 2 0 0 -2 0 1 -1 1 -2 0 1 2 1
-1 1 0 -1 0 1 -5 4 -1 -1 -2 -1 -1 1 4 2 -2 -1 -3 3 1 -2 -4 0
0 1 3 2 2 3 -12 10 -3 -5 -4 -6 -2 1 10 1 -6 2 -8 8 0 -6 -10 -3
0 0 -1 -1 -1 -1 2 -2 0 1 1 2 1 0 -2 0 1 -1 1 -2 0 1 2 1
1 0 3 4 2 1 -6 6 -1 -4 0 -6 0 -2 4 -2 -2 5 -3 4 -2 -4 -5 -3
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 -1 -1 -1 0 1 -1 0 1 -1 1 0 1 0 1 -1 -2 -1 0 1 1 0 1
0 0 -1 -1 -1 0 2 -2 0 1 1 2 0 0 -2 0 1 -1 1 -2 0 1 2 1
1 0 0 1 0 -1 4 -3 1 1 3 0 1 -2 -4 -3 2 3 3 -3 -2 1 4 -1
-1 1 -1 -2 -1 1 -3 2 -1 0 -2 1 0 1 2 2 -1 -3 -2 1 2 -1 -3 2
0 0 -3 -3 -2 -1 6 -6 1 3 2 5 0 1 -5 0 3 -4 4 -5 1 4 6 3
0 0 1 1 0 -1 2 -1 1 0 1 0 0 -1 -2 -1 1 2 2 -1 -1 0 2 -1
0 0 -2 -2 -1 -1 5 -5 1 3 1 4 0 1 -4 0 2 -3 3 -4 1 3 5 2
1 0 1 2 1 1 -3 3 -1 -1 0 -3 1 -1 2 -2 -2 3 -3 2 -1 -2 -3 -1
0 -1 -1 0 -1 -2 7 -6 2 3 3 3 2 -1 -6 -2 3 1 4 -5 -1 3 6 1
0 0 1 2 2 1 -4 4 -1 -2 -1 -3 -1 0 3 0 -2 2 -2 3 -1 -3 -3 -2
0 0 -1 -2 -1 1 0 -1 0 0 -2 2 -1 2 1 2 -1 -4 -1 0 2 1 0 1
-1 0 -1 -2 -1 0 1 -2 0 1 0 3 0 1 -1 1 1 -3 1 -2 1 1 1 2
-1 0 -4 -5 -3 -2 9 -9 2 5 2 8 1 2 -7 1 4 -6 5 -7 2 6 8 4
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PROPERTIES
Modular=1
-
REFERENCES
G. Nebe, Endliche rationale Matrixgruppen vom Grad 24.
Dissertation RWTH Aachen (1995).
G. Nebe, Some cyclo-quaternionic lattices, J. Alg. 199 (1998), 472-498.
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NOTES
CycloQuaternionic lattice of type Delta2
Extremal 3-modular lattice.
Official name is ^((5+sqrt(13))/2)L_24,2
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe