The Lattice A_11.otimes(3).A_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 13:12:24 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
A_11.otimes(3).A_2
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DIMENSION
20
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GRAM
20 0
4
-2 4
-2 0 4
-2 2 0 4
1 -2 -1 -2 4
1 1 -2 -1 0 4
1 -2 -1 0 0 -1 4
-2 1 1 0 -1 0 -1 4
-2 2 1 2 -2 -1 0 0 4
-1 -1 2 -1 1 -2 0 0 1 4
-2 0 2 1 -1 -2 1 0 2 1 4
1 1 -2 -1 0 2 -1 0 0 -1 -1 4
-2 1 2 1 -2 0 -1 1 1 0 1 -1 4
-2 2 2 1 -1 -1 -1 0 2 1 1 -1 1 4
-2 2 1 0 0 0 -2 2 0 0 0 0 1 2 4
-2 2 1 2 -2 -1 -1 2 1 0 0 0 1 1 1 4
1 -2 1 -1 0 0 0 -1 -1 0 1 0 1 -1 -1 -1 4
-2 1 1 0 -1 1 0 2 0 0 1 0 1 0 1 1 0 4
-1 -1 1 1 -1 -2 1 1 0 0 2 -1 1 0 0 1 1 0 4
1 -2 -1 0 0 0 2 0 -1 0 0 -1 0 -2 -2 -1 1 0 1 4
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DIVISORS
11^2
-
MINIMAL_NORM
4
-
KISSING_NUMBER
12540
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HERMITE_NUMBER
3.14717
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GROUP_ORDER
2^5 * 3^2 * 5 * 11
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GROUP_NAME
(L_2(11) otimes D_12) .2
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GROUP_GENERATORS
3
20 20
-1 0 -3 -1 -1 -1 -1 1 -1 0 1 -1 0 1 -1 0 1 0 -1 -1
1 -1 2 1 1 1 1 -1 1 0 0 1 0 -1 2 1 -1 0 0 1
2 -1 0 1 1 0 -1 0 1 0 0 0 1 0 0 0 -1 1 1 0
-1 1 2 0 0 0 1 -1 1 0 -2 1 -1 -1 1 -1 0 0 1 1
0 2 0 0 0 1 1 1 -1 1 0 -1 0 0 -1 0 1 -1 0 -1
0 -1 1 1 0 1 1 0 -1 0 1 1 0 0 1 1 0 -1 -1 0
-1 2 -1 -1 0 -1 0 1 -1 0 0 0 0 1 -2 -1 1 0 0 0
-2 -3 -1 -1 -2 -1 -1 -1 0 -1 0 0 0 0 0 0 -1 0 -1 0
2 1 3 1 2 1 1 0 1 0 0 1 0 -1 1 0 -1 0 1 1
1 1 1 0 1 1 0 0 1 0 0 -1 0 -1 0 0 0 0 1 0
3 1 2 1 2 0 0 0 1 0 0 1 1 0 0 0 -1 1 1 1
1 -1 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 -1 0
1 -1 2 1 1 0 0 -1 1 -1 -1 1 0 0 1 0 -1 1 1 1
1 0 1 0 1 1 0 -1 1 0 0 0 0 -1 1 1 -1 0 1 1
-1 -1 1 -1 0 0 0 -2 1 -1 -1 0 0 -1 1 1 -1 0 0 1
0 -3 -1 0 -1 0 -1 -1 1 0 0 0 0 0 1 0 -1 1 0 0
0 0 0 -1 0 -1 -1 -1 1 -1 -1 0 0 0 0 0 0 1 1 0
1 0 1 1 1 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0
0 -2 -1 -1 -1 -1 -2 -1 1 -1 0 0 0 1 0 0 -1 1 0 1
-2 1 0 -1 -1 -1 0 0 0 -1 -1 0 -1 0 -1 -1 1 0 0 0
20 20
1 -1 1 1 1 1 0 0 0 0 1 1 0 0 1 1 -1 0 0 1
-1 1 -2 -1 -1 -2 0 0 0 0 -1 -1 0 0 -1 -1 1 1 0 -1
-1 -1 -1 -1 -1 -1 -1 0 0 -1 0 0 0 1 -1 0 0 0 -1 0
0 0 1 0 0 0 1 -1 1 0 -1 0 0 -1 1 0 0 0 0 0
-3 0 -1 -2 -2 0 -1 -1 -1 0 0 -1 -1 -1 0 0 0 -1 0 0
0 1 0 0 0 -1 0 0 0 0 -1 0 0 0 0 -1 0 1 1 0
4 -2 1 3 2 2 0 1 0 1 2 1 1 1 1 1 -1 0 0 0
1 2 0 1 1 0 1 2 -1 1 0 0 1 1 -2 -1 1 0 0 -1
-2 0 -1 -2 -1 -1 0 -1 1 -1 -1 -1 -1 0 0 0 1 0 0 0
-4 0 -2 -3 -2 -1 -1 -1 0 -1 -1 -1 -1 0 -1 0 1 -1 0 0
1 0 1 0 1 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0
-1 2 1 0 0 0 1 0 0 0 -1 0 -1 -1 0 -1 1 0 1 0
3 0 0 1 1 0 0 1 1 0 0 0 1 1 0 0 0 1 0 0
-1 -1 -3 -1 -2 -1 -1 0 -1 0 1 -1 0 1 -1 0 0 0 -1 -1
0 1 -3 0 -1 -1 0 2 -2 1 1 -1 1 1 -2 -1 1 0 -1 -2
0 1 0 1 0 0 1 1 0 1 -1 0 0 0 -1 -1 1 0 0 -1
1 -1 2 1 1 1 0 0 1 -1 0 1 0 0 1 0 -1 0 0 1
1 -1 -1 1 0 -1 -1 1 0 0 0 0 1 1 -1 -1 0 1 0 -1
4 2 3 3 3 2 2 2 0 1 1 1 1 0 0 0 0 -1 0 0
3 0 3 2 3 2 1 0 1 0 0 1 1 0 1 1 -1 0 1 1
20 20
-1 1 0 0 0 0 1 1 0 0 -1 0 0 0 -1 -1 1 -1 0 -1
0 -1 1 0 0 -1 -1 -1 0 -1 0 1 0 0 0 0 -1 1 0 1
-1 1 1 -1 0 0 0 -1 1 0 -1 0 -1 -1 1 0 0 0 1 1
0 -2 -1 -1 -1 -1 -2 -1 0 -1 1 0 0 1 0 1 -1 1 -1 1
0 1 0 1 0 1 2 1 -1 1 0 0 0 0 0 0 1 -1 0 -1
3 0 2 2 2 1 1 1 0 0 1 1 1 0 0 0 -1 0 0 0
-1 1 -3 -2 -1 -1 -1 0 0 0 0 -2 0 0 -1 0 1 0 0 -1
2 -2 0 2 0 1 -1 0 0 1 1 0 0 0 1 0 -1 1 0 0
0 0 0 -1 1 -1 -1 -1 1 -1 0 0 0 0 0 1 0 1 0 1
0 2 0 0 1 0 1 0 0 1 -1 0 0 0 0 0 1 0 1 0
0 0 -1 -1 0 0 -1 0 0 0 1 -1 0 0 0 1 0 0 0 0
2 0 2 2 2 1 1 1 0 0 0 1 1 0 0 0 0 0 0 0
0 -1 0 -1 0 -1 -1 -1 1 -1 0 0 0 0 1 0 -1 1 0 1
-4 0 -1 -3 -2 -2 -1 -2 0 -1 -1 0 -1 -1 0 0 0 0 0 1
-3 0 0 -1 -2 -1 0 -1 -1 0 -1 0 -1 -1 0 -1 0 0 0 0
1 -1 1 1 0 0 -1 -1 0 0 0 1 0 0 1 0 -1 1 0 1
0 1 1 0 1 1 1 1 0 0 0 0 0 0 0 0 0 -1 0 0
4 1 1 2 2 1 0 1 0 1 1 0 1 0 0 0 -1 1 1 0
-1 -3 -2 -1 -2 0 -2 -1 0 0 1 -1 0 0 1 1 -1 0 -1 0
2 -1 -3 1 0 0 -1 2 -1 1 2 -1 1 2 -1 0 0 0 -1 -1
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PROPERTIES
-
REFERENCES
T. Shioda, Mordell-Weil lattices and sphere packings,
Amer. J. Math. 113 (1991), 931-948.
W. Plesken, G. Nebe, Finite rational matrix groups.
AMS-Memoir No. 556, vol. 116 (1995), p. 50.
G. Nebe, Some cyclo-quaternionic lattices, J. Alg. 199 (1998), 472-498.
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NOTES
CycloQuaternionic lattice of type Delta6
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe