The Lattice LAMBDA(U)
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 13:17:52 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
GRAM
DET
MINIMAL_NORM
MINVECS
KISSING_NUMBER
DENSITY
HERMITE_NUMBER
GROUP_ORDER
GROUP_GENERATORS
BACHER_POLYNOMIALS
PROPERTIES
REFERENCES
NOTES
LAST_LINE
-
NAME
LAMBDA(U)
-
DIMENSION
32
-
GRAM
32 0
4
0 4
0 0 4
0 0 0 4
0 -2 2 -2 4
2 0 -2 -2 0 4
2 -2 0 2 0 0 4
2 2 2 0 0 0 0 4
0 0 0 0 0 0 0 0 4
0 0 0 0 0 0 0 0 0 4
0 0 0 0 0 0 0 0 -2 2 4
1 1 2 0 1 -1 0 2 -2 0 2 4
0 0 0 0 0 0 0 0 -2 2 2 1 4
-1 2 0 -1 -1 0 -2 0 -2 0 1 1 2 4
0 0 -1 -2 0 2 -1 -1 1 -1 0 -1 0 1 4
-2 -1 1 -1 2 -1 -1 -1 -1 -1 -1 0 -1 0 -1 4
0 0 0 0 0 0 0 0 2 -2 -2 -1 -2 -1 1 0 4
0 0 0 0 0 0 0 0 -2 2 2 1 2 1 -1 0 -2 4
0 -2 1 0 2 0 1 0 -1 -1 1 1 0 -1 0 1 0 1 4
-1 -1 -1 2 -1 -1 1 -2 -1 -1 -1 -1 0 0 -1 1 -1 0 0 4
0 0 0 0 0 0 0 0 -2 2 2 1 2 1 -1 0 -2 2 0 0 4
0 1 -2 0 -2 1 -1 -1 0 0 0 -1 0 1 1 -1 -1 -1 -2 1 -1 4
-1 1 0 1 -1 -1 -1 0 1 1 1 0 0 0 0 -1 1 1 0 -1 -1 0 4
-2 1 0 -1 0 -1 -2 -1 -1 -1 -1 0 0 2 0 2 0 0 -1 1 1 0 -1 4
0 0 0 0 0 0 0 0 2 -2 -2 -1 -2 -1 1 0 2 -2 0 0 -2 0 0 0 4
0 1 0 1 -1 0 0 1 0 2 1 0 1 0 -1 -1 0 2 0 -1 1 -1 2 -1 0 4
-1 0 1 0 0 -1 -1 0 1 -1 0 0 -1 0 1 0 2 0 1 -1 -1 -1 2 0 2 1 4
0 2 -1 1 -2 0 -1 1 -1 -1 1 1 0 1 0 -1 0 0 0 0 0 1 1 0 -1 0 0 4
-1 -1 0 0 0 -1 0 -1 -1 1 1 0 2 1 0 0 0 1 0 0 2 -1 0 1 0 1 1 -1 4
0 -1 0 0 0 0 1 -1 1 1 0 -1 1 0 1 -1 0 1 0 0 1 -1 0 0 1 1 1 -2 2 4
2 0 0 0 0 1 1 1 0 0 -1 0 -1 -1 -1 0 0 -1 -1 0 -1 1 -1 -1 1 0 -1 -1 -1 -1 4
0 0 0 0 0 0 0 0 0 -1 0 0 0 0 1 0 1 0 1 0 -1 0 1 0 0 0 1 1 0 0 0 4
-
DET
1
-
MINIMAL_NORM
4
-
MINVECS
-
KISSING_NUMBER
146880
-
DENSITY
-
HERMITE_NUMBER
4
-
GROUP_ORDER
2^28 3^2 7
-
GROUP_GENERATORS
11
32 32
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32 32
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0 -1 1 0 -1 0 -1 0 1 -1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 -1 0 0 0 0 0
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32 32
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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32 32
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32 32
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32 32
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32 32
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32 32
2 0 0 0 -1 -1 -2 -1 0 1 0 0 0 0 0 0 0 0 1 0 -1 -1 -1 0 0 0 0 0 0 0 0 0
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0 -1 0 0 0 0 -1 0 -1 1 -1 0 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 -2 1 0 -2 0 -1 -1 -4 5 -2 0 -1 1 -1 -1 1 0 -1 -1 0 -1 -1 -1 5 -1 -1 -1 -2 -2 -4 2
0 -1 1 0 -1 0 0 -1 -3 3 -2 0 -1 0 0 -1 0 0 0 -1 0 0 0 0 3 0 -1 0 -1 -1 -2 1
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0 2 -1 0 2 -1 0 1 3 -5 3 -1 1 -1 1 1 0 0 1 1 0 1 1 1 -4 1 0 0 1 2 3 -2
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0 1 1 -2 0 0 2 -1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 1 -1 0 0
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32 32
-2 0 0 1 0 1 0 1 2 -1 1 0 1 0 0 0 1 2 0 0 1 0 0 0 0 -2 0 0 0 0 2 0
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0 1 0 -1 0 -1 1 1 3 -3 2 -1 2 -1 1 1 1 1 1 1 1 1 1 1 -2 0 0 0 0 0 2 -2
0 1 -2 1 2 0 0 1 -2 1 -1 0 -1 0 0 0 -1 -2 0 0 -1 0 0 0 -2 0 2 0 0 2 0 0
-1 -4 1 2 -3 2 -3 -1 -4 5 -2 2 -2 2 -2 -2 1 1 -2 -2 0 -2 -2 -2 6 -2 -2 -2 -2 -2 -4 4
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0 1 0 -1 0 0 1 -1 0 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 0 -1 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 0 0
1 0 0 1 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 0 0
0 3 -1 1 3 0 1 1 3 -3 1 -1 1 -1 1 1 -1 0 1 1 0 1 1 1 -4 0 2 1 2 1 3 -2
0 -1 0 0 -1 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 -1 0 0 -1 0 -1 -1 -2 2 -1 1 -1 1 -1 -1 0 0 -1 -1 0 -1 -1 -1 3 0 -1 -1 -1 -1 -2 2
1 0 -1 0 1 -1 0 0 -2 1 -1 0 -1 0 0 0 -1 -2 0 0 -1 0 0 0 -1 1 1 0 0 1 -1 0
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0 -2 0 1 -1 1 -1 1 0 1 0 1 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 0 0 0 0 0
0 0 -1 1 1 0 0 1 -1 1 0 0 0 0 0 0 0 -1 0 0 -1 0 0 1 -1 0 1 0 -1 1 0 0
0 -1 0 0 -1 -1 -1 1 -2 1 0 0 0 -1 1 0 1 0 0 0 0 0 0 0 1 0 -1 -1 -1 0 -1 0
1 -1 0 0 -1 0 -1 1 1 0 1 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 -1 1 1 -1 0 -2 -1 -1 0 0 0 -1 0 0 -1 0 1 -1 -1 0 -1 -1 -1 2 0 -2 -1 0 -1 -1 1
1 1 0 0 0 0 0 -1 2 -2 1 0 0 0 0 0 -1 0 1 0 -1 0 0 1 -2 1 0 0 1 0 1 -1
1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 -1 0 0 -1 0 0 0 0 1 0 0 1 0 -1 0
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0 -1 1 -1 -2 1 0 -1 2 -1 0 1 1 0 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 -1 0 0
0 2 -1 -1 2 -1 2 0 4 -4 1 0 1 0 1 1 -1 0 1 1 0 1 1 1 -4 2 1 1 1 1 3 -2
0 0 1 1 0 1 0 0 2 -1 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 -1 0 1 -1 0 0
1 0 0 -2 -1 -1 0 0 1 -1 0 0 1 0 0 1 0 -1 1 1 0 0 1 0 -1 1 0 1 0 1 1 -1
0 -1 0 -1 -2 0 0 0 0 1 0 1 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 -1 0 0 0
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1 0 0 0 -1 0 0 0 1 0 1 0 0 0 0 1 -1 0 0 0 -1 -1 0 1 0 0 0 0 0 0 0 0
32 32
1 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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0 -1 1 1 -1 1 -1 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 -1 -1 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 0 0 0
1 -1 1 0 -1 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 0 0
0 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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-1 0 0 0 1 0 1 1 1 -1 0 0 0 0 0 0 1 2 0 0 1 2 0 0 0 0 0 0 0 0 0 0
0 0 0 -1 0 0 1 0 0 -1 -1 0 0 0 0 0 -1 0 0 0 1 0 2 0 0 0 0 0 0 0 0 0
0 0 0 1 1 1 0 0 0 -1 0 0 0 0 0 0 -1 0 -1 0 0 -1 1 0 0 0 0 0 0 0 0 0
0 0 0 1 0 0 0 -1 0 -1 -1 0 0 0 0 0 -1 1 0 -2 0 0 0 0 0 0 0 0 0 0 0 0
0 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 -1 -1 -1 0 1 0 0 0 0 0 0 0 0
0 0 -1 -1 0 -1 1 0 -1 0 -1 0 0 0 0 0 -1 -1 0 -1 0 0 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 -1 0 0 1 1 0 0 0 0 0 1 0 0 1 -1 -1 -1 0 0 0 0 0 0 0 0 0
0 0 -1 1 1 0 -1 1 -2 1 0 0 -1 0 0 0 0 -2 0 0 -1 0 0 0 -1 0 0 0 0 2 0 0
0 1 -1 0 1 0 1 0 0 0 -1 0 0 0 0 0 -1 0 0 0 0 0 0 0 -1 0 2 0 0 0 0 0
0 0 0 0 0 1 0 0 -1 1 -1 0 0 0 0 0 -1 -1 0 0 0 -1 1 0 0 -1 1 0 0 0 0 0
0 -1 1 0 -2 0 -1 -1 2 -1 1 0 1 0 0 0 0 1 0 0 0 -1 -1 0 0 0 0 0 0 -1 1 0
0 -1 0 -1 -1 -1 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 -2 0 0 0
0 0 1 -1 -1 0 1 -1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 -1 1 1 -1 0 0
-1 1 -1 1 2 1 1 1 -1 0 -1 0 -1 0 0 0 -1 -1 0 0 0 1 1 0 -1 0 1 0 1 1 0 0
0 2 -1 -1 1 -2 1 0 3 -3 2 -1 2 -1 1 1 0 0 1 1 0 0 0 1 -3 1 1 1 0 1 3 -2
1 1 0 0 1 -1 0 0 -1 0 1 -2 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 -1 1 2 0 0 1 -1 0 0 -1 -1 0 0 0 0 0 0 0 0 1 0 0 -1 0 1 0 0 1 0 0
0 1 -1 0 1 0 1 1 -1 0 0 -1 0 0 0 1 -1 -2 0 0 0 0 1 0 -1 0 1 0 0 1 0 0
0 0 0 0 -1 1 0 -1 0 0 -1 1 0 0 0 0 -1 -1 0 0 0 -1 1 0 0 0 0 0 0 0 0 0
0 0 0 0 0 -1 0 0 -1 0 0 -1 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 -1 1 0 0
0 0 0 -1 0 -1 1 0 0 -1 0 -1 1 0 -1 0 0 0 0 -1 1 1 0 0 0 0 1 0 -1 0 0 0
1 0 0 1 1 0 -1 1 1 0 2 -1 -1 1 0 0 1 1 0 1 -1 0 -1 0 0 0 -1 0 1 0 0 0
0 1 -1 0 1 0 1 0 2 -1 0 0 0 1 0 1 -1 -1 1 0 0 0 1 0 -2 0 1 1 1 1 2 -1
-
BACHER_POLYNOMIALS
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
x^5352*8 x^5208*96 x^5112*64 x^4968*48 x^4872*768 x^4716*256 (21504x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
x^5160*56 x^4872*1184 (49152x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0
x^5544*120 x^5208*384 x^5160*544 x^4968*192 (2688x)
1 32
0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
x^5544*344 x^5352*896 (96x)
-
PROPERTIES
Unimodular=1
-
REFERENCES
H. Koch, B. B. Venkov,
\"Uber ganzzahlige unimodulare euklidische Gitter.
Journal f\"ur die reine und angewandte Mathematik 398 (1989), 144-168
H. Koch, B.B. Venkov, \"Uber gerade unimodulare
Gitter der Dimension 32, III
Mathem. Nachr. 152 (1991), 191-213
-
NOTES
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe