The Lattice DualExtremal(20,11)
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 13:28:02 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME (required)
DIMENSION (required)
GRAM (floating point or integer Gram matrix)
DIVISORS (elementary divisors)
MINIMAL_NORM
THETA_SERIES
GROUP_ORDER
PROPERTIES
REFERENCES
NOTES
URL (links to other sites for this lattice)
LAST_LINE (required)
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NAME (required)
DualExtremal(20,11)
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DIMENSION (required)
20
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GRAM (floating point or integer Gram matrix)
20
28 -8 14 14 10 10 0 0 -12 14 12 -1 13 1 1 -1 7 -7 13 12
-8 28 -14 -14 10 0 10 10 -6 -16 -2 5 7 -11 9 5 -3 -10 3 -7
14 -14 28 6 0 10 -10 -10 -6 8 3 5 6 12 3 -6 10 3 -1 8
14 -14 6 28 0 10 -10 -10 -6 8 3 -6 -5 1 -8 5 10 3 -1 8
10 10 0 0 32 16 -6 -6 -9 -1 16 13 -1 6 16 13 13 -3 8 -3
10 0 10 10 16 32 -16 -16 -9 0 13 13 4 12 13 13 14 9 6 -1
0 10 -10 -10 -6 -16 32 10 0 -1 3 -11 6 -17 -8 0 -12 -12 2 -2
0 10 -10 -10 -6 -16 10 32 0 -1 -8 0 6 -17 -8 -11 -12 -12 13 9
-12 -6 -6 -6 -9 -9 0 0 24 -6 -2 2 -4 -2 -2 2 -3 3 -4 -2
14 -16 8 8 -1 0 -1 -1 -6 28 9 -6 -4 11 -2 -6 -3 1 3 4
12 -2 3 3 16 13 3 -8 -2 9 26 9 -3 9 4 9 6 0 9 -3
-1 5 5 -6 13 13 -11 0 2 -6 9 24 -4 9 9 2 8 3 7 -2
13 7 6 -5 -1 4 6 6 -4 -4 -3 -4 38 -4 8 -4 1 -11 7 5
1 -11 12 1 6 12 -17 -17 -2 11 9 9 -4 32 9 -2 8 13 -6 -10
1 9 3 -8 16 13 -8 -8 -2 -2 4 9 8 9 26 9 6 0 -2 -3
-1 5 -6 5 13 13 0 -11 2 -6 9 2 -4 -2 9 24 8 3 -4 -2
7 -3 10 10 13 14 -12 -12 -3 -3 6 8 1 8 6 8 20 0 -3 1
-7 -10 3 3 -3 9 -12 -12 3 1 0 3 -11 13 0 3 0 20 -4 -5
13 3 -1 -1 8 6 2 13 -4 3 9 7 7 -6 -2 -4 -3 -4 26 8
12 -7 8 8 -3 -1 -2 9 -2 4 -3 -2 5 -10 -3 -2 1 -5 8 20
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DIVISORS (elementary divisors)
11^18
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MINIMAL_NORM
20
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THETA_SERIES
1 + 132*q^20 + 660*q^24 + 1320*q^26 + 2640*q^28 + 4752*q^30 + 8580*q^32 +
14520*q^34 + 24420*q^36 + 39600*q^38 + 63492*q^40 + 96360*q^42 + 12540*q^44
+ 219120*q^46
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GROUP_ORDER
<2, 5>, <3, 2>, <5, 1>, <11, 1>
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PROPERTIES
INTEGRAL = 1 (lattices are real unless stated otherwise)
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REFERENCES
Boecherer, Nebe: On theta series attached to maximal lattices and their adjoints.
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NOTES
The dual of a maximal integral lattice of level 11
with highest possible minimum.
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URL (links to other sites for this lattice)
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LAST_LINE (required)
Haftungsausschluss/Disclaimer
Gabriele Nebe