The Lattice DualExtremal(16,10)a
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 13:28:11 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
PROPERTIES
REFERENCES
NOTES
URL (links to other sites for this lattice)
LAST_LINE (required)
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NAME (required)
DualExtremal(16,10)a
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DIMENSION (required)
16
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GRAM (floating point or integer Gram matrix)
16
22 13 0 0 8 3 0 10 0 1 10 0 -1 1 -12 -10
13 26 10 -10 13 -7 -10 10 0 3 10 10 -5 5 -20 -10
0 10 20 0 0 -10 -10 10 0 0 0 10 0 10 -20 0
0 -10 0 20 -10 0 0 0 0 0 0 10 0 0 0 0
8 13 0 -10 26 -9 0 0 -10 5 10 0 -13 3 -6 0
3 -7 -10 0 -9 26 10 -10 -10 10 0 -20 12 -12 14 0
0 -10 -10 0 0 10 20 -10 0 0 0 -10 0 -10 20 10
10 10 10 0 0 -10 -10 20 10 -10 0 10 0 10 -20 -10
0 0 0 0 -10 -10 0 10 40 -20 -10 10 0 10 0 0
1 3 0 0 5 10 0 -10 -20 22 0 -10 6 -6 2 0
10 10 0 0 10 0 0 0 -10 0 20 10 -10 0 -10 0
0 10 10 10 0 -20 -10 10 10 -10 10 40 -10 10 -20 0
-1 -5 0 0 -13 12 0 0 0 6 -10 -10 22 -2 4 0
1 5 10 0 3 -12 -10 10 10 -6 0 10 -2 22 -24 0
-12 -20 -20 0 -6 14 20 -20 0 2 -10 -20 4 -24 48 10
-10 -10 0 0 0 0 10 -10 0 0 0 0 0 0 10 20
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DIVISORS (elementary divisors)
10^14
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MINIMAL_NORM
12
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THETA_SERIES
1 + 6*q^12 + 72*q^14 + 54*q^16 + 432*q^18 + 42*q^20 + 1728*q^22 + 1008*q^24 +
5472*q^26 + 3078*q^28 + 2472*q^30 + 7650*q^32 + 35424*q^34 + 17916*q^36 +
77472*q^38 + 6120*q^40
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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 10
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