The Lattice DualExtremal(16,10)f
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 13:28:09 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)f
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DIMENSION (required)
16
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GRAM (floating point or integer Gram matrix)
16
20 10 -10 10 -10 10 0 0 0 -20 0 20 -10 10 0 0
10 20 -10 10 -10 10 0 0 0 -20 0 20 -10 10 10 0
-10 -10 26 -19 3 1 -9 -6 9 12 -3 -12 16 -2 5 0
10 10 -19 26 3 -4 1 -1 -6 -8 -3 13 -9 3 -10 0
-10 -10 3 3 26 -7 6 -7 1 26 -6 -23 3 -5 -11 0
10 10 1 -4 -7 26 1 -1 4 -8 -3 13 -9 13 10 0
0 0 -9 1 6 1 18 3 -5 2 4 -5 -9 -3 -9 0
0 0 -6 -1 -7 -1 3 14 -7 -2 7 6 4 0 -3 0
0 0 9 -6 1 4 -5 -7 14 -2 -11 -7 -1 -1 8 0
-20 -20 12 -8 26 -8 2 -2 -2 44 -6 -34 12 -14 -10 0
0 0 -3 -3 -6 -3 4 7 -11 -6 26 13 7 5 1 10
20 20 -12 13 -23 13 -5 6 -7 -34 13 46 -2 18 1 0
-10 -10 16 -9 3 -9 -9 4 -1 12 7 -2 26 -2 -5 0
10 10 -2 3 -5 13 -3 0 -1 -14 5 18 -2 22 7 0
0 10 5 -10 -11 10 -9 -3 8 -10 1 1 -5 7 38 10
0 0 0 0 0 0 0 0 0 0 10 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