The Lattice DualExtremal(20,3)
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 13:27:57 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(20,3)
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DIMENSION (required)
20
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GRAM (floating point or integer Gram matrix)
20
6 0 0 0 3 3 3 0 0 0 0 3 -3 3 0 3 3 3 -3 0
0 6 0 0 3 3 3 -3 -3 -3 -3 0 -3 3 3 -3 3 -3 0 3
0 0 6 0 -3 -3 -3 -3 3 3 3 -3 0 0 0 0 0 0 3 0
0 0 0 6 -3 -3 -3 -3 0 0 0 -3 -3 0 0 -3 3 0 0 -3
3 3 -3 -3 10 7 7 0 -5 -5 -5 3 -3 5 3 2 3 -2 -5 5
3 3 -3 -3 7 10 7 3 -5 -5 -5 6 0 2 3 2 0 -2 -5 2
3 3 -3 -3 7 7 10 0 -5 -5 -5 6 -3 5 3 2 0 1 -5 2
0 -3 -3 -3 0 3 0 10 2 -1 2 5 5 -4 -3 4 -4 1 -2 -2
0 -3 3 0 -5 -5 -5 2 8 5 5 -2 1 -3 -3 1 -2 3 3 -2
0 -3 3 0 -5 -5 -5 -1 5 8 5 -2 1 -3 -3 1 -2 3 3 -2
0 -3 3 0 -5 -5 -5 2 5 5 8 -2 1 -3 -3 1 -2 3 3 -2
3 0 -3 -3 3 6 6 5 -2 -2 -2 10 1 1 0 5 -2 2 -4 -1
-3 -3 0 -3 -3 0 -3 5 1 1 1 1 10 -5 -3 2 -5 -1 2 -1
3 3 0 0 5 2 5 -4 -3 -3 -3 1 -5 8 3 0 4 1 -2 3
0 3 0 0 3 3 3 -3 -3 -3 -3 0 -3 3 6 -3 0 -3 0 3
3 -3 0 -3 2 2 2 4 1 1 1 5 2 0 -3 8 -1 3 -3 -1
3 3 0 3 3 0 0 -4 -2 -2 -2 -2 -5 4 0 -1 10 -1 -1 2
3 -3 0 0 -2 -2 1 1 3 3 3 2 -1 1 -3 3 -1 8 -1 -3
-3 0 3 0 -5 -5 -5 -2 3 3 3 -4 2 -2 0 -3 -1 -1 8 0
0 3 0 -3 5 2 2 -2 -2 -2 -2 -1 -1 3 3 -1 2 -3 0 8
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DIVISORS (elementary divisors)
3^18
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MINIMAL_NORM
6
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THETA_SERIES
1 + 60*q^6 + 4860*q^8 + 34992*q^10 + 45360*q^12 + 719280*q^14 + 2405700*q^16
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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 3
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