The Lattice DualExtremal(20,5)b
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 13:27:55 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)
-
NAME (required)
DualExtremal(20,5)b
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DIMENSION (required)
20
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GRAM (floating point or integer Gram matrix)
20
10 0 5 0 0 -5 5 5 -5 5 0 -5 0 0 0 0 0 0 0 0
0 10 0 0 5 10 0 -5 -5 -5 0 5 -10 -5 0 0 0 0 -5 0
5 0 10 0 5 0 5 0 -5 0 0 -5 0 0 0 0 0 0 -5 0
0 0 0 10 -5 5 0 -5 5 0 0 5 0 0 0 0 0 5 5 -5
0 5 5 -5 18 10 10 0 -9 -10 0 -5 -9 -10 0 5 -4 -5 -10 5
-5 10 0 5 10 26 5 -11 -2 -15 0 6 -17 -15 -2 2 -5 0 -5 0
5 0 5 0 10 5 20 5 -5 0 -5 -10 -5 -10 5 0 -10 -5 -5 -5
5 -5 0 -5 0 -11 5 16 2 10 0 -11 7 0 2 -2 0 -5 0 5
-5 -5 -5 5 -9 -2 -5 2 16 5 0 -2 11 5 4 -4 2 0 5 0
5 -5 0 0 -10 -15 0 10 5 20 -5 -10 15 10 10 -10 0 0 0 -5
0 0 0 0 0 0 -5 0 0 -5 10 5 -5 0 -5 5 5 0 5 5
-5 5 -5 5 -5 6 -10 -11 -2 -10 5 26 -12 -5 -17 7 5 5 10 0
0 -10 0 0 -9 -17 -5 7 11 15 -5 -12 26 15 9 -9 2 0 0 0
0 -5 0 0 -10 -15 -10 0 5 10 0 -5 15 20 10 -5 5 5 0 -5
0 0 0 0 0 -2 5 2 4 10 -5 -17 9 10 24 -9 -5 0 -10 -10
0 0 0 0 5 2 0 -2 -4 -10 5 7 -9 -5 -9 14 5 0 5 5
0 0 0 0 -4 -5 -10 0 2 0 5 5 2 5 -5 5 12 0 5 5
0 0 0 5 -5 0 -5 -5 0 0 0 5 0 5 0 0 0 10 0 -5
0 -5 -5 5 -10 -5 -5 0 5 0 5 10 0 0 -10 5 5 0 20 0
0 0 0 -5 5 0 -5 5 0 -5 5 0 0 -5 -10 5 5 -5 0 20
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DIVISORS (elementary divisors)
5^18
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MINIMAL_NORM
8
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THETA_SERIES
1 + 30*q^8 + 36*q^10 + 1680*q^12 + 6600*q^14 + 22050*q^16 + 62760*q^18 +
27168*q^20
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GROUP_ORDER
<2, 11>, <3, 8>, <5, 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 5
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