The Lattice DualExtremal(20,2)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 13:27:59 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(20,2)b
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DIMENSION (required)
20
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GRAM (floating point or integer Gram matrix)
20
4 -2 -2 0 2 -2 2 -2 2 -2 2 2 -2 2 -2 2 -2 -2 2 -2
-2 4 2 0 -2 2 -2 2 -2 2 -2 -2 2 -2 0 -2 2 0 -2 0
-2 2 4 0 0 0 0 2 0 2 -2 0 0 -2 2 0 0 2 0 2
0 0 0 4 2 -2 2 2 2 2 -2 0 0 0 2 0 0 0 0 0
2 -2 0 2 6 -4 4 1 4 1 -1 3 -3 0 1 3 -3 -1 3 1
-2 2 0 -2 -4 6 -2 -1 -4 -1 1 -3 3 0 -1 -1 1 -1 -1 1
2 -2 0 2 4 -2 6 -1 4 -1 1 3 -3 0 1 3 -3 -1 3 1
-2 2 2 2 1 -1 -1 6 -1 4 -4 -2 2 -2 3 -2 2 2 -2 2
2 -2 0 2 4 -4 4 -1 6 -1 1 3 -3 0 1 3 -3 -1 3 -1
-2 2 2 2 1 -1 -1 4 -1 6 -4 0 2 -2 3 -2 2 2 -2 2
2 -2 -2 -2 -1 1 1 -4 1 -4 6 2 -2 2 -3 2 -2 -2 2 -2
2 -2 0 0 3 -3 3 -2 3 0 2 6 -4 0 -1 2 -2 0 2 0
-2 2 0 0 -3 3 -3 2 -3 2 -2 -4 6 0 1 -2 2 0 -2 0
2 -2 -2 0 0 0 0 -2 0 -2 2 0 0 4 -2 2 -2 -2 2 -2
-2 0 2 2 1 -1 1 3 1 3 -3 -1 1 -2 6 -1 1 3 -1 3
2 -2 0 0 3 -1 3 -2 3 -2 2 2 -2 2 -1 6 -4 -2 4 0
-2 2 0 0 -3 1 -3 2 -3 2 -2 -2 2 -2 1 -4 6 2 -4 0
-2 0 2 0 -1 -1 -1 2 -1 2 -2 0 0 -2 3 -2 2 6 -2 2
2 -2 0 0 3 -1 3 -2 3 -2 2 2 -2 2 -1 4 -4 -2 6 0
-2 0 2 0 1 1 1 2 -1 2 -2 0 0 -2 3 0 0 2 0 6
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DIVISORS (elementary divisors)
2^18
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MINIMAL_NORM
4
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THETA_SERIES
1 + 120*q^4 + 15360*q^6 + 67320*q^8 + 1511424*q^10 + 2607840*q^12 + O(q^13)
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GROUP_ORDER
<2, 20>, <3, 9>, <5, 4>
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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 2
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