The Lattice DualExtremal(20,2)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 13:28:00 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(20,2)a
-
DIMENSION (required)
20
-
GRAM (floating point or integer Gram matrix)
20
4 2 -2 0 0 0 2 0 -2 2 -2 2 -2 2 -2 2 2 -2 -2 -2
2 4 -2 0 0 0 2 0 -2 2 -2 2 -2 2 0 0 0 -2 -2 0
-2 -2 4 0 0 0 0 0 0 -2 2 -2 0 -2 0 0 -2 2 2 0
0 0 0 4 2 2 -2 -2 2 2 -2 -2 -2 2 -2 2 2 -2 -2 2
0 0 0 2 4 2 -2 0 2 2 -2 -2 -2 2 -2 0 0 -2 -2 2
0 0 0 2 2 4 -2 -2 2 0 0 0 -2 0 -2 2 2 -2 -2 2
2 2 0 -2 -2 -2 6 2 -4 1 1 1 -1 0 1 0 -1 0 1 -3
0 0 0 -2 0 -2 2 4 -2 0 0 0 0 0 2 -2 -2 0 2 -2
-2 -2 0 2 2 2 -4 -2 6 1 -1 -3 1 0 -1 0 1 0 -1 3
2 2 -2 2 2 0 1 0 1 6 -4 -2 -2 3 -1 1 1 -3 -2 0
-2 -2 2 -2 -2 0 1 0 -1 -4 6 0 2 -3 1 -1 -1 3 2 0
2 2 -2 -2 -2 0 1 0 -3 -2 0 6 0 -1 1 1 1 -1 0 -2
-2 -2 0 -2 -2 -2 -1 0 1 -2 2 0 6 -3 3 -3 -1 3 2 0
2 2 -2 2 2 0 0 0 0 3 -3 -1 -3 6 -3 0 1 -2 -3 1
-2 0 0 -2 -2 -2 1 2 -1 -1 1 1 3 -3 6 -3 -2 1 3 -1
2 0 0 2 0 2 0 -2 0 1 -1 1 -3 0 -3 6 3 -2 -1 -1
2 0 -2 2 0 2 -1 -2 1 1 -1 1 -1 1 -2 3 6 -1 -3 1
-2 -2 2 -2 -2 -2 0 0 0 -3 3 -1 3 -2 1 -2 -1 6 1 1
-2 -2 2 -2 -2 -2 1 2 -1 -2 2 0 2 -3 3 -1 -3 1 6 -2
-2 0 0 2 2 2 -3 -2 3 0 0 -2 0 1 -1 -1 1 1 -2 6
-
DIVISORS (elementary divisors)
2^18
-
MINIMAL_NORM
4
-
THETA_SERIES
1 + 120*q^4 + 15360*q^6 + 67320*q^8 + 1511424*q^10 + 2607840*q^12 + O(q^13)
-
GROUP_ORDER
<2, 33>, <3, 7>, <5, 1>
-
PROPERTIES
INTEGRAL = 1 (lattices are real unless stated otherwise)
-
REFERENCES
Boecherer, Nebe: On theta series attached to maximal lattices and their adjoints.
-
NOTES
The dual of a maximal integral lattice of level 2
with highest possible minimum.
-
URL (links to other sites for this lattice)
-
LAST_LINE (required)
Haftungsausschluss/Disclaimer
Gabriele Nebe