The Lattice DualExtremal(20,5)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 13:27:56 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)a
-
DIMENSION (required)
20
-
GRAM (floating point or integer Gram matrix)
20
10 0 5 -5 0 0 5 0 5 5 -5 -5 0 -5 0 0 0 0 5 0
0 10 0 5 -5 0 -5 0 -5 5 5 5 0 0 5 0 -5 -5 10 0
5 0 20 -5 -5 5 5 -5 5 10 0 0 0 -10 10 -5 -5 5 15 5
-5 5 -5 20 -5 0 -5 -5 -5 -5 10 10 0 5 -5 0 -5 -5 0 -5
0 -5 -5 -5 10 0 0 5 0 -5 -5 -5 0 0 0 0 10 5 -5 5
0 0 5 0 0 10 -5 0 5 0 0 0 0 0 5 0 5 5 5 5
5 -5 5 -5 0 -5 12 -1 3 5 -5 -3 0 -5 -3 0 -7 0 -3 -5
0 0 -5 -5 5 0 -1 14 -6 5 -10 6 5 -5 10 5 5 5 5 5
5 -5 5 -5 0 5 3 -6 16 0 0 -11 -5 5 -9 0 -1 0 -9 -5
5 5 10 -5 -5 0 5 5 0 20 -5 5 0 -10 10 0 -10 0 15 0
-5 5 0 10 -5 0 -5 -10 0 -5 20 -5 -5 5 -5 -5 -10 0 -5 -5
-5 5 0 10 -5 0 -3 6 -11 5 -5 26 10 0 9 5 -4 -5 14 0
0 0 0 0 0 0 0 5 -5 0 -5 10 10 0 5 5 0 0 5 0
-5 0 -10 5 0 0 -5 -5 5 -10 5 0 0 20 -15 5 0 -10 -15 -10
0 5 10 -5 0 5 -3 10 -9 10 -5 9 5 -15 28 0 2 10 23 15
0 0 -5 0 0 0 0 5 0 0 -5 5 5 5 0 10 0 -5 -5 -5
0 -5 -5 -5 10 5 -7 5 -1 -10 -10 -4 0 0 2 0 28 5 2 15
0 -5 5 -5 5 5 0 5 0 0 0 -5 0 -10 10 -5 5 20 5 10
5 10 15 0 -5 5 -3 5 -9 15 -5 14 5 -15 23 -5 2 5 38 15
0 0 5 -5 5 5 -5 5 -5 0 -5 0 0 -10 15 -5 15 10 15 20
-
DIVISORS (elementary divisors)
5^18
-
MINIMAL_NORM
8
-
THETA_SERIES
1 + 30*q^8 + 36*q^10 + 1680*q^12 + 6600*q^14 + 22050*q^16 + 62760*q^18 +
27168*q^20
-
GROUP_ORDER
<2, 14>, <3, 5>
-
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 5
with highest possible minimum.
-
URL (links to other sites for this lattice)
-
LAST_LINE (required)
Haftungsausschluss/Disclaimer
Gabriele Nebe