The Lattice Q8(1)
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 13:16:28 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DET
GRAM
DIVISORS
MINIMAL_NORM
KISSING_NUMBER
GROUP_ORDER
GROUP_NAME
GROUP_GENERATORS
PROPERTIES
NOTES
REFERENCES
THETA_SERIES
LAST_LINE
-
NAME
Q8(1)
-
DIMENSION
8
-
DET
625
-
GRAM
8 8
4 -2 1 1 -1 -2 0 2
-2 4 -1 0 -1 1 1 -1
1 -1 4 -1 1 -2 -2 0
1 0 -1 4 1 1 2 1
-1 -1 1 1 4 1 -1 -2
-2 1 -2 1 1 4 2 0
0 1 -2 2 -1 2 4 1
2 -1 0 1 -2 0 1 4
-
DIVISORS
1 1 1 1 5 5 5 5
-
MINIMAL_NORM
4
-
KISSING_NUMBER
120
-
GROUP_ORDER
28800
-
GROUP_NAME
(SL(25) Y SL(25)):(C2 x C2)
-
GROUP_GENERATORS
3
8
0 0 0 0 0 0 0 1
0 0 0 0 1 0 0 0
0 0 0 0 0 0 1 0
0 1 0 0 1 -1 0 1
0 1 0 0 0 0 0 0
1 1 0 -1 1 0 0 0
0 0 1 0 0 0 0 0
1 0 0 0 0 0 0 0
8
-1 -1 0 0 0 -1 1 0
0 0 0 0 0 1 -1 0
0 0 0 -1 0 0 1 0
0 -1 1 1 -1 1 0 -1
1 0 1 0 -1 1 0 -1
0 0 1 1 -1 1 -1 0
0 0 0 0 1 0 0 1
-1 -1 0 1 -1 0 0 0
8
1 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0
0 0 1 0 0 0 0 0
0 0 0 1 0 0 0 0
0 0 0 0 1 0 0 0
0 0 0 0 0 1 0 0
0 0 0 1 -1 1 -1 0
0 -1 1 1 -2 1 0 -1
-
PROPERTIES
INTEGRAL=1
MODULAR=5
-
NOTES
The icosian (or Maass) lattice Q_8(1) in LDL II (see references).
The minimal vectors are the 120 unit icosians (SPLAG, Chap. 8).
Also called H4.
-
REFERENCES
Plesken & Pohst, Math. Comp. 31 (1977), 552-573.
Conway-Sloane, "Low-Dimensional Lattices II: Subgroups of GL(n,Z)",
Proc. Royal Soc. London, A 419 (1988), 29-68.
-
THETA_SERIES
1,0,120,240,600,1440,2400,3120,5400,7200,12360,12000,18720,20640,
28800,39120,43800,45120,62040,62400,102120
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe