The Lattice OLeech^2
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 13:21:22 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME (required)
DIMENSION (required)
GRAM
DIVISORS (elementary divisors)
MINIMAL_NORM
PROPERTIES
NOTES
LAST_LINE (required)
-
NAME (required)
OLeech^2
-
DIMENSION (required)
48
-
GRAM
48 0
8
0 8
0 0 8
4 4 4 8
-2 -4 0 -2 8
4 -2 2 2 0 8
0 -2 -2 -4 0 0 8
0 -4 2 -2 4 4 4 8
-2 2 -2 -2 -2 -2 -2 -2 8
-2 -2 -2 -2 2 -2 2 2 0 8
2 2 -2 2 2 -2 -2 -2 0 0 8
0 0 -4 -2 0 -4 0 -2 4 4 4 8
-4 2 2 0 2 -2 0 2 0 2 0 0 8
-2 -4 0 -4 2 2 4 4 -2 0 -2 -2 0 8
-2 0 -4 -2 0 -4 2 -2 0 2 0 2 0 0 8
-4 0 -2 -4 0 -2 4 2 0 2 -2 0 4 4 4 8
-4 2 0 -2 -2 -4 0 -2 2 0 0 2 4 0 2 4 8
-2 -4 -2 -4 4 -2 2 2 0 2 2 2 0 4 2 2 0 8
0 2 -4 0 0 -2 -2 -4 0 -2 2 0 -2 -2 4 0 0 0 8
-2 0 -4 -4 0 -4 2 -2 0 0 2 2 0 2 4 4 4 4 4 8
-4 2 0 -2 0 -2 0 0 4 0 -2 0 2 0 0 2 2 0 -2 0 8
-2 -4 -2 -4 2 0 2 2 0 4 -2 2 0 2 2 2 0 2 0 2 0 8
0 2 -4 0 0 -2 0 -2 2 2 4 4 0 -2 2 0 2 0 2 2 0 0 8
-2 0 -4 -4 0 -2 2 0 4 2 0 4 0 0 2 2 2 0 0 2 4 4 4 8
4 4 0 4 -3 1 -1 -2 0 -2 2 0 -1 -3 -1 -2 -1 -3 1 -1 -1 -3 1 -1 8
-4 4 0 0 -1 -3 -1 -2 2 0 0 0 3 -1 1 2 3 -1 1 1 3 -1 1 1 0 8
0 0 4 0 -1 1 1 2 0 -2 -2 -2 1 1 -3 0 1 -1 -3 -1 1 -1 -3 -1 0 0 8
0 4 4 4 -2 0 -2 -1 0 -2 0 -2 2 -2 -2 -1 1 -3 -1 -2 1 -3 -1 -2 4 4 4 8
1 -3 1 0 4 4 0 4 -2 0 0 -2 0 2 -2 -1 -3 1 -1 -2 -1 1 -1 -1 -2 -4 0 -2 8
3 1 1 2 -4 4 0 0 0 -2 -2 -2 -2 0 -2 -1 -1 -3 -1 -2 -1 -1 -1 -1 4 -2 2 2 0 8
1 -1 -3 -2 0 0 4 0 -2 0 0 0 -2 2 2 1 -1 1 1 2 -1 1 1 1 0 -2 -2 -4 0 0 8
2 -2 0 -1 0 4 4 4 -2 0 -2 -2 -1 3 -1 1 -2 0 -2 -1 -1 1 -1 0 0 -4 2 -2 4 4 4 8
-2 0 -2 -2 0 -2 0 0 4 4 0 4 1 -1 1 1 1 1 -1 0 2 2 2 3 -2 2 -2 -2 -2 -2 -2 -2 8
0 -2 0 0 2 0 2 2 -4 4 0 0 1 1 1 1 -1 1 -1 0 -2 2 0 -1 -2 -2 -2 -2 2 -2 2 2 0 8
0 2 0 2 2 0 -2 0 0 0 4 0 1 -1 -1 -1 -1 1 1 0 0 -2 2 -1 2 2 -2 2 2 -2 -2 -2 0 0 8
0 0 -2 0 2 -2 0 0 0 4 4 4 1 -1 1 0 0 2 0 1 -1 1 3 1 0 0 -4 -2 0 -4 0 -2 4 4 4 8
-3 -1 1 -2 2 0 2 3 -1 1 -1 -1 4 4 0 4 2 2 -2 1 1 1 -1 0 -4 2 2 0 2 -2 0 2 0 2 0 0 8
1 -3 -1 -2 0 2 2 1 -1 -1 -1 -1 -4 4 0 0 -2 2 0 1 -1 1 -1 0 -2 -4 0 -4 2 2 4 4 -2 0 -2 -2 0 8
-1 -1 -1 0 2 -2 0 -1 -1 1 1 1 0 0 4 0 0 2 2 1 -1 1 1 0 -2 0 -4 -2 0 -4 2 -2 0 2 0 2 0 0 8
-2 -2 -2 -3 1 -1 3 1 -1 1 -1 0 0 4 4 4 1 3 1 3 0 2 0 1 -4 0 -2 -4 0 -2 4 2 0 2 -2 0 4 4 4 8
-3 -1 -1 -3 1 -3 1 0 1 1 1 2 2 2 2 3 4 4 0 4 1 1 1 1 -4 2 0 -2 -2 -4 0 -2 2 0 0 2 4 0 2 4 8
1 -3 -1 -1 3 1 1 2 -1 1 1 0 -2 2 0 -1 -4 4 0 0 -1 1 -1 -1 -2 -4 -2 -4 4 -2 2 2 0 2 2 2 0 4 2 2 0 8
-1 1 -1 1 1 -1 -3 -2 1 -1 1 0 0 -2 2 -1 0 0 4 0 -1 -1 1 -1 0 2 -4 0 0 -2 -2 -4 0 -2 2 0 -2 -2 4 0 0 0 8
-1 -1 -3 -2 2 -2 0 -1 0 0 2 1 -1 1 3 1 0 4 4 4 -1 1 1 0 -2 0 -4 -4 0 -4 2 -2 0 0 2 2 0 2 4 4 4 4 4 8
-3 -1 -1 -3 1 -1 1 1 2 2 -2 1 1 1 1 2 1 1 -1 1 4 4 0 4 -4 2 0 -2 0 -2 0 0 4 0 -2 0 2 0 0 2 2 0 -2 0 8
1 -3 -1 -1 1 1 1 1 -2 2 0 1 -1 1 1 0 -1 1 1 1 -4 4 0 0 -2 -4 -2 -4 2 0 2 2 0 4 -2 2 0 2 2 2 0 2 0 2 0 8
-1 1 -1 1 1 -1 -1 -1 0 2 2 1 1 -1 1 0 1 1 1 1 0 0 4 0 0 2 -4 0 0 -2 0 -2 2 2 4 4 0 -2 2 0 2 0 2 2 0 0 8
-1 -1 -3 -2 1 -1 1 0 1 3 1 3 0 0 2 1 1 1 1 2 0 4 4 4 -2 0 -4 -4 0 -2 2 0 4 2 0 4 0 0 2 2 2 0 0 2 4 4 4 8
-
DIVISORS (elementary divisors)
2^24
-
MINIMAL_NORM
8
-
PROPERTIES
MODULAR = 2
-
NOTES
Sublattice of index 2^12 in Leech + Leech,
= { (a,b) in Leech + Leech : a+(1+i)Leech = b+(1+i)Leech },
where i is an automorphism of Leech i^2=-1.
-
LAST_LINE (required)
Haftungsausschluss/Disclaimer
Gabriele Nebe