The Lattice Z2P48n
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 Wed Feb 22 16:55:25 CET 2012
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DET
MINIMUM
GRAM
NOTES
LAST_LINE
-
NAME
Z2P48n
-
DIMENSION
48
-
DET
2^24
-
MINIMUM
8
-
GRAM
48x48
18
6 8 -14 5 -3 -3 -2 -9 3 -7 0 7 -5 -2 -6 -2 7
-3 8 9 4 -1 7 -15 -5 0 3 -11 -5 -1 15 -6 1 3
-4 -8 -11 6 0 -4 -8 -5 -10 4 6 -10 0 6 24 -2
4 10 9 -3 7 -1 8 4 -4 -1 -5 7 -5 -8 14 -16
-8 7 5 7 7 -1 2 1 -10 -1 -3 -4 9 -9 2 8 -11
7 9 -8 -9 -11 1 -10 3 -9 -8 0 -6 8 -2 18 -16
5 0 5 0 -9 5 -13 -7 4 5 -7 -6 3 -2 -1 10 -1
10 0 -5 -12 -4 -7 3 1 1 1 1 0 -1 4 -7 -10
-12 -4 4 3 2 -5 -12 3 3 -4 -5 -14 4 -16 36
-10 -11 -12 1 18 0 25 2 -7 -12 14 -2 0 -7 5
-25 0 -14 -4 -3 20 6 -8 1 10 -10 -9 -19 -9 7
-6 12 11 19 0 2 -5 9 -4 23 6 -6 3 3 5 10 5
-10 16 11 0 10 -4 10 -5 -1 1 8 -3 -4 -3 12 -6
0 0 6 5 1 -1 3 0 -2 1 3 1 9 -6 -3 12 -8 4
-6 -11 -6 2 1 -2 -1 -10 1 -6 -4 -3 9 0 -11 11
30 11 4 -3 4 -16 -2 -4 14 -4 4 -2 10 -15 10
-3 5 11 5 3 1 13 -12 10 13 7 10 9 -3 8 -17 0
5 -16 -8 -3 -3 9 -8 -22 -6 10 -10 -3 -3 5 -12
0 11 22 0 -11 -5 -7 5 -1 11 -8 9 -4 -2 -2 11
1 2 5 -5 -7 -7 13 -7 -5 10 5 1 13 -3 -6 -9
-5 1 0 -3 5 0 1 -6 -10 -12 16 1 -2 7 0 1 10
4 0 24 6 13 10 -4 -11 12 6 7 -4 10 -2 -11 -3
1 -1 -7 1 -2 -1 -5 6 0 0 -7 -5 -6 8 -2 12 -4
-10 1 6 7 -2 7 -14 3 -10 -5 -9 -1 -9 18 -4 -3
-11 6 22 4 12 -5 -11 0 13 1 4 -3 2 -11 -6 -7
-4 2 14 3 -8 1 15 -7 -3 -13 -1 1 -4 8 11 8
-6 5 -2 2 8 10 -4 6 -5 -5 3 8 5 0 10 4 -5
13 4 24 -2 -7 -3 6 2 -5 4 10 -6 -10 -4 3 -2
-3 -7 -4 0 2 13 -2 -7 -1 -11 -3 17 -2 -2 -4
-14 5 -3 5 -4 2 -1 3 -12 -2 -7 4 -13 25 -5
-16 -7 10 12 -2 36 11 -7 -7 13 5 -7 1 11 -25
8 -16 -3 -1 10 -2 -5 -1 -9 -12 -6 -13 -6 4 -8
13 16 10 7 -1 -1 4 -9 25 0 -6 -1 7 0 -4 -7 2
-1 -2 5 -4 -5 -7 11 30 7 8 -9 2 -4 1 14 -5 7
-18 1 6 6 -4 10 1 -16 0 5 4 4 -1 -8 5 -4 -3
8 -5 3 -8 -6 15 0 -7 4 13 7 -1 4 -7 1 -4 -1
-11 -11 -3 -7 7 16 -6 -10 -9 -1 0 4 6 4 -1 1
2 -5 1 0 5 -11 -1 1 10 -1 2 0 0 -9 -6 5 -4
-4 -3 -6 -3 10 -1 3 4 -5 -5 5 -12 8 14 11 12
0 6 -7 8 -6 36 -9 4 1 1 6 6 -10 -1 1 -4 8 0
1 -8 8 10 12 -6 11 -5 0 -7 -8 -14 -13 0 11 4
2 3 -17 4 -4 0 -2 7 -7 14 -3 -4 -8 6 13 2 13
-9 -10 -9 20 5 -2 3 -2 -9 3 1 -2 2 5 1 -5 1
4 -5 -7 -2 -3 3 -3 5 8 10 2 0 -6 -1 3 7 -3
0 -2 0 -6 -5 -6 -2 -4 4 9 7 1 -5 5 2 -9 4 5
22 -3 3 0 -2 0 2 3 -3 -2 -7 14 -5 -5 9 4 0
10 -7 -2 0 7 4 6 -1 5 -6 8 -1 -9 -3 6 5 -2
-8 3 0 -3 -2 -4 -4 4 4 -7 -4 -1 1 -2 -3 12
-7 0 -1 -6 3 -1 -1 0 -2 -3 5 11 2 1 -5 1 0
4 2 -5 -1 -3 6 1 0 4 -4 6 7 -5 0 7 14 -2 -7
12 10 -2 10 -3 10 1 1 0 1 3 3 -7 22 -10 -2 4
2 4 9 -8 -3 9 -6 -6 1 -3 15 -5 -4 12 -6 5 -1
-6 -5 -7 -5 -2 0 -10 -3 -4 -2 -3 -16 -1 5 -6
-15 -2 -2 2 -6 11 14 4 6 -2 0 0 -10 28 -1 2
-14 -9 -7 10 2 -7 14 -8 -5 0 -9 2 2 -11 17 -8
-12 10 4 9 0 0 13 9 6 -4 13 8 -8 10 -25 0 10
11 -11 -11 -10 -25 -5 6 6 -9 -2 -1 -2 -1 36 -1
5 -2 5 -8 2 2 1 -3 5 6 13 14 0 -9 -7 -16 -13
3 1 0 -6 10 -20 -4 5 6 -7 9 7 -1 0 0 -3 1
-3 -6 -4 8 7 4 -10 3 0 -6 4 2 -1 18 -6 4 6
-5 -6 4 0 -16 -6 -3 7 -2 6 -3 -1 -3 1 9 -4
-8 -7 -6 0 0 -4 3 4 4 5 10 -14 6 5 2 1 -7 3
-16 -18 -1 -1 1 2 3 2 -14 5 -6 28 7 -4 -10 2
-2 -3 3 10 3 9 0 -4 10 -10 2 0 -3 -4 3 1 1
-16 -1 2 -2 -2 -1 7 0 -4 5 11 5 -1 -4 -2 -3
1 1 1 -2 3 -1 4 -9 -2 4 7 14 4 1 -2 6 -9 -3
7 6 5 5 1 4 -11 5 7 -4 -9 -4 -3 0 -5 -10 -6
9 -2 7 7 -5 -3 1 5 -5 -7 2 -3 -1 6 2 -4 2
-3 -1 9 -7 5 6 -4 4 22 -3 -1 6 -5 -5 -5 1 13
3 0 0 -2 0 4 2 -3 -12 -13 1 -1 -3 0 -1 -3
-15 -1 -12 20 -1 3 -7 1 14 -7 10 6 -5 8 5 -2
0 -8 10 -8 -5 -10 1 -3 36 17 -12 0 11 1 4 -14
1 5 -8 4 6 5 -7 -6 4 7 4 18 -7 2 2 1 -5 2
-4 6 3 1 -7 -2 3 -4 -2 -4 1 0 1 -7 -2 -3 2
2 -6 2 -2 -1 17 20 -11 3 7 0 0 0 -6 1 1 3 3
0 -3 -5 4 6 1 7 2 3 -3 0 0 1 -7 -8 0 13 13
-1 -8 0 -5 10 0 1 -5 14 -3 9 -7 2 4 -2 6 6
-12 -11 30 -5 -8 9 1 12 8 -8 5 -4 1 7 4 -4
-2 -12 6 -5 -7 -10 11 6 3 -10 3 1 -2 -12 -7
-5 1 2 -1 1 5 -8 1 -5 5 -6 14 1 0 -3 -9 -5
0 3 -5 22 -1 -4 -8 2 -7 -1 0 14 -6 -7 7 5 5
-3 3 3 15 6 -8 9 -11 -1 1 10 1 10 -5 6 15 13
-9 -16 -11 8 4 -5 11 -6 -8 -3 -16 3 -3 -5 11
7 -8 -1 36 1 -1 -15 -3 -1 8 -2 0 5 -19 9 1
11 8 1 -4 7 -5 -12 -5 -3 1 -10 3 13 10 0 -7
-2 -12 0 -1 10 -5 9 2 1 -5 5 -6 10 7 -5 1 0
9 -4 1 18 7 6 9 -4 4 -8 -2 1 -3 -6 6 -1 6
-7 -8 -4 8 3 -1 -4 1 -9 1 7 5 0 -3 -7 -6 5
1 12 -7 4 1 -3 0 6 -3 3 6 1 4 0 1 -8 -1 7
16 2 11 -2 -3 -7 0 -5 -1 -5 4 -3 3 -4 -8 4 2
-3 15 9 1 -19 9 10 1 -7 -13 -1 -13 4 10 -6 -2
0 -5 15 -9 13 7 9 5 13 -14 0 12 2 -15 6 2 36
1 -2 6 -6 -6 -2 7 -11 -6 -16 2 -9 -2 -2 0 6
-6 -9 0 -9 -6 9 13 -5 -1 -11 -6 4 -1 11 -3 10
1 -5 2 14 -2 0 5 3 1 -6 8 -7 -3 9 11 1 26
-2 -12 -4 -5 2 2 -3 -2 -6 7 -6 -11 -3 15 -2 1
2 -1 7 -3 -3 -3 -6 1 -3 4 -1 2 -5 3 -7 0 -4
2 0 6 -4 1 0 5 1 -8 -1 -1 -4 -2 -2 -2 14 -7
-1 -6 3 2 -1 -5 4 -1 1 1 0 3 1 3 8 4 -6 12
8 -6 8 -4 17 -8 -8 0 0 -3 -2 4 12 -11 -9 -3
10 4 0 -8 1 5 0 8 4 -3 6 -12 -7 28 -5 3 -3
-12 -1 -2 0 -3 -4 2 3 -11 -2 -4 -11 -7 12 -8
-17 -9 -2 8 -2 13 5 0 -7 5 0 2 -6 17 -7 -1
-10 -11 -2 4 3 -4 14 -2 -8 -7 -6 -4 -1 -5 22
1 -1 10 7 4 0 2 12 13 5 -6 10 -8 7 -10 11 4
0 -5 12 11 -2 16 -4 -9 -8 8 7 -5 5 -8 -16 -3
2 5 0 6 3 1 -6 0 -2 0 -6 -5 -6 3 1 34 14 -4
-6 4 2 4 6 -9 -3 1 -9 -11 9 -12 19 -6 5 1 -4
8 -4 10 -3 -6 -14 10 4 -1 -1 -12 -13 1 0 7 4
5 0 7 -7 5 1 -5 -2 2 3 -3 -1 14 30 -1 -5 -8
1 2 7 -4 -15 16 -3 6 -8 -4 0 -11 -16 0 -10 -6
-14 7 8 5 -13 2 6 -3 -6 10 3 9 -3 -4 2 -7 -3
4 7 -19 -3 -1 7 2 2 -12 10 -4 -1 26 1 3 -8
-1 0 11 1 1 13 0 -9 4 2 -6 -8 -3 1 5 5 -1
-5 -4 0 0 -1 6 -5 4 1 -4 -4 -9 -3 -6 -5 -4 5
9 -6 -5 -11 -3 -1 -1 7 -6 -5 1 16 3 4 2 -3 7
7 -8 -3 -4 -11 3 -5 2 -3 5 6 -2 -3 -1 3 -4
11 -6 5 1 -7 9 0 -8 3 -4 -12 4 4 -2 5 1 6 4
-6 -2 -5 -2 4 4 -8 3 3 22 5 5 1 -1 5 -6 5
-8 1 2 9 1 -3 0 7 2 5 4 -8 -3 4 -1 -6 0 -5
0 -6 -7 1 -3 -13 7 6 -12 -3 11 -1 -3 -16 -6 4
0 0 2 1 -8 4 5 20 -6 5 0 -1 0 -4 -5 -10 -5
-4 -2 9 1 -2 8 -4 -9 -6 -6 2 3 8 4 -2 0 10
-6 1 0 1 4 1 6 3 8 6 3 2 7 -1 -3 2 4 2 -1
2 5 -6 24 -9 -8 7 3 -3 -10 3 -12 23 -1 -8 -6
7 10 2 25 15 -3 3 7 -1 -4 0 13 -20 0 -16 -5
-1 18 7 -5 3 1 -7 -4 -9 -6 1 -4 12 6 7 0 -3
1 5 -9 32 2 -7 -2 9 4 -9 3 6 -10 -22 -10 -14
-4 -1 0 0 10 -17 -3 -9 6 -10 9 -4 0 -1 -10 -3
-7 2 -7 15 -4 -8 -8 -2 -11 1 2 13 -9 -4 11 7
-1 0 -8 2 32 3 -7 10 6 -8 3 -6 1 -6 -12 3 6
3 -6 -7 -1 4 0 -3 7 -3 6 5 -4 2 -6 0 2 3
-10 6 7 -4 4 -2 -3 0 3 5 -3 -15 1 7 5 -1 7
-7 3 24 -19 -3 -10 0 -4 3 -6 10 16 -10 -5 -12
-1 4 3 -4 -2 6 -5 -4 -4 6 3 -2 9 -1 2 -3 11
-8 -5 8 2 0 15 3 -11 -6 1 16 1 -8 -6 0 3 -2
-7 -19 30 -1 0 -6 -5 3 -4 -10 1 -5 -5 -2 7 13
4 0 0 5 0 -2 13 -7 4 -2 -2 -3 1 0 6 9 -12 3
-3 6 -2 1 -2 10 -9 -3 13 -3 5 -4 -3 9 10 -3
-1 26
-
NOTES
Constructed by Gabriele Nebe from the structure of P48n over sqrt{5},sqrt{13} using a totally positive generator Z2 of
one of the prime ideals diving 2
This lattice is invariant under the derived subgroup of
the (subgroup of the) automorphism group of P48n
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe