The Lattice dim24modular13Group6912
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 Di 9. Jun 19:06:07 CEST 2020
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIM
GRAM
DET
GROUP_ORDER
GROUP_GENERATORS
PROPERTIES
MINIMAL_NORM
KISSING_NUMBER
NOTES
REFERENCES
LAST_LINE
-
NAME
dim24modular13Group6912
-
DIM
24
-
GRAM
24 24
12 -6 6 6 4 4 0 0 0 0 -3 -1 2 -5 5 -2 -5 5 4 -3 -4 -6 6 -5
-6 10 -6 0 -4 0 0 0 0 0 -2 -1 -2 0 -4 2 0 -5 -2 0 0 5 -1 5
6 -6 10 0 0 2 0 0 0 0 -2 2 -1 0 5 1 0 5 3 0 -3 -1 3 -3
6 0 0 10 2 0 0 0 0 0 -5 -3 0 -4 0 0 -4 1 3 -5 -1 -3 1 1
4 -4 0 2 12 -4 0 0 0 0 1 -3 0 -6 -1 0 -6 6 3 -1 -2 -4 1 -7
4 0 2 0 -4 12 0 0 0 0 -1 -2 5 0 0 -5 0 -1 3 0 -5 -1 4 0
0 0 0 0 0 0 12 -6 6 6 3 -6 5 -2 -3 5 2 3 3 -3 -4 0 -3 0
0 0 0 0 0 0 -6 10 -6 0 -5 3 -5 4 5 -5 0 -3 -3 0 4 2 0 0
0 0 0 0 0 0 6 -6 10 0 1 -1 4 0 -3 4 0 3 5 0 -1 2 2 -2
0 0 0 0 0 0 6 0 0 10 -2 -1 0 -3 0 0 -1 -2 0 -5 -3 0 -3 -2
-3 -2 -2 -5 1 -1 3 -5 1 -2 12 -2 3 -1 -2 3 2 3 -3 5 0 -4 -4 -1
-1 -1 2 -3 -3 -2 -6 3 -1 -1 -2 12 -6 4 3 0 1 -2 -2 1 4 3 1 -3
2 -2 -1 0 0 5 5 -5 4 0 3 -6 12 0 -4 -1 0 1 3 0 -4 -3 3 2
-5 0 0 -4 -6 0 -2 4 0 -3 -1 4 0 14 2 0 7 -4 0 1 7 7 -2 4
5 -4 5 0 -1 0 -3 5 -3 0 -2 3 -4 2 12 -1 0 -1 -2 0 2 -1 2 -3
-2 2 1 0 0 -5 5 -5 4 0 3 0 -1 0 -1 12 0 4 1 0 -2 2 -4 -1
-5 0 0 -4 -6 0 2 0 0 -1 2 1 0 7 0 0 12 -3 0 0 2 5 -4 5
5 -5 5 1 6 -1 3 -3 3 -2 3 -2 1 -4 -1 4 -3 12 3 2 -3 -4 1 -5
4 -2 3 3 3 3 3 -3 5 0 -3 -2 3 0 -2 1 0 3 12 -3 -5 2 3 -2
-3 0 0 -5 -1 0 -3 0 0 -5 5 1 0 1 0 0 0 2 -3 10 1 0 2 0
-4 0 -3 -1 -2 -5 -4 4 -1 -3 0 4 -4 7 2 -2 2 -3 -5 1 12 1 -3 2
-6 5 -1 -3 -4 -1 0 2 2 0 -4 3 -3 7 -1 2 5 -4 2 0 1 12 0 3
6 -1 3 1 1 4 -3 0 2 -3 -4 1 3 -2 2 -4 -4 1 3 2 -3 0 12 -2
-5 5 -3 1 -7 0 0 0 -2 -2 -1 -3 2 4 -3 -1 5 -5 -2 0 2 3 -2 14
-
DET
13^12
-
GROUP_ORDER
2^8 * 3^3
-
GROUP_GENERATORS
[ 1 0 0 0 0 0 0 0 0 0 0 0 -1 -4 8 -2 -2 0 -1 -4 8 -2 -2 0]
[ 0 1 0 0 0 0 0 0 0 0 0 0 0 -1 4 8 -2 -2 0 -1 4 8 -2 -2]
[ 0 0 1 0 0 0 0 0 0 0 0 0 0 -3 7 -4 -2 0 0 -3 7 -4 -2 0]
[ 0 0 0 1 0 0 0 0 0 0 0 0 1 -1 6 7 -4 -2 1 -1 6 7 -4 -2]
[ 0 0 0 0 1 0 0 0 0 0 0 0 1 -3 10 -2 -3 -2 1 -3 10 -2 -3 -2]
[ 0 0 0 0 0 1 0 0 0 0 0 0 0 -6 15 -3 -5 -1 0 -6 15 -3 -5 -1]
[ 0 0 0 0 0 0 1 0 0 0 0 0 -1 -4 8 -2 -2 0 -1 -4 8 -2 -2 0]
[ 0 0 0 0 0 0 0 1 0 0 0 0 0 -1 4 8 -2 -2 0 -1 4 8 -2 -2]
[ 0 0 0 0 0 0 0 0 1 0 0 0 0 -3 7 -4 -2 0 0 -3 7 -4 -2 0]
[ 0 0 0 0 0 0 0 0 0 1 0 0 1 -1 6 7 -4 -2 1 -1 6 7 -4 -2]
[ 0 0 0 0 0 0 0 0 0 0 1 0 1 -3 10 -2 -3 -2 1 -3 10 -2 -3 -2]
[ 0 0 0 0 0 0 0 0 0 0 0 1 0 -6 15 -3 -5 -1 0 -6 15 -3 -5 -1]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1]
[ 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0]
[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0]
[-1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[2 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[-4 0 4 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 -17 -5 -2 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[-7 -3 27 6 -1 -13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[-6 0 2 -1 -2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 2 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 -4 0 4 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 -17 -5 -2 13 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 -7 -3 27 6 -1 -13 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 -6 0 2 -1 -2 3 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -6 -9 13 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -3 -4 5 0 1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 -4 7 4 -1 -1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 4 -9 -5 4 1]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -11 -21 36 21 -5 -5]
[-4 -2 -4 1 1 0 9 -2 -4 1 1 0 -1 0 0 0 0 0 0 0 0 0 0 0]
[9 1 -2 0 -1 0 -17 1 11 0 -1 0 6 9 -13 0 0 0 0 0 0 0 0 0]
[3 0 -2 0 -1 1 -7 0 3 0 0 1 3 4 -5 0 -1 0 0 0 0 0 0 0]
[-1 0 -8 -2 -1 6 0 -1 10 3 1 -7 2 4 -7 -4 1 1 0 0 0 0 0 0]
[-2 -2 4 2 -1 -2 0 1 -16 -4 0 11 -1 -4 9 5 -4 -1 0 0 0 0 0 0]
[-2 2 -37 -10 -5 28 -3 -6 54 16 5 -37 11 21 -36 -21 5 5 0 0 0 0 0 0]
[-1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[-8 2 -12 -6 -3 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[-2 2 -7 -2 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[-22 7 -30 -17 -9 38 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[-2 7 -18 -4 2 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[-11 6 -21 -9 -3 19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 -8 2 -12 -6 -3 14 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 -2 2 -7 -2 0 4 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 -22 7 -30 -17 -9 38 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 -2 7 -18 -4 2 6 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 -11 6 -21 -9 -3 19 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 -3 -2 -64 3 14 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 1 0 -5 -46 3 10 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 -2 2 -19 0 4 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 2 6 -14 -38 5 8 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 -11 11 -99 0 21 0 0 0 0 0 0]
[-9 2 4 -1 -1 0 4 2 4 -1 -1 0 0 0 0 0 0 0 1 0 0 0 0 0]
[-52 17 -80 -40 -19 91 52 -9 76 38 20 -91 0 0 0 0 0 0 -1 3 2 64 -3 -14]
[-41 14 -59 -30 -14 67 37 -6 56 26 13 -63 0 0 0 0 0 0 -1 0 5 46 -3 -10]
[-17 6 -21 -12 -6 26 16 -3 21 11 6 -26 0 0 0 0 0 0 0 2 -2 19 0 -4]
[-40 16 -55 -28 -12 60 27 -5 47 18 7 -44 0 0 0 0 0 0 -2 -6 14 38 -5 -8]
[-86 30 -111 -62 -31 136 83 -16 109 58 32 -137 0 0 0 0 0 0 0 11 -11 99 0
-21]
[2 -2 -4 1 1 0 -3 2 4 -1 -1 0 2 8 -16 4 4 0 0 0 0 0 0 0]
[-3 2 -4 -3 -2 6 3 -3 6 4 2 -7 2 0 2 -12 -2 2 0 0 0 0 0 0]
[4 -1 -1 2 1 -2 -4 2 7 -1 -1 -2 2 8 -16 6 4 0 0 0 0 0 0 0]
[2 3 10 1 -1 -6 -2 -4 -11 0 1 7 2 -6 20 0 -10 -2 0 0 0 0 0 0]
[1 1 -14 -1 -1 10 4 0 39 7 2 -29 4 18 -40 -10 12 6 0 0 0 0 0 0]
[6 -1 -1 3 1 -3 -6 2 10 -1 -1 -3 4 12 -22 8 4 0 0 0 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 -2 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 -1 -6 -1 0 4 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 1 -1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 -5 -1 -25 -6 -1 19 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 -1 -9 -2 0 6 0 0 0 0 0 0 0 0 0 0 0 0]
[-10 8 16 -4 -4 0 14 -6 -12 3 3 0 -7 -26 52 -13 -13 0 0 0 0 0 0 0]
[12 -10 20 14 8 -26 -9 14 -28 -17 -6 26 -9 -5 1 45 5 -7 0 0 0 0 0 0]
[4 -4 20 8 4 -18 -1 7 -27 -11 -3 20 -9 -14 22 26 -2 -5 0 0 0 0 0 0]
[-2 0 2 0 0 0 3 1 -2 -1 0 0 -3 -5 7 1 0 0 0 0 0 0 0 0]
[0 0 30 6 2 -20 2 3 -42 -11 -2 28 -11 -27 51 20 -11 -6 0 0 0 0 0 0]
[-6 -2 6 2 2 -2 14 6 -2 -4 0 -5 -13 -16 17 9 5 0 0 0 0 0 0 0]
[1 -6 -12 3 3 0 -10 8 16 -4 -4 0 6 26 -52 13 13 0 1 0 0 0 0 0]
[-9 1 -2 -4 -6 13 12 -10 20 14 8 -26 4 -5 14 -33 -8 6 5 10 -15 -12 3 1]
[-5 -1 -3 -1 -3 7 4 -4 20 8 4 -18 5 6 -9 -17 -1 4 4 8 -13 -9 3 1]
[0 -1 -1 1 0 0 -2 0 2 0 0 0 2 4 -6 1 0 0 1 1 -1 -2 0 0]
[-2 -3 -3 2 -1 2 0 0 30 6 2 -20 7 18 -34 -9 6 4 4 9 -17 -11 5 2]
[-5 -3 -7 1 -3 8 -6 -2 6 2 2 -2 8 10 -11 -3 -5 1 5 6 -6 -6 0 -1]
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PROPERTIES
INTEGRAL=1
MODULAR=13
-
MINIMAL_NORM
8
-
KISSING_NUMBER
72
-
NOTES
Even 13-modular lattice constructed from totally definite quaternion algebra over maximal real subfield of cyclotomic field.
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REFERENCES
Xiaolu Hou, "Algebraic Constructions of Modular Lattices (Doctoral Thesis)", in preparation, Nanyang Technological University, Singapore.
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe