The Lattice LAMBDA(G1)
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 13:17:38 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
GRAM
DET
MINIMAL_NORM
MINVECS
KISSING_NUMBER
DENSITY
HERMITE_NUMBER
GROUP_ORDER
GROUP_GENERATORS
BACHER_POLYNOMIALS
PROPERTIES
REFERENCES
NOTES
LAST_LINE
-
NAME
LAMBDA(G1)
-
DIMENSION
32
-
GRAM
32 0
4
0 4
0 0 4
0 0 0 4
0 -2 -2 -2 4
2 0 2 -2 0 4
2 -2 0 2 0 0 4
-2 -2 2 0 0 0 0 4
0 0 0 0 0 0 0 0 4
0 0 0 0 0 0 0 0 0 4
0 0 0 0 0 0 0 0 -2 2 4
0 0 0 0 0 0 0 0 -2 2 2 4
0 0 0 0 0 0 0 0 -2 2 2 2 4
1 -1 0 2 -1 0 2 0 -1 -1 1 0 1 4
0 0 0 0 0 0 0 0 -2 2 2 2 2 0 4
2 -1 0 0 1 1 2 0 2 0 -1 -1 -1 0 0 4
0 0 0 0 0 0 0 0 -2 2 2 2 2 0 2 -1 4
0 -2 1 -1 1 1 1 2 -1 -1 0 0 -1 0 1 1 0 4
1 0 1 1 -1 0 1 0 0 0 0 1 -1 0 1 1 -1 1 4
0 0 1 0 0 1 0 1 0 2 0 0 1 -1 1 1 1 0 -1 4
0 0 0 0 0 0 0 0 -2 2 2 2 2 0 2 -1 2 0 0 1 4
-2 0 0 2 -1 -2 0 1 0 2 1 1 1 0 1 -1 1 -1 0 1 2 4
0 0 0 -1 0 1 0 0 -1 1 1 0 1 0 0 -1 0 0 -1 1 1 0 4
-1 0 0 -1 1 0 -2 1 1 1 0 0 -1 -2 0 0 0 0 0 1 -1 0 -1 4
1 0 -1 0 0 0 1 -1 -1 1 0 0 1 0 1 0 0 0 0 1 1 0 2 -1 4
-1 0 0 0 0 -1 0 1 2 0 -1 -1 -1 -1 -1 1 0 0 -1 0 0 1 -1 0 -1 4
1 1 -1 0 0 0 0 -1 1 1 -1 0 0 -1 0 1 0 -1 0 1 -1 -1 0 1 1 0 4
0 0 1 0 0 0 0 0 -1 1 1 2 0 -1 0 -1 1 0 1 0 0 0 0 1 -1 -1 0 4
0 -1 1 0 0 0 1 1 -1 -1 0 -1 -1 0 0 0 -1 2 1 0 -1 -1 1 0 1 -1 -1 1 4
2 -1 0 0 1 1 1 -1 0 0 -1 1 0 0 0 1 0 0 1 0 0 -1 -1 0 0 -1 1 1 -1 4
0 0 -1 1 0 -1 0 -1 2 0 -1 -2 -1 0 -2 0 -1 -2 -1 0 -2 0 0 1 0 0 1 0 0 0 4
0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 -1 -1 1 1 1 0 0 0 1 0 0 -1 0 1 4
-
DET
1
-
MINIMAL_NORM
4
-
MINVECS
-
KISSING_NUMBER
146880
-
DENSITY
-
HERMITE_NUMBER
4
-
GROUP_ORDER
2^13 3 5
-
GROUP_GENERATORS
13
32 32
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32 32
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1 1 0 0 1 0 1 1 2 -1 0 0 0 0 1 -2 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
-1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0
0 0 -1 0 0 1 -1 1 -2 3 0 -1 -1 0 -1 0 -1 0 0 0 -1 0 -1 -2 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 0 1 0 0 0 0 0 0 0 0
0 0 -2 0 -1 1 0 1 2 -2 0 -1 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 2 0 0 0 0
0 1 1 0 0 -1 0 1 -1 2 -1 0 -1 0 0 2 0 0 -2 -2 1 0 0 0 0 -1 0 0 0 0 0 0
1 1 0 -1 0 -1 1 1 -3 3 -1 -1 -1 0 0 0 -1 0 0 0 -2 0 0 0 0 0 -1 0 -2 0 0 0
0 0 2 0 1 -1 0 -1 -1 1 0 1 -1 0 -1 0 0 0 0 0 -1 0 0 0 0 0 0 -1 0 0 0 0
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0 -1 0 1 0 0 -1 -1 -1 2 0 -1 0 0 -1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 -1 0
0 -1 2 2 1 -1 -1 -2 2 0 0 0 0 0 -1 0 1 0 -1 -1 0 0 1 1 0 -1 1 -1 1 0 -3 1
32 32
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 0 0 0 0 0 0 0
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0 -1 -1 1 -1 1 0 0 1 -1 1 0 1 -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 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
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0 -1 -1 4 0 1 -3 -1 5 -2 1 0 2 -1 -1 0 2 1 -1 -1 1 0 1 0 0 -1 1 0 3 1 -3 1
32 32
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 0 0 0 0 0 0 0
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32 32
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32 32
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1 -1 1 2 1 -1 -1 -2 4 -2 1 0 1 0 0 -2 1 1 0 1 -1 0 1 1 1 0 0 0 0 0 -3 1
32 32
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1 0 3 0 1 -2 0 0 -3 3 -2 0 -2 0 0 2 -1 0 -2 -2 0 0 0 0 0 -2 0 0 -2 -2 0 0
0 -1 -2 4 0 1 -3 -2 10 -6 3 2 3 -1 -1 -2 3 2 0 1 1 0 1 0 1 -1 1 0 4 1 -3 2
1 -2 -1 4 1 1 -3 -2 11 -8 4 2 3 -1 0 -4 3 1 1 2 1 0 1 0 1 0 2 0 4 1 -3 2
1 -1 1 -1 0 -1 0 -1 -2 0 0 0 -1 0 0 0 -1 0 0 1 -1 1 0 0 0 0 0 0 -2 -1 0 0
1 -1 2 0 1 -1 0 -1 -2 1 0 0 -1 0 0 0 -1 0 0 0 -1 0 0 0 0 0 0 0 -2 -2 0 0
0 -1 2 0 1 -1 0 -1 -2 1 0 0 -1 0 0 0 -1 0 0 0 -1 0 0 0 0 0 0 0 -2 -1 0 0
1 -1 -1 0 0 1 0 0 1 -3 1 0 1 -1 1 -1 0 0 1 1 -1 1 0 0 1 1 0 1 -1 -1 0 0
0 0 0 3 1 0 -2 -1 7 -4 2 1 1 0 0 -2 2 1 0 1 0 0 1 0 1 -1 1 0 2 1 -3 2
1 -1 0 -1 0 0 1 -1 1 -3 0 0 1 0 1 -1 0 0 1 1 0 1 1 1 0 1 0 1 -1 -1 0 0
-1 1 0 -1 -1 -1 1 1 -1 2 0 -1 -1 0 0 1 0 0 -1 -1 0 -1 0 0 0 -1 -1 0 -1 1 0 0
0 0 1 0 0 0 0 0 -3 2 -1 -1 -1 0 0 1 -1 0 -1 -1 0 0 0 0 0 0 0 0 -1 0 0 0
1 -2 1 4 1 -1 -3 -2 7 -4 2 2 1 -1 0 -2 2 1 0 1 0 -1 1 0 1 -1 1 -1 2 0 -3 2
1 -2 -2 3 0 1 -3 -2 10 -7 3 2 3 -1 0 -3 3 1 1 2 0 1 1 0 1 0 1 0 4 1 -3 2
0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0
0 1 0 -1 0 0 1 1 0 -1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0
1 2 2 -4 1 -2 3 2 -6 4 -2 0 -3 1 1 0 -2 -1 0 0 -1 0 -1 -1 -1 0 -1 -1 -3 -1 3 -1
-
BACHER_POLYNOMIALS
1 32
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 0 1
x^4980*10 x^4953*4 x^4905*10 x^4884*40 x^4881*120 x^4872*20 x^4857*180 x^4848*2 x^4836*100 x^4833*322 x^4824*80 x^4812*120 x^4809*140 x^4800*40 x^4785*20 x^4764*10 x^4752*10 x^4728*8 x^4713*4 (3072x)
1 32
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
x^5016*8 x^5004*4 x^4992*2 x^4956*8 x^4944*12 x^4932*64 x^4920*16 x^4908*20 x^4905*32 x^4896*8 x^4893*64 x^4884*64 x^4872*52 x^4869*128 x^4860*16 x^4857*64 x^4848*146 x^4845*32 x^4836*64 x^4833*128 x^4824*52 x^4812*88 x^4809*16 x^4800*8 x^4797*32 x^4785*32 x^4776*32 x^4773*32 x^4737*16 (3840x)
1 32
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
x^5160*8 x^5052*8 x^5028*24 x^5016*4 x^4980*16 x^4968*16 x^4956*48 x^4941*128 x^4932*32 x^4929*32 x^4920*32 x^4908*136 x^4905*32 x^4884*64 x^4881*288 x^4872*12 x^4848*32 x^4836*40 x^4833*128 x^4812*64 x^4809*32 x^4800*32 x^4740*32 (960x)
1 32
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
x^5016*4 x^4992*2 x^4944*6 x^4941*8 x^4932*4 x^4920*4 x^4917*16 x^4908*16 x^4905*8 x^4896*16 x^4893*8 x^4884*4 x^4881*16 x^4872*204 x^4869*32 x^4860*72 x^4857*80 x^4848*120 x^4845*128 x^4836*24 x^4833*128 x^4824*24 x^4821*104 x^4812*88 x^4809*8 x^4800*16 x^4797*8 x^4788*4 x^4785*48 x^4776*12 x^4773*16 x^4740*12 (7680x)
1 32
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
x^5040*2 x^5004*4 x^4992*4 x^4965*16 x^4941*16 x^4932*16 x^4908*12 x^4896*90 x^4884*104 x^4881*32 x^4872*128 x^4869*96 x^4860*24 x^4857*64 x^4848*80 x^4845*80 x^4836*96 x^4833*96 x^4824*16 x^4821*80 x^4812*56 x^4809*96 x^4800*16 x^4752*16 (3840x)
1 32
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
x^5076*2 x^5028*2 x^5016*4 x^5004*4 x^4980*2 x^4968*8 x^4956*16 x^4944*8 x^4941*8 x^4932*10 x^4929*6 x^4920*16 x^4917*8 x^4908*4 x^4905*12 x^4896*52 x^4893*80 x^4884*84 x^4881*70 x^4872*44 x^4869*48 x^4860*72 x^4857*40 x^4848*24 x^4845*104 x^4836*80 x^4833*68 x^4824*64 x^4821*96 x^4812*48 x^4809*56 x^4800*8 x^4797*24 x^4785*56 x^4761*8 x^4737*4 (7680x)
1 32
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
x^5076*2 x^5028*6 x^5004*4 x^4980*6 x^4977*4 x^4968*28 x^4965*8 x^4956*12 x^4953*4 x^4944*8 x^4941*8 x^4932*18 x^4929*10 x^4920*32 x^4917*8 x^4908*20 x^4905*12 x^4893*104 x^4884*76 x^4881*50 x^4872*68 x^4869*32 x^4860*44 x^4857*78 x^4848*44 x^4845*96 x^4836*80 x^4833*80 x^4824*32 x^4821*96 x^4812*64 x^4809*10 x^4800*8 x^4797*16 x^4785*24 x^4752*16 x^4740*16 x^4737*16 (7680x)
1 32
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
x^5112*4 x^5064*8 x^5052*8 x^5016*20 x^5004*32 x^4980*8 x^4968*4 x^4956*32 x^4944*8 x^4932*16 x^4920*20 x^4908*24 x^4881*32 x^4872*48 x^4869*64 x^4860*96 x^4857*288 x^4848*152 x^4845*64 x^4833*32 x^4824*16 x^4821*64 x^4812*32 x^4800*64 x^4788*8 x^4776*64 x^4737*32 (960x)
1 32
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
x^5052*8 x^5016*2 x^4980*32 x^4968*16 x^4944*40 x^4932*8 x^4920*34 x^4908*8 x^4881*32 x^4872*20 x^4860*128 x^4857*32 x^4848*200 x^4836*24 x^4833*160 x^4824*48 x^4821*64 x^4812*224 x^4809*32 x^4800*96 x^4776*32 (960x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 1 0
x^5124*4 x^5064*2 x^5016*2 x^4980*8 x^4977*32 x^4968*14 x^4965*32 x^4956*8 x^4953*16 x^4944*4 x^4932*24 x^4929*16 x^4920*18 x^4917*64 x^4905*16 x^4893*32 x^4884*80 x^4872*132 x^4860*32 x^4857*144 x^4848*36 x^4836*12 x^4833*96 x^4824*40 x^4812*48 x^4809*176 x^4800*16 x^4797*96 x^4788*16 x^4776*8 x^4737*16 (1920x)
1 32
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
x^5400*8 x^5304*16 x^5208*40 x^5136*64 x^5124*80 x^5112*8 x^5064*16 x^5028*16 x^5016*128 x^5004*64 x^4980*16 x^4968*128 x^4956*64 x^4932*16 x^4920*128 x^4908*320 x^4785*128 (240x)
1 32
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 1 -1
x^4953*4 x^4944*2 x^4929*8 x^4920*16 x^4908*10 x^4905*4 x^4896*18 x^4893*72 x^4884*100 x^4881*32 x^4872*124 x^4869*80 x^4860*92 x^4857*64 x^4848*92 x^4845*168 x^4836*56 x^4833*68 x^4824*28 x^4821*120 x^4812*28 x^4809*28 x^4800*8 x^4797*8 x^4788*2 x^4776*8 (30720x)
1 32
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
x^5208*2 x^5064*4 x^5016*6 x^4980*8 x^4968*16 x^4956*16 x^4953*32 x^4944*8 x^4932*120 x^4920*20 x^4896*32 x^4872*104 x^4869*64 x^4860*8 x^4857*32 x^4848*88 x^4845*128 x^4836*64 x^4833*320 x^4824*64 x^4812*40 x^4788*32 x^4740*32 (960x)
1 32
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
x^5304*8 x^5256*16 x^5208*48 x^5160*8 x^5148*64 x^5112*40 x^5064*16 x^5028*64 x^4992*32 x^4980*64 x^4968*16 x^4944*128 x^4932*192 x^4896*160 x^4884*128 x^4848*128 x^4752*128 (120x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
x^5208*48 x^5112*40 x^5088*64 x^4908*640 x^4872*320 x^4713*128 (48x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0
x^5400*8 x^5304*32 x^5208*32 x^5160*24 x^5148*64 x^5112*16 x^5100*64 x^5064*32 x^5028*64 x^5016*32 x^4992*32 x^4980*192 x^4968*32 x^4944*64 x^4932*128 x^4920*8 x^4896*128 x^4884*128 x^4848*32 x^4764*128 (120x)
1 32
0 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
x^5400*40 x^5208*8 x^5160*40 x^5148*64 x^5112*160 x^5064*80 x^5016*80 x^4944*320 x^4932*320 x^4848*128 (24x)
1 32
0 0 0 0 0 0 0 0 5 -6 1 1 1 0 1 0 2 0 0 0 2 1 1 1 1 -1 1 1 1 0 0 0
x^5148*22 x^5136*20 x^5100*10 x^5088*4 x^4953*44 x^4932*80 x^4929*80 x^4905*50 x^4896*60 x^4893*160 x^4881*120 x^4869*80 x^4857*220 x^4836*60 x^4833*42 x^4824*80 x^4809*20 x^4773*80 x^4728*8 (1536x)
1 32
0 0 0 0 0 0 0 1 -2 2 0 0 -2 0 0 0 -1 -1 -1 0 0 -1 -1 -1 0 0 0 0 0 0 0 0
x^5256*8 x^5160*8 x^5124*32 x^5064*8 x^4980*32 x^4968*64 x^4944*64 x^4920*96 x^4908*64 x^4896*96 x^4872*64 x^4860*64 x^4836*96 x^4824*256 x^4821*256 x^4752*16 x^4740*16 (480x)
1 32
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
x^5400*4 x^5304*12 x^5208*4 x^5112*24 x^5076*128 x^5064*32 x^5040*32 x^5016*44 x^4992*96 x^4980*64 x^4968*80 x^4932*128 x^4920*48 x^4872*96 x^4836*128 x^4824*64 x^4788*256 (120x)
1 32
0 0 0 0 0 0 1 0 -2 1 0 0 0 -1 0 -1 -1 0 1 1 -1 -1 0 0 0 1 -1 -1 -1 0 1 0
x^5124*32 x^5112*24 x^4968*128 x^4896*320 x^4860*256 x^4857*128 x^4821*256 x^4812*64 x^4740*32 (480x)
-
PROPERTIES
Unimodular=1
-
REFERENCES
H. Koch, B.B. Venkov,
\"Uber ganzzahlige unimodulare euklidische Gitter.
Journal f\"ur die reine und angewandte Mathematik 398 (1989), 144-168
H. Koch, B.B. Venkov, \"Uber gerade unimodulare
Gitter der Dimension 32, III
Mathem. Nachr. 152 (1991), 191-213
-
NOTES
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe