The Lattice LAMBDA(C4)
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 13:17:34 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(C4)
-
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 2 0 -1 0 0 2 0 0 -1 1 -1 4
0 0 0 0 0 0 0 0 -2 2 2 2 2 0 4
1 -1 0 2 -1 0 2 0 0 -2 -1 -1 -1 0 0 4
0 0 0 0 0 0 0 0 -2 2 2 2 2 0 2 -1 4
1 2 0 0 -1 1 0 -2 0 0 -1 -1 0 -1 0 0 -1 4
1 2 0 0 -1 0 0 -2 0 0 0 0 -1 0 -1 -1 1 1 4
0 1 1 -1 -1 1 -1 0 0 -2 -1 -1 -2 1 0 1 -2 1 0 4
1 1 2 0 -2 2 0 0 -1 -1 0 1 0 1 0 1 -1 1 0 2 4
2 0 0 1 -1 1 2 -1 -1 1 1 2 1 0 1 1 0 1 0 0 2 4
-1 1 0 0 0 -1 -1 0 -1 -1 0 -1 1 -1 -1 -1 1 0 1 -1 -1 -2 4
-1 0 1 2 -2 -1 1 1 0 0 1 1 0 1 0 1 0 -1 0 0 1 1 -1 4
0 0 0 0 0 0 0 0 -2 2 2 2 2 0 2 -1 2 0 0 -1 0 1 0 0 4
2 1 -1 1 -1 0 1 -2 0 0 -1 -1 0 -1 0 1 0 2 1 0 0 1 0 -1 1 4
1 -1 1 -1 0 2 0 1 1 1 0 -1 0 0 0 0 0 0 -1 0 0 0 -1 -1 -1 0 4
1 0 0 -2 1 2 -1 -1 1 -1 -1 -2 -1 -1 -1 0 -1 1 0 1 0 -1 0 -2 0 1 1 4
1 0 -1 -1 1 0 0 -1 -1 1 0 0 2 -1 1 -1 1 1 0 -1 -1 0 1 -2 0 1 1 0 4
-1 1 -1 2 -1 -2 0 0 -1 -1 0 0 0 -1 0 1 0 0 0 0 0 0 1 1 -1 0 -1 -2 0 4
0 0 0 -2 1 1 -1 0 1 -1 -1 -1 -2 1 -2 -1 -1 0 1 1 0 -1 0 -1 0 0 0 2 -1 -2 4
0 0 1 -1 0 1 -1 1 -1 0 1 1 0 1 1 0 0 -1 -1 1 1 0 -1 0 1 -1 0 0 -1 -1 1 4
-
DET
1
-
MINIMAL_NORM
4
-
MINVECS
-
KISSING_NUMBER
146880
-
DENSITY
-
HERMITE_NUMBER
4
-
GROUP_ORDER
2^16 3
-
GROUP_GENERATORS
13
32 32
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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 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
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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
1 0 -1 0 -1 0 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0
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0 1 -1 1 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 -1 0 0
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0 -1 0 0 1 1 -1 0 2 -1 1 1 -1 1 0 0 0 1 0 0 0 0 1 1 1 1 0 0 1 1 -1 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
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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32 32
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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
1 0 -1 1 0 1 -1 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0
0 0 -1 0 0 1 0 0 0 1 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 1 0 0
-1 -1 0 1 2 -1 0 0 2 -1 0 1 0 0 0 -1 1 1 1 1 1 1 2 1 0 1 2 1 0 0 -1 2
0 2 1 -1 -1 0 1 0 -3 0 -1 0 0 -1 -1 0 -1 -1 -1 -1 -1 -1 -2 -1 0 0 0 -1 -1 -1 0 -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^5004*4 x^4980*16 x^4965*8 x^4956*4 x^4941*16 x^4932*4 x^4920*8 x^4917*24 x^4908*52 x^4905*16 x^4896*36 x^4893*48 x^4884*80 x^4881*8 x^4872*90 x^4869*104 x^4860*96 x^4857*80 x^4848*84 x^4845*64 x^4836*20 x^4833*40 x^4824*82 x^4821*184 x^4812*40 x^4809*32 (12288x)
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^5100*2 x^5076*4 x^5052*4 x^5016*2 x^4980*4 x^4977*16 x^4968*16 x^4965*2 x^4956*10 x^4941*4 x^4932*40 x^4920*2 x^4917*8 x^4905*16 x^4896*24 x^4893*60 x^4884*48 x^4881*8 x^4872*92 x^4869*52 x^4860*68 x^4857*8 x^4848*72 x^4845*186 x^4836*48 x^4833*48 x^4824*28 x^4821*116 x^4812*88 x^4809*32 x^4800*16 x^4797*32 x^4788*8 x^4776*16 x^4773*44 x^4764*8 x^4749*4 x^4701*4 (6144x)
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^5112*2 x^5088*4 x^5064*2 x^5040*4 x^5016*4 x^4992*4 x^4977*32 x^4968*2 x^4965*8 x^4956*22 x^4953*16 x^4944*4 x^4932*16 x^4929*16 x^4920*4 x^4917*16 x^4908*16 x^4905*16 x^4896*36 x^4893*24 x^4884*12 x^4881*32 x^4872*6 x^4869*24 x^4860*58 x^4857*208 x^4848*172 x^4845*72 x^4836*112 x^4833*16 x^4824*18 x^4812*80 x^4809*48 x^4800*48 x^4797*32 x^4788*4 x^4776*18 x^4773*16 x^4752*16 (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 1 1 0
x^5100*2 x^5052*2 x^5040*4 x^5016*4 x^4980*8 x^4968*8 x^4965*6 x^4956*12 x^4944*8 x^4941*4 x^4932*8 x^4929*16 x^4920*4 x^4917*16 x^4908*24 x^4905*16 x^4896*80 x^4893*12 x^4884*16 x^4872*80 x^4869*88 x^4860*68 x^4848*76 x^4845*118 x^4836*64 x^4824*132 x^4821*124 x^4812*32 x^4800*96 x^4797*48 x^4788*16 x^4776*16 x^4773*16 x^4749*12 x^4701*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 1 0 0 0 0
x^5208*4 x^5172*16 x^5160*4 x^5112*4 x^5076*16 x^5064*12 x^4968*72 x^4956*32 x^4920*16 x^4917*64 x^4884*208 x^4872*8 x^4860*64 x^4848*160 x^4836*128 x^4824*160 x^4797*192 x^4788*16 x^4776*64 (384x)
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^5268*8 x^5172*16 x^5160*4 x^5112*8 x^5076*16 x^5064*12 x^5040*16 x^5016*4 x^4980*8 x^4968*72 x^4944*32 x^4932*64 x^4920*12 x^4917*64 x^4908*128 x^4893*64 x^4884*136 x^4872*200 x^4860*128 x^4848*80 x^4845*64 x^4824*32 x^4788*8 x^4773*64 (384x)
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 1 0 0 0 0 0 0 0
x^5496*8 x^5304*24 x^5208*32 x^5160*24 x^5124*64 x^5112*112 x^5064*48 x^5052*64 x^5040*64 x^5016*80 x^4992*64 x^4968*16 x^4956*128 x^4932*128 x^4920*192 x^4860*64 x^4848*128 (96x)
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*6 x^5064*4 x^4980*8 x^4968*4 x^4956*16 x^4944*8 x^4932*48 x^4920*54 x^4896*48 x^4884*48 x^4881*64 x^4872*68 x^4860*64 x^4857*64 x^4848*88 x^4845*64 x^4833*64 x^4812*96 x^4809*256 x^4800*32 x^4797*32 x^4788*8 x^4776*32 x^4773*32 x^4752*32 (768x)
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 1 0 0 0
x^4992*2 x^4980*24 x^4968*16 x^4956*40 x^4953*8 x^4944*10 x^4941*8 x^4932*24 x^4929*8 x^4920*12 x^4917*16 x^4908*32 x^4905*8 x^4896*56 x^4893*72 x^4884*64 x^4881*16 x^4872*36 x^4869*88 x^4860*16 x^4857*8 x^4848*40 x^4845*136 x^4836*104 x^4833*56 x^4824*48 x^4821*88 x^4812*72 x^4809*56 x^4800*4 x^4797*8 x^4788*8 x^4776*16 x^4773*32 x^4752*8 (6144x)
1 32
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
x^5112*4 x^5040*6 x^5016*8 x^4992*16 x^4968*16 x^4956*16 x^4944*8 x^4941*64 x^4932*56 x^4920*8 x^4908*16 x^4896*86 x^4893*80 x^4884*56 x^4872*44 x^4869*32 x^4860*224 x^4857*16 x^4848*64 x^4845*112 x^4836*16 x^4833*16 x^4824*48 x^4821*48 x^4812*64 x^4800*4 x^4797*16 x^4788*32 x^4776*16 x^4773*32 x^4764*16 (3072x)
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 0 0
x^5112*4 x^5076*8 x^5064*8 x^5016*20 x^4992*8 x^4980*32 x^4968*4 x^4956*16 x^4932*48 x^4920*20 x^4884*48 x^4869*32 x^4857*320 x^4848*136 x^4836*64 x^4833*128 x^4824*112 x^4812*96 x^4797*96 x^4788*8 x^4752*32 (768x)
1 32
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 0
x^5004*2 x^4968*4 x^4956*4 x^4953*8 x^4941*12 x^4932*20 x^4920*8 x^4917*16 x^4908*12 x^4896*64 x^4893*6 x^4884*44 x^4881*16 x^4872*48 x^4869*40 x^4860*58 x^4857*16 x^4848*120 x^4845*168 x^4836*136 x^4833*32 x^4824*128 x^4821*108 x^4812*72 x^4809*24 x^4800*24 x^4797*24 x^4773*10 x^4764*16 (6144x)
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 -1 0 0 0 0 0 0 0
x^5400*8 x^5304*32 x^5208*24 x^5160*24 x^5124*64 x^5112*32 x^5076*64 x^5064*16 x^5016*32 x^4968*32 x^4956*128 x^4944*128 x^4932*256 x^4920*144 x^4860*128 x^4752*128 (96x)
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*16 x^5208*40 x^5160*32 x^5124*64 x^5112*24 x^5064*8 x^5040*64 x^5016*48 x^4980*64 x^4968*64 x^4956*32 x^4944*256 x^4920*32 x^4908*128 x^4896*32 x^4884*64 x^4872*80 x^4860*32 x^4848*32 x^4740*128 (192x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 -1 1 0 0 0 -1 0 0 0 0 0 1 0
x^5040*4 x^4944*16 x^4920*24 x^4917*32 x^4908*16 x^4896*42 x^4893*16 x^4884*32 x^4881*32 x^4872*128 x^4869*208 x^4860*112 x^4857*16 x^4848*2 x^4845*96 x^4836*32 x^4833*64 x^4824*80 x^4821*80 x^4812*128 x^4809*32 x^4785*16 x^4776*16 x^4773*16 (3072x)
1 32
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 1 -1
x^4992*4 x^4965*16 x^4956*8 x^4944*4 x^4941*32 x^4932*8 x^4908*16 x^4896*50 x^4893*64 x^4884*96 x^4881*56 x^4872*8 x^4869*48 x^4860*136 x^4857*32 x^4848*74 x^4845*192 x^4836*112 x^4833*32 x^4824*96 x^4821*96 x^4812*16 x^4800*36 x^4785*8 (6144x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 1 0 0 1 0 -1 -1 0 0 0 0 0 0 0 0 0
x^5268*16 x^5172*16 x^5112*20 x^5088*16 x^5076*32 x^5064*12 x^5040*16 x^5016*12 x^4968*12 x^4956*160 x^4932*128 x^4920*232 x^4896*64 x^4893*64 x^4872*56 x^4848*128 x^4845*64 x^4800*64 x^4797*64 x^4773*64 (384x)
1 32
0 0 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 0 0 0 0 0
x^5304*8 x^5256*16 x^5208*48 x^5172*64 x^5160*8 x^5112*48 x^5052*64 x^5040*32 x^4992*32 x^4980*128 x^4968*16 x^4956*64 x^4944*32 x^4920*8 x^4908*128 x^4896*288 x^4872*64 x^4824*64 x^4740*128 (96x)
1 32
0 0 0 0 0 0 0 0 0 0 0 1 -1 0 1 0 -1 0 0 0 -1 1 2 1 0 0 1 1 0 0 0 0
x^5256*8 x^5160*24 x^5112*24 x^4992*32 x^4968*72 x^4956*64 x^4944*64 x^4932*64 x^4920*56 x^4896*256 x^4884*32 x^4872*64 x^4860*192 x^4836*192 x^4800*32 x^4764*64 (384x)
1 32
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
x^5544*8 x^5400*16 x^5208*80 x^5172*128 x^5160*80 x^5040*128 x^5016*32 x^4992*128 x^4956*384 x^4848*128 x^4800*128 (24x)
1 32
0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
x^5496*16 x^5304*32 x^5160*104 x^5124*64 x^5112*144 x^5064*64 x^5052*128 x^5016*32 x^4968*16 x^4956*256 x^4896*256 x^4884*128 (24x)
1 32
0 0 0 0 0 0 0 0 0 0 1 -1 1 1 -2 0 1 0 0 1 0 0 -1 -1 0 0 -1 0 0 0 -1 0
x^5088*2 x^5040*8 x^4992*8 x^4977*32 x^4968*8 x^4965*32 x^4956*40 x^4944*18 x^4941*32 x^4932*32 x^4920*56 x^4917*64 x^4908*32 x^4896*56 x^4884*64 x^4872*72 x^4869*80 x^4860*32 x^4848*4 x^4836*224 x^4833*32 x^4824*104 x^4821*96 x^4800*16 x^4776*16 x^4773*64 x^4749*16 (3072x)
1 32
0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0 0 0 0
x^5304*16 x^5208*32 x^5160*24 x^5112*48 x^5028*64 x^4968*32 x^4956*384 x^4944*128 x^4896*128 x^4872*256 x^4788*128 (24x)
1 32
0 0 0 0 0 0 0 0 0 1 0 -1 -1 0 -1 0 1 0 -1 0 1 0 0 0 0 0 -1 0 1 0 0 0
x^5172*12 x^5124*34 x^5076*8 x^5028*2 x^4977*4 x^4953*4 x^4932*128 x^4929*36 x^4905*112 x^4896*48 x^4881*128 x^4857*168 x^4848*64 x^4836*16 x^4833*136 x^4824*288 x^4809*32 x^4761*4 x^4752*4 x^4740*12 (1536x)
1 32
0 0 0 0 0 0 0 0 1 -1 1 0 0 0 0 0 0 0 0 0 1 -1 -1 -1 1 0 0 -1 0 0 0 -1
x^5028*4 x^4992*8 x^4977*4 x^4953*4 x^4929*4 x^4905*48 x^4896*50 x^4884*30 x^4881*16 x^4872*32 x^4860*32 x^4857*40 x^4848*88 x^4836*136 x^4833*296 x^4824*96 x^4812*32 x^4809*192 x^4800*74 x^4788*2 x^4785*16 x^4761*4 x^4752*8 x^4740*24 (3072x)
1 32
0 0 0 0 0 0 0 1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 1 -1 1 0 0 0 0
x^5160*24 x^5112*32 x^4968*128 x^4920*64 x^4908*256 x^4896*128 x^4872*32 x^4848*256 x^4824*128 x^4812*128 x^4740*64 (96x)
1 32
0 0 0 0 0 0 0 1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 -1 1 0 0 0 0
x^5160*48 x^4968*40 x^4908*128 x^4896*128 x^4884*128 x^4872*32 x^4848*384 x^4812*256 x^4776*32 x^4740*64 (48x)
1 32
0 0 0 0 0 0 0 1 -1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 1 -1 1 0 0 0 0
x^5544*8 x^5160*8 x^5112*32 x^5064*96 x^5028*128 x^4968*40 x^4920*32 x^4908*128 x^4896*64 x^4872*512 x^4800*128 x^4752*64 (48x)
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^5208*24 x^5160*24 x^5064*32 x^5016*8 x^5004*128 x^4992*128 x^4956*128 x^4920*96 x^4872*160 x^4860*256 x^4800*256 (48x)
1 32
0 0 0 0 0 1 -1 -1 -1 0 0 -2 0 1 0 0 -1 -1 0 -1 0 0 -1 0 1 0 0 -1 0 0 0 -1
x^4929*8 x^4920*24 x^4917*16 x^4905*16 x^4896*20 x^4893*48 x^4884*72 x^4872*72 x^4869*128 x^4860*104 x^4857*64 x^4848*138 x^4845*128 x^4836*120 x^4833*32 x^4824*40 x^4821*128 x^4812*24 x^4809*40 x^4800*2 x^4788*16 (12288x)
1 32
0 0 0 0 0 1 0 0 -1 0 0 1 0 0 0 0 -1 0 0 0 -1 -1 0 1 -1 1 0 0 0 0 0 0
x^5160*24 x^5112*32 x^5004*64 x^4992*96 x^4968*72 x^4944*32 x^4920*16 x^4908*64 x^4896*64 x^4884*320 x^4872*128 x^4848*192 x^4812*64 x^4776*72 (384x)
1 32
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 0 0
x^5544*8 x^5208*16 x^5160*8 x^5100*128 x^5064*96 x^5016*16 x^4968*104 x^4956*128 x^4944*128 x^4920*96 x^4860*128 x^4824*128 x^4800*256 (24x)
1 32
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 0 0 0 0
x^5544*8 x^5208*16 x^5160*32 x^5112*64 x^5100*128 x^5088*64 x^5064*32 x^5040*64 x^5016*48 x^4968*48 x^4956*256 x^4920*160 x^4824*256 x^4776*64 (48x)
-
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