格子LAMBDA(G3)
格目录中的条目,这是一个联合项目
Gabriele Nebe,亚琛RWTH大学(nebe@math.rwth-aachen.de公司)和
尼尔·J·A·斯隆(njasloane@gmail.com)
上次修改时间:2014年7月18日星期五13:17:41 CEST
索引文件|缩写
此文件的内容
名称
尺寸
格拉姆
DET公司
最小_形式
MINVECS公司
亲吻_编号
密度
HERMITE_NUMBER公司
组订单(_O)
发电机组
学士_心理学
属性
参考文献
笔记
最后一行
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名称
兰巴达(G3)
-
尺寸
32
-
格拉姆
32 0
4
0 4
0 0 4
0 -1 -1 4
-1 0 1 1 4
1 -1 0 1 0 4
-1 1 0 0 1-1 4
1 0 -1 0 -1 1 0 4
0 1 1 -1 1 -1 1 -1 4
0 1 0 0 1 1 1 0 1 4
0 -1 1 0 0 -1 -1 -2 1 0 4
-1 0 -1 -1 0 -1 1 0 0 -1 -1 4
-1 -1 0 0 -1 0 -1 -1 -1 -1 1 0 4
1 0 -1 1 -1 0 -1 -1 -1 0 1 -1 0 4
-1 2 0 -1 1 0 1 1 1 1 -2 1 -1 -2 4
1 0 1 1 1 1 0 0 0 0 0 -1 1 -1 0 4
1 2 1 -1 0 -1 0 0 1 1 1 -1 0 0 0 1 4
-1 1 1 -1 0 -1 0 0 0 1 1 0 0 0 1 -1 2 4
0 1 1 0 1 1 -1 0 0 0 -1 -1 -1 -1 1 1 0 -1 4
0 1 0 -1 0 -1 0 0 0 -1 0 0 0 0 0 0 1 1 0 4
0 0 0 0 -1 -1 1 0 -1 -1 0 2 0 1 -1 -1 0 1 -2 0 4
-1 0 -1 2 0 1 -1 0 -1 -1 -1 -1 1 1 0 0 -1 -1 1 0 -1 4
0 -1 -2 0 -1 -1 0 0 -2 -1 0 2 1 1 -1 -1 -1 0 -2 0 2 -1 4
0 1 0 -1 -1 -1 -1 0 0 -2 0 0 2 0 0 1 1 0 0 2 0 1 0 4
1 -1 -1 2 0 -1 0 0 -1 -1 1 0 0 2 -2 0 0 0 -2 0 2 0 2 0 4
0 1 0 -1 -1 0 0 0 -1 0 0 0 2 0 0 0 1 1 -1 1 1 0 1 2 0 4
-1 1 1 -1 0 1 0 0 0 2 0 -1 1 -1 1 0 1 1 1 -1 -1 0 -1 0 -2 2 4
0 1 -1 -1 -1 -1 0 2 -1 -1 -1 1 1 -1 1 0 1 1 -1 1 1 0 1 2 0 2 0 4
1 -1 1 0 0 0 -1 -1 1 -1 1 -1 -1 1 -1 0 -1 -1 1 1 -1 0 -1 0 0 -2 -2 -2 4
0 1-1 1 0-1 1 1-1-1 0 0 1 1 0-1 1 1 1 1 1 2 2 0 2-2 4
0-1 1 0 2-1 0 0 1-1 0-1 0 1 1 0 1-1 0 1 0 0 0 0 1 4
1 0 0 1 -1 0 -1 -1 -1 -1 1 -1 2 2 -2 1 1 0 -1 1 1 1 1 2 2 2 0 0 0 2 0 4
-
DET公司
1
-
最小_形式
4
-
MINVECS公司
-
亲吻_编号
146880
-
密度
-
HERMITE_NUMBER公司
4
-
组订单(_O)
2^15 3^2
-
发电机组
12
32 32
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32 32
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32 32
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1 32
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x ^5124*8 x ^5112*6 x ^5064*10 x ^5040*16 x ^ 5028*40 x ^5016*6 x×^5004*4 x ^4992*8 x×^4968*34 x ^4965*128 x ^4956*32 x ^4932*64 x ^4920*16 x*^4908*16 x 16 x ^4788*32 x ^4776*32 x*4761*32 x*^4728*32 x x ^4713*32(1152x)
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 -1 -1 0 0 0 1 0 0
x ^5124*8 x ^5112*8 x ^5088*8 x ^5076*48 x ^5064*4 x ^5028*72 x ^5016*12 x ^4992*24 x ^4980*16 x ^4968*32 x ^4956*32 x ^4944*32 x ^4929*256 x ^4917*128 x ^4896*64 x ^4872*16 x ^4860*128 x ^4848*16 x ^4836*64 x ^4833*64 x ^4824*64 x ^4800*16 x ^4764*32 x ^4761*64 x ^4740*32(576倍)
1 32个
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 -1 0 1 0 0
x^5400*2 x ^5304*2 x×^5256*4 x ^5208*16 x ^5160*16 x×^5124*48 x ^5088*8 x ^5076*24 x ^5040*16 x^5028*24 x×^5016*48 x 64 x ^4812 x 48 x ^4788 x ^4761 x ^4713 x ^32(576 x)
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 ^5028*2 x ^5016*4 x ^5004*2 x*4992*4 x*4980*4 x*^4965*16 x ^4956*26 x ^4944*8 x ^4941*8 x*4929*8 x*^ 4920*40 x ^4917*68 x ^4908*72 x ^4905*36 x ^4896*28 x ^4893*60 x ^4884*46 x ^4881*12 x ^4872*100 x ^4869*76 x ^4860*24 x ^4857*136 x ^4845*92 x ^4836*20 x ^4833*16 x ^4824*4 x ^4821*36 x ^4812*72 x ^4809*40 x ^4797*12 x ^4788*80 x ^4785*32 x ^4776*8 x ^4761*18 x ^4752*8x^4737*16 x^4713*6(9216x)
1 32
0 0 0 0 0 0 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
x^5400*8 x ^5304*24 x ^5256*24 x×^5208*24 x^5172*96 x ^5124*72 x ^5076*96 x×^5064*8 x^5016*96 x^5004*32 x ^4980*48 x ^4968*96 x
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 -1 -1 0 0 0 0 1 1
x^5052*2 x ^5040*8 x ^5028*4 x ^5016*2 x×^5004*8 x×^4980*20 x ^4968*18 x ^4965*16 x ^4956*8 x*^4944*38 x ^4941*24 x ^4932*44 x ^4929*8 x^4920*20 x^4917*16 x 108 x ^4845*68 x ^4836*20 x ^4833*32 x ^4824*48 x ^4821*32 x*4812*90 x ^4809*20 x*4800*40 x ^4788*6 x ^4785*64x ^4776*20 x ^4764*2 x ^4740*10 x ^4728*12 x ^ 4725*8(9216x)
1 32个
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 1 0 0 0 -1 -1 0 0
x^5400*8 x ^5352*32 x ^5304*32 x×^5256*48 x ^5232*32 x^5208*64 x ^5160*24 x ^5136*96 x ^5112*64 x×^5088*32 x*^5064*32 x x ^5016*16 x ^4992*192 x ^4968*16 x×^4944*288 x ^4932*128 x ^4920*8 x^4812*128(72 x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 -1 -2 0 -1 0 1 2 0 1
x ^5076*6 x ^4980*10 x ^4968*2 x ^4932*12 x ^4920*44 x ^4917*16 x ^4908*8 x ^4896*72 x ^4893*16 x qu4884*18 x ^4872*66 x ^4869*32 x ^4848*32 x qu4845*64 x ^4836*88 x ^4833*128 x ^4824*64 x 88 x ^4761*32 x ^4740*8 x ^4728*16 x ^4713*16(2304x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 -1 0 -1 0 1 1 0 0
x ^5220*2 x ^5028*4 x ^5004*8 x ^4980*84 x ^4968*4 x×^4941*16 x ^4932*34 x ^4920*40 x ^4908*24 x ^4884*6 x ^4872*24 x^4869*16 x×^4860*240 x ^4848*96 x ^4836*96 x*8(768倍)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 -1 0 0 0 0 1 -1 -1 0 1 -1 -1
x^5100*8 x ^5088*2 x ^5076*16 x ^5052*8 x×^5040*2 x×^5016*8 x^5004*24 x^4992*44 x ^4980*32 x ^4968*24 x ^4965*64 x ^4956*96 x ^4944*8 x*4932*32 x*^4929*32 x 160 x ^4845*32 x ^4833*32 x×^4821*48 x ^4812*32 x*^4797*16 x ^4785*32 x^4752*32 x
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 -1 0 0 1 1 0 0 0 1 0 1 0 0 -1
x^5400*4 x ^5304*12 x ^5208*36 x ^5112*124 x ^5064*8 x ^5040*48 x ^4992*96 x ^4980*96 x×^4968*20 x ^4944*96 x^4932*208 x ^4896*112 x ^4884*192 x ^4872*12 x
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 -1 0 1 1 0 0 0 0 1 0 1 0 0 -1
x ^5304*48 x ^5220*32 x ^5124*96 x ^5112*24 x ^5064*16 x ^5028*16 x×^5004*192 x ^4980*48 x×^4968*96 x×^ 4956*128 x ^4920*224 x ^4872*96 x
1 32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
x^5304*8 x ^5208*32 x ^5172*64 x ^5112*48 x ^5052*128 x ^5004*64 x^4968*128 x×^4920*384 x ^4908*128 x
1 32
0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 -1 -1 0 -1 0 0 -1 0 0 1 -1 0
x ^5232*2 x ^5208*8 x ^5196*16 x ^5184*2 x ^5160*8 x ^5136*4 x ^5124*4 x ^5100*8 x ^5088*8 x ^5076*36 x ^5052*8 x ^5040*8 x ^5028*32 x ^5004*48 x ^4992*32 x ^4980*4 x ^4968*24 x ^4965*64 x ^4956*48 x ^4944*80 x ^4932*32 x ^4917*64 x ^4908*80 x ^4896*32 x ^4893*64 x ^4884*12 x ^4872*128 x ^4860*64 x ^4857*64 x ^4848*48 x ^4836*56 x ^4824*8 x ^4812*16 x ^4809*32 x ^4785*32 x ^4761*32x ^4752*32(2304x)
1 32
0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 -1 0 0 0 0 0 -1 1 1 0 0 1 0 0 -1
x ^5136*6 x ^5124*12 x ^5088*26 x ^5076*12 x×^4968*24 x ^4920*120 x ^4908*96 x ^4896*48 x ^4872*64 x ^4869*192 x ^4857*96 x
1 32
0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 -1 0 1 0 0 0 -1 2 0 1 0 1 0 -1 -1
x ^5004*10 x ^4992*2 x ^4944*6 x ^4941*4 x ^4932*10 x×^4920*8 x ^4917*12 x ^ 4908*24 x ^4905*12 x*^4896*82 x ^4893*12 x×^4881*36 x ^4872*12 x `4869*100 x ^4860*34 x ^4857*60 x ^4848*42 x ^4845*24 x^4836*18 x ^4833*88 x ^4824*96 x ^4821*64 x ^4812*84 x ^4809*12 x 144 x ^4797*24 x ^4788*16 x ^4785*72 x ^4776*12 x ^4773*48 x ^4761*24 x
1 32
0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 -1 0 -1 -1 1 0 1 1 1 0 0 1
x ^5400*32 x ^5304*24 x ^5220*32 x×^5172*192 x ^5076*96 x ^5064*32 x^5004*320 x ^4872*384 x ^4833*128(24 x)
1 32
0 0 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 -1 0 0 0 0 0 0 -1 -2 -1 0 1 0 1 0 2
x^5088*24 x ^5076*144 x ^5064*12 x ^5028*8 x ^5016*12 x×^5004*32 x ^4992*24 x^4977*256 x ^4920*112 x ^4908*48 x ^4884*56 x ^4845*192 x ^4836*192 x ^4785*96 x ^4689*32(192x)
1 32
0 0 0 0 0 0 0 0 1 0-1 0 0-1 0 0 0 0 0 0-1-1 0 0 1 0 1 0 1
x ^5112*6 x ^5028*8 x ^5004*24 x ^4992*48 x ^4968*108 x ^4932*32 x ^4920*118 x ^4905*256 x ^4884*8 x×^4869*192 x ^4860*216 x ^4833*32 x×^4809*96 x ^4800*96(192x)
1 32
0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 -1 0 0 0 0 0 -1 0 0 0 1 0 0 0 1
x^5088*2 x ^4968*48 x ^4944*54 x ^4920*120 x ^4905*192 x ^4896*24 x ^4872*64 x ^4869*192 x×^4860*96 x ^4836*160 x ^4824*96 x
1 32
0 0 0 0 0 0 0 0 1 -1 0 -1 -1 -1 0 1 1 -1 -1 1 1 2 2 0 1 0 2 0 0 -2 0 -1
x^5208*4 x ^5172*8 x ^5124*8 x×^5112*20 x ^5076*16 x ^5052*16 x×^5028*8 x*^5004*16 x*^4980*8 x*^4944*80 x ^4941*64 x ^4920*64 x^4908*64 x*^4896*80 x×^4872*64 x 64(1152倍)
1 32
0 0 0 0 0 0 0 0 1 -1 0 -1 1 0 1 0 1 -1 0 1 1 1 1 -1 1 0 1 0 0 -1 0 -1
x^5352*4 x ^5256*4 x*^5196*16 x ^5172*24 x ^5124*16 x*^512*16 x×^5088*16 x s^5076*8 x ^5028*32 x ^5004*16 x^4992*16 x q^4980*16 x x^4968*80 x ^4956*64 x ^4944*8 x×^4932*64 x q^ 4920*16 x 64 x ^4836*16 x ^4833*64 x ^ 4824*16 x*^4797*64 x*^ 4740*64(1152x)
1 32
0 0 0 0 1 -2 0 1 -1 -1 -1 0 0 0 0 1 0 0 -1 1 -1 0 -1 0 2 1 1 -1 -1 -3 -1 0
x ^4980*12 x ^4968*12 x×^4920*14 x ^4905*16 x ^4896*16 x×^4884*2 x ^4881*24 x ^4872*108 x ^4860*48 x ^4857*164 x ^4836*108 x×^ 4833*326 x ^ 4824*12 x
1 32
0 0 0 0 1 -1 -1 0 -1 0 0 -1 0 -1 1 0 1 -1 -1 0 1 0 0 0 0 0 0 -1 0 0 -1 0
x ^5028*6 x ^4992*14 x ^4980*6 x×^4977*4 x ^ 4965*24 x ^4956*14 x×^ 4944*36 x ^4941*6 x x ^4932*48 x ^4929*12 x ^4920*14 x 44 x ^4824*54 x ^4821*66 x ^4812*6 x ^4809*48 x ^4800*42 x ^4788*46 x ^4785*6 x×^4776*18 x ^4773*36 x ^4761*4(24576倍)
1 32
0 0 0 0 1 -1 -1 0 -1 0 0 0 0 0 0 0 0 0 -1 0 0 -1 -1 -1 -1 0 0 0 1 2 -1 0
x^4992*6 x ^4941*24 x ^4920*24 x×^4908*36 x ^4896*48 x ^4893*48 x×^4884*24 x*^4881*12 x ^4872*80 x ^4869*144 x ^4860*90 x ^4857*36 x^4848*78 x ^4845*144 x ^4836*62 x ^4833*72 x ^4824*48 x
1 32
0 1 0 0 0 -1 0 1 0 -1 -1 0 0 -1 0 1 0 0 -1 0 0 1 0 0 2 1 1 -1 0 -3 0 0
x ^5220*32 x ^5112*24 x ^5100*192 x ^5028*96 x ^4992*256 x ^4956*256 x ^4857*128 x ^4821*256(96 x)
1 32个
0 1 0 0 0 -1 0 1 0 -1 -1 0 0 -1 0 1 1 -1 -2 1 0 2 0 0 3 1 2 -1 0 -4 0 -1
x ^5220*32 x ^5160*24 x ^5004*192 x ^4980*48 x ^4944*48 x×^4920*320 x ^4908*192 x ^4884*32 x×^4821*256 x ^4776*96(96 x)
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属性
单一模块=1
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参考文献
H.Koch、B.B.Venkov、,
\“Uber ganzzahlige unimodulare euklidische记事本。
期刊f“ur die reine und angewandte Mathematik 398(1989),144-168
H.Koch,B.B.Venkov,“Uber gerade unimodulare”
Gitter der Dimension 32,III型
马塞姆。纳克里斯。152 (1991), 191-213
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笔记
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最后一行
Haftungsausschluss/免责声明
加布里埃尔·内布