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日星期五13:26:56 CEST

索引文件|缩写

此文件的内容

名称
尺寸
决定性因素
最小_形式
亲吻_编号
属性
组订单（_O）
笔记
参考文献
BASIS（需要除以97）
克
组生成器
最后一行

• 名称
  第27页
  

• 尺寸
  27
  

• 决定性因素
  1
  

• 最小_形式
  三
  

• 亲吻_编号
  1640
  

• 属性
  积分=1
  

• 组订单（_O）
  1268047872
  

• 笔记
  最小范数3和群___的Borcherds单模27直径格。
  

• 参考文献
  SPLAG，第三版。
  博彻兹的论文。
  巴赫和文科夫，Re'seaux entiers unimodularies。。。
  

• BASIS（需要除以97）
  27 27
  1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 37 39 41 43 45 47 51 59 61
  0 97 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8633
  0 0 97 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1843
  0 0 0 97 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 4462
  0 0 0 0 97 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7081
  0 0 0 0 0 97 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 291
  0 0 0 0 0 0 97 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2910
  0 0 0 0 0 0 0 97 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5529
  0 0 0 0 0 0 0 0 97 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8148
  0 0 0 0 0 0 0 0 0 97 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1358
  0 0 0 0 0 0 0 0 0 0 97 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3977
  0 0 0 0 0 0 0 0 0 0 0 97 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6596
  0 0 0 0 0 0 0 0 0 0 0 0 97 0 0 0 0 0 0 0 0 0 0 0 0 0 9215
  0 0 0 0 0 0 0 0 0 0 0 0 0 97 0 0 0 0 0 0 0 0 0 0 0 0 2425
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 97 0 0 0 0 0 0 0 0 0 0 0 5044
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 97 0 0 0 0 0 0 0 0 0 0 7663
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 97 0 0 0 0 0 0 0 0 0 873
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 97 0 0 0 0 0 0 0 0 3492
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 97 0 0 0 0 0 0 0 6111
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 97 0 0 0 0 0 0 8730
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 97 0 0 0 0 0 1940
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 97 0 0 0 0 4559
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 97 0 0 0 7178
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 97 0 0 388
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 97 0 5626
  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 97 6693
  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 9409
  

• 克
  27 27
  3 0 0 0 -1 0 -1 0 0 -1 -1 -1 0 0 -1 0 -1 0 -1 -1 1 -1 0 -1 -1 -1 -2
  0 3 0 0 1 0 0 0 0 0 0 1 -1 -1 1 1 0 -1 -1 0 0 -1 0 -1 -1 0 1
  0 0 3 0 1 1 0 -1 1 1 0 1 0 0 0 0 0 -1 -1 -1 0 0 0 -1 0 -1 0
  0 0 0 3 1 1 1 0 0 1 1 0 0 -1 0 -1 1 1 1 1 -1 1 1 1 1 -1 -1
  -1 1 1 1 3 1 1 -1 1 1 1 1 -1 -1 1 -1 1 0 0 0 0 0 0 0 0 -1 1
  0 0 1 1 1 3 1 0 1 0 1 1 -1 -1 1 -1 1 1 -1 1 1 -1 0 -1 1 -2 -1
  -1 0 0 1 1 1 3 0 0 0 1 1 0 -1 0 -1 1 1 1 1 0 0 0 0 0 -1 1
  0 0-1 0-1 0 3-1 0-1 1 1 0 1 0 0-1 1 1-1 1-1 0 0 1-1
  0 0 1 0 1 1 0 -1 3 0 0 0 -1 -1 1 -1 1 0 0 0 2 -1 0 0 0 -1 1
  -1 0 1 1 1 0 0 -1 0 3 1 1 0 0 0 0 1 -1 1 -1 -1 1 1 1 1 1 0
  -1 0 0 1 1 1 0 1 3 1-1 0 0-1 1 1 1 0 1 0 0 1 0 0 2-1 0
  -1 1 1 0 1 1 1 -1 0 1 1 3 -1 0 0 0 0 -1 0 0 0 -1 1 -1 1 0 1
  0 -1 0 0 -1 -1 0 1 -1 0 -1 -1 3 1 -1 1 -1 -1 0 -1 -1 1 -1 1 -1 1 -1
  0-1 0-1-1-1 1-1 0 0 1 3-1 1-1 0-1 1-1 1 0 1 1 2-1
  -1 1 0 0 1 1 0 0 1 0 0 0 -1 -1 3 0 1 1 -1 1 0 -1 0 0 0 0 1
  0 1 0 -1 -1 -1 -1 1 -1 0 -1 0 1 1 0 3 -1 -2 -1 -1 -1 0 0 0 -1 2 0
  -1 0 0 1 1 1 1 0 1 1 1 0 -1 -1 1 -1 3 1 1 1 0 1 0 1 1 0 1
  0 -1 -1 1 0 1 1 0 0 -1 1 -1 -1 -1 1 -2 1 4 1 2 0 0 0 0 1 -2 0
  -1 -1 -1 1 0 -1 1 -1 0 1 1 0 0 0 -1 -1 1 1 4 0 0 1 1 2 1 0 1
  -1 0 -1 1 0 1 1 1 0 -1 0 0 -1 -1 1 -1 1 2 0 4 -1 0 1 0 1 0 1
  1 0 0 -1 0 1 0 -1 2 -1 0 0 -1 -1 0 -1 0 0 0 -1 4 -2 -1 -1 -1 -2 0
  -1 -1 0 1 0 -1 0 1 -1 1 1 -1 1 1 -1 0 1 0 1 0 -2 4 -1 2 1 1 0
  0 0 0 1 0 0 0 -1 0 1 0 1 -1 0 0 0 0 0 1 1 -1 -1 4 0 1 1 0
  -1 -1 -1 1 0 -1 0 0 0 1 0 -1 1 1 0 0 1 0 2 0 -1 2 0 4 1 2 0
  -1 -1 0 1 0 1 0 0 0 1 2 1 -1 1 0 -1 1 1 1 1 -1 1 1 1 4 0 -1
  -1 0 -1 -1 -1 -2 -1 1 -1 1 -1 0 1 2 0 2 0 -2 0 0 -2 1 1 2 0 5 1
  -2 1 0 -1 1 -1 1 -1 1 0 0 1 -1 -1 1 0 1 0 1 1 0 0 0 0 -1 1 5
  

• 组生成器
  2
  27 27
  0 0 0 -1 1 0 0 2 0 1 -1 0 0 -1 -1 0 -1 1 -1 -1 0 0 1 1 1 -1 1
  0 0 0 -1 0 1 0 1 0 0 -1 1 0 -1 0 0 -1 1 0 -1 0 1 1 1 0 0 0
  1 0 1 -1 1 -1 -1 2 -1 0 0 1 1 -2 0 0 0 1 0 0 1 0 1 1 1 0 0
  0 1 -1 0 -1 1 1 -2 1 1 0 -2 0 2 0 0 0 -1 0 1 -1 0 -1 -1 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
  1 0 1 -2 0 0 -1 3 0 0 0 2 0 -3 0 -1 -1 1 0 -1 0 1 1 2 0 0 0
  -1 0 0 1 -2 0 0 -1 1 -1 1 0 -1 1 0 -1 1 -1 0 0 -2 -1 -1 0 -2 0 -1
  -1 0 0 1 -1 1 0 -1 0 0 1 -1 -1 1 0 0 0 -1 0 0 -1 -1 -1 0 -1 0 0
  1 0 1 -1 1 -1 -1 2 0 -1 0 2 1 -3 0 0 -1 2 0 -1 1 1 1 1 1 1 0
  0 1 -1 1 -1 1 1 -3 0 1 0 -3 0 3 1 0 0 -2 1 2 0 0 -1 -2 0 0 0
  0 0 -2 1 -2 1 1 -3 2 1 1 -1 -1 3 1 0 0 -2 1 2 -2 0 -2 -2 -2 0 -1
  1 0 0 -1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 -1 0 -1
  0 0 1 1 0 -1 0 -1 -1 0 1 -1 0 1 0 0 1 -1 0 1 0 -2 -1 0 0 0 0
  0 0 -1 1 0 0 0 -2 0 1 1 -1 0 3 0 1 1 -1 0 2 0 -1 -1 -1 -1 -1 0
  0 0 1 0 0 1 -1 2 -1 -1 -1 1 0 -2 0 -1 -1 1 0 -2 1 1 1 1 1 1 1
  0 0 1 -1 1 0 -1 1 -1 0 0 1 1 -1 0 0 0 1 0 0 1 0 1 1 0 0 0
  -2 1 -1 1 -2 1 0 -1 1 0 0 -1 -1 1 -1 -1 0 0 -1 -1 -1 0 0 0 -1 0 0
  -1 0 -1 1 -1 1 0 1 1 0 -1 0 -1 0 -1 -1 0 0 -1 -2 -1 0 0 0 0 0 1
  -1 1-2 1-1 0 1-3 2 0-1 0 3 0 1-1 0 1-1 0-1 2-1 0-1
  0 0 0 0 0 1 0 0 0 -1 0 0 0 -1 0 0 0 0 0 -1 0 1 0 0 0 1 0
  1 -1 1 -2 1 -2 -1 3 1 -1 0 4 0 -4 0 0 -1 2 0 -1 0 1 1 2 0 0 -1
  -2 1-2 2 1-4 1 1 1-4-1 4-1 0 1-2 0 1-2-2-2-2-2-1 0 0
  1 1 -1 0 1 0 1 -2 0 1 -1 -1 2 2 1 1 0 0 0 2 2 2 0 -2 1 0 0
  -1 1 -1 1 -1 1 0 -3 1 0 1 -2 0 3 -1 0 1 -1 0 1 -1 -1 -1 -1 -1 0 0
  1 1-2 0-1 2 1-3 1 1 1-2 0 3 1 0 0-2 1 2-1 1-1-2-1 0 0
  -1 0 0 2 0 0 0 -3 -1 0 1 -2 0 3 0 1 1 -1 0 2 1 -1 -1 -1 -1 0 0
  -1 -1 0 1 0 -1 -1 0 0 -2 0 2 0 -1 0 0 1 1 0 -1 0 0 0 0 -1 1 -1
  27 27
  0 1 0 0 0 1 0 1 0 1 -1 -1 0 0 0 -1 -1 0 0 -1 0 0 0 0 1 0 1
  -1 1 0 0 0 1 0 2 0 1 -2 0 0 -1 -2 0 -1 2 -1 -2 1 0 1 1 1 0 1
  0 -1 0 2 -1 0 1 -1 -1 0 0 -2 -1 1 1 0 0 -2 0 0 0 -1 -1 -1 1 0 1
  0 0 0 -1 0 -1 -1 1 0 0 0 2 1 -1 0 0 0 1 -1 0 1 1 1 1 0 -1 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 0 0 -1 2 1 -1 -1 0 0 -3 0 1 1 -1 -1 -2 1 0 0 0 0 -1 1 0 1
  -1 0 -1 0 -1 1 0 -1 0 0 0 -1 -1 1 0 0 0 -1 0 0 -1 0 0 0 -1 -1 0
  0 1 -1 0 1 1 1 -2 0 1 -1 -2 1 2 0 1 0 0 0 1 1 1 0 -2 1 0 0
  0 0 1 1 0 -1 0 1 -1 0 0 -1 0 0 0 0 0 0 0 0 1 -1 0 0 1 0 1
  0 -1 1 -1 0 -1 -1 2 0 -1 1 2 0 -3 -1 0 0 1 -1 -1 0 0 1 2 0 0 0
  -1 0 0 0 -1 0 0 -1 1 -1 1 0 0 0 0 0 0 0 0 0 -1 0 0 0 -1 0 -1
  0 -1 0 0 -1 0 0 0 0 0 1 0 -1 0 0 0 0 -1 0 0 -1 -1 0 1 -1 -1 0
  2 -1 0 -1 2 -1 0 0 -1 0 0 1 1 -1 1 1 0 0 0 1 1 1 0 0 1 0 0
  1 -1 -1 0 0 -1 1 -2 1 1 1 0 0 2 1 1 1 -1 0 2 -1 0 -1 -1 -1 -1 -1
  0 1 0 0 0 1 1 0 0 0 -1 -1 0 0 0 0 -1 0 1 0 1 1 0 -1 1 1 0
  0 0 0 0 1 -1 1 0 0 1 -1 0 0 0 -1 1 0 1 -1 0 1 0 0 0 1 0 0
  -1 0 1 -1 0 0 -1 2 0 -1 0 1 0 -2 -1 0 0 1 0 -1 0 0 1 1 0 0 0
  -1 1 -1 0 -1 1 0 -1 1 -1 0 0 0 1 1 -1 0 -1 1 0 -1 1 0 -1 -1 0 -1
  -1 -1 0 -1 0 -2 -2 2 1 -1 1 4 0 -2 -1 0 1 2 -1 -1 -1 0 1 2 -2 -1 -1
  -1 1 -1 1 -1 1 0 -2 0 0 0 -1 0 3 0 0 1 -1 0 1 0 0 0 -1 -1 -1 0
  0 1 1 0 0 1 0 1 -1 0 0 -2 0 -1 0 -1 -1 0 1 -1 0 -1 0 0 1 1 1
  0 -1 1 -1 1 -2 -1 1 0 -1 0 3 1 -2 0 1 1 2 -1 0 1 1 1 1 0 0 -1
  -1 0 -2 1 -2 0 0 -2 2 1 1 0 -1 3 -1 0 1 -1 -1 1 -2 -1 -1 0 -2 -2 0
  1 -1 1 -2 1 -3 -1 2 0 0 1 4 1 -2 0 1 1 2 -1 1 1 1 1 2 -1 -1 -1
  0 -1 0 0 -1 -1 0 -1 1 -1 2 1 0 1 1 0 1 -1 0 1 -1 0 0 0 -2 -1 -1
  1 -1 0 -1 1 -2 0 0 1 1 1 2 0 0 -1 2 1 1 -1 2 0 0 0 1 -1 -1 -1
  -1 -1 1 1 0 -2 -1 1 0 -1 0 2 -1 -1 -1 1 1 1 0 0 0 -1 0 1 -1 0 -1
  

• 最后一行
  

  ---

  Haftungsausschluss/免责声明
  
  
  加布里埃尔·内布