The Lattice E8

An entry from the Catalogue of Lattices, which is a joint project of
Neil J. A. Sloane, AT&T Labs-Research (njas@research.att.com) and
Gabriele Nebe, University of Ulm (nebe@mathematik.uni-ulm.de)

Last modified Sat Sep 11 13:40:38 EDT 1999

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIM
BASIS
TRIANGULAR_BASIS
GRAM
DET
GLUE_VECTORS
PROPERTIES
MINIMAL_NORM
KISSING_NUMBER
DENS
HERMITE_NUMBER
DIVISORS
GROUP_ORDER
GROUP_NAME
REFERENCES
LAST_LINE

• NAME
  E8
  
• DIM
  8
  
• BASIS
  8 8
  2 0 0 0 0 0 0 0
  -1 1 0 0 0 0 0 0
  0 -1 1 0 0 0 0 0
  0 0 -1 1 0 0 0 0
  0 0 0 -1 1 0 0 0
  0 0 0 0 -1 1 0 0
  0 0 0 0 0 -1 1 0
  .5 .5 .5 .5 .5 .5 .5 .5
  
• TRIANGULAR_BASIS
  8 8
  2 0 0 0 0 0 0 0
  -1 1 0 0 0 0 0 0
  0 -1 1 0 0 0 0 0
  0 0 -1 1 0 0 0 0
  0 0 0 -1 1 0 0 0
  0 0 0 0 -1 1 0 0
  0 0 0 0 0 -1 1 0
  .5 .5 .5 .5 .5 .5 .5 .5
  
• GRAM
  8 8
  4 -2 0 0 0 0 0 1
  -2 2 -1 0 0 0 0 0
  0 -1 2 -1 0 0 0 0
  0 0 -1 2 -1 0 0 0
  0 0 0 -1 2 -1 0 0
  0 0 0 0 -1 2 -1 0
  0 0 0 0 0 -1 2 0
  1 0 0 0 0 0 0 2
  
• DET
  1
  
• GLUE_VECTORS
  0 0 0 0 0 0 0 0
  
• PROPERTIES
  INTEGRAL=1
  
• MINIMAL_NORM
  2
  
• KISSING_NUMBER
  240
  
• DENS
  0.625000000000D-01
  
• HERMITE_NUMBER
  0.200000000000D+01
  
• DIVISORS
  1 1 1 1 1 1 1 1
  
• GROUP_ORDER
  696729600
  
• GROUP_NAME
  W(E8)
  
• REFERENCES
  SPLAG 120.
  
• LAST_LINE
  

INDEX FILE | ABBREVIATIONS

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