The Lattice st15moddim8b

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 Thu Jul 22 15:39:05 EDT 1999

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME (required)
DIMENSION (required)
GRAM (floating point or integer Gram matrix)
DIVISORS (elementary divisors)
MINIMAL_NORM
KISSING_NUMBER
GENUS
GROUP_ORDER
GROUP_GENERATORS
PROPERTIES
REFERENCES
NOTES
URL (links to other sites for this lattice)
LAST_LINE (required)

• NAME (required)
  st15moddim8b
  
• DIMENSION (required)
  
• GRAM (floating point or integer Gram matrix)
  8 0
  6
  -1 6
  1 -3 6
  -3 1 1 6
  -3 -1 1 3 6
  3 1 0 0 -3 6
  -1 3 -3 0 -1 -1 6
  2 -3 0 -2 -1 1 -3 6
  
• DIVISORS (elementary divisors)
  1^4*15^4
  
• MINIMAL_NORM
  6
  
• KISSING_NUMBER
  48
  
• GENUS
  +
  
• GROUP_ORDER
  2^5 * 3^2
  
• GROUP_GENERATORS
  4
  8
  0 0 0 0 0 0 0 1
  0 0 0 0 0 -1 0 0
  0 0 0 0 -1 0 0 0
  0 0 0 0 0 0 1 0
  0 1 0 0 0 0 0 0
  0 -1 -1 0 0 0 0 0
  1 0 0 1 0 -1 0 0
  0 0 0 -1 1 1 0 0
  8
  -1 0 0 -1 0 1 0 0
  0 0 0 0 0 0 -1 -1
  0 0 0 0 0 0 0 1
  1 0 0 0 1 0 0 0
  1 0 0 0 0 -1 0 0
  -1 0 0 -1 1 1 0 0
  0 1 1 0 0 0 0 0
  0 0 -1 0 0 0 0 0
  8
  1 0 0 0 0 0 0 0
  0 -1 -1 0 0 0 -1 -1
  0 0 0 0 0 0 1 1
  -1 0 0 -1 0 0 0 0
  -1 0 0 0 -1 0 0 0
  0 0 0 -1 1 1 0 0
  0 -1 0 0 0 0 0 -1
  0 1 1 0 0 0 0 1
  8
  1 0 0 0 0 0 0 0
  0 0 -1 0 0 0 0 0
  0 0 0 0 0 0 -1 0
  -1 0 0 -1 1 1 0 0
  0 0 0 0 1 0 0 0
  0 0 0 -1 0 0 0 0
  0 1 0 0 0 0 0 0
  0 0 1 0 0 0 1 1
  
• PROPERTIES
  INTEGRAL = 1
  MODULAR = 15
  
• REFERENCES
  
• NOTES
  extremal strongly 15-modular lattice
  
• URL (links to other sites for this lattice)
  the other extremal strongly 15-modular lattice in this genus is
  st15moddim8a
  
• LAST_LINE (required)
  
  

INDEX FILE | ABBREVIATIONS

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