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 13:19:29 CEST 2014

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
DET
MINIMAL_NORM
KISSING_NUMBER
BASIS
TRIANGULAR_BASIS
GRAM
PROPERTIES
REFERENCES
NOTES
LAST_LINE

• NAME
  LAMBDA24 (The Leech Lattice)
  

• DIMENSION
  24
  

• DET
  1
  

• MINIMAL_NORM
  4
  

• KISSING_NUMBER
  196560
  

• BASIS
  24 24
  .800000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .400000000000E+01 .400000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .400000000000E+01 .000000000000E+00 .400000000000E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .400000000000E+01 .000000000000E+00 .000000000000E+00
  .400000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .400000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .400000000000E+01 .000000000000E+00
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  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .400000000000E+01 .000000000000E+00 .000000000000E+00
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  .400000000000E+01 .000000000000E+00 .000000000000E+00
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  .400000000000E+01 .000000000000E+00 .000000000000E+00
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  .000000000000E+00 .000000000000E+00 .000000000000E+00
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  .000000000000E+00 .200000000000E+01 .200000000000E+01
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  .200000000000E+01 .000000000000E+00 .000000000000E+00
  .200000000000E+01 .200000000000E+01 .200000000000E+01
  .000000000000E+00 .000000000000E+00 .200000000000E+01
  .000000000000E+00 .200000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .200000000000E+01 .000000000000E+00
  .200000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .200000000000E+01 .200000000000E+01 .000000000000E+00
  .000000000000E+00 .200000000000E+01 .000000000000E+00
  .200000000000E+01 .000000000000E+00 .200000000000E+01
  .000000000000E+00 .000000000000E+00 .200000000000E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .200000000000E+01 .000000000000E+00
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  .000000000000E+00 .200000000000E+01 .200000000000E+01
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  .000000000000E+00 .200000000000E+01 .200000000000E+01
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  .100000000000E+01 .100000000000E+01 .100000000000E+01
  .100000000000E+01 .100000000000E+01 .100000000000E+01
  

• TRIANGULAR_BASIS
  24 24
  .282842712475E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
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  .141421356237E+01 .141421356237E+01 .000000000000E+00
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  .707106781187E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .707106781187E+00 .707106781187E+00 .000000000000E+00
  .000000000000E+00 .707106781187E+00 -.157009245868E-15
  .707106781187E+00 .157009245868E-14 .707106781187E+00
  -.471027737605E-15 -.471027737605E-15 .707106781187E+00
  .314018491737E-15 -.125607396695E-14 -.125607396695E-14
  .219812944216E-14 .707106781187E+00 .000000000000E+00
  -.628036983474E-15 .707106781187E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .707106781187E+00 .707106781187E+00
  .707106781187E+00 .707106781187E+00 -.628036983474E-15
  -.628036983474E-15 .282616642563E-14 .707106781187E+00
  -.785046229342E-15 -.785046229342E-15 .314018491737E-14
  .707106781187E+00 .408224039258E-14 .408224039258E-14
  -.502429586779E-14 .707106781187E+00 -.125607396695E-14
  .533831435952E-14 -.628036983474E-15 .707106781187E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .707106781187E+00
  .707106781187E+00 -.314018491737E-15 .157009245868E-14
  .707106781187E+00 .707106781187E+00 -.125607396695E-14
  .188411095042E-14 .707106781187E+00 .707106781187E+00
  .000000000000E+00 .000000000000E+00 .707106781187E+00
  .707106781187E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .707106781187E+00
  -.157009245868E-15 .707106781187E+00 .157009245868E-14
  .707106781187E+00 .235513868803E-14 .707106781187E+00
  .188411095042E-14 .707106781187E+00 .000000000000E+00
  .707106781187E+00 .628036983474E-15 .707106781187E+00
  .131887766529E-13 .707106781187E+00 .000000000000E+00
  -.106066017178E+01 .353553390593E+00 .353553390593E+00
  .353553390593E+00 .353553390593E+00 .353553390593E+00
  .353553390593E+00 .353553390593E+00 .353553390593E+00
  .353553390593E+00 .353553390593E+00 .353553390593E+00
  .353553390593E+00 .353553390593E+00 .353553390593E+00
  .353553390593E+00 .353553390593E+00 .353553390593E+00
  .353553390593E+00 .353553390593E+00 .353553390593E+00
  .353553390593E+00 .353553390593E+00 .353553390593E+00
  

• GRAM
  24 24
  8 4 4 4 4 4 4 2 4 4 4 2 4 2 2 2
  4 2 2 2 0 0 0 -3
  4 4 2 2 2 2 2 2 2 2 2 2 2 2 1 1
  2 1 1 2 1 0 0 -1
  4 2 4 2 2 2 2 2 2 2 2 2 2 1 2 1
  2 2 1 1 1 0 0 -1
  4 2 2 4 2 2 2 2 2 2 2 2 2 1 1 2
  2 1 2 1 1 0 0 -1
  4 2 2 2 4 2 2 2 2 2 2 1 2 2 2 2
  2 2 2 2 1 0 0 -1
  4 2 2 2 2 4 2 2 2 2 2 1 2 2 1 1
  2 1 2 1 0 0 0 -1
  4 2 2 2 2 2 4 2 2 2 2 1 2 1 2 1
  2 1 1 2 0 0 0 -1
  2 2 2 2 2 2 2 4 1 1 1 2 1 2 2 2
  1 2 2 2 2 0 0 1
  4 2 2 2 2 2 2 1 4 2 2 2 2 2 2 2
  2 2 2 2 1 1 1 -1
  4 2 2 2 2 2 2 1 2 4 2 2 2 2 1 1
  2 2 1 1 0 1 0 -1
  4 2 2 2 2 2 2 1 2 2 4 2 2 1 2 1
  2 1 2 1 0 0 1 -1
  2 2 2 2 1 1 1 2 2 2 2 4 1 2 2 2
  1 2 2 2 2 1 1 1
  4 2 2 2 2 2 2 1 2 2 2 1 4 2 2 2
  2 1 1 1 1 1 1 -1
  2 2 1 1 2 2 1 2 2 2 1 2 2 4 2 2
  1 2 2 2 2 2 1 1
  2 1 2 1 2 1 2 2 2 1 2 2 2 2 4 2
  1 2 2 2 2 1 2 1
  2 1 1 2 2 1 1 2 2 1 1 2 2 2 2 4
  1 2 2 2 2 1 1 1
  4 2 2 2 2 2 2 1 2 2 2 1 2 1 1 1
  4 2 2 2 1 1 1 -1
  2 1 2 1 2 1 1 2 2 2 1 2 1 2 2 2
  2 4 2 2 2 2 1 1
  2 1 1 2 2 2 1 2 2 1 2 2 1 2 2 2
  2 2 4 2 2 1 2 1
  2 2 1 1 2 1 2 2 2 1 1 2 1 2 2 2
  2 2 2 4 2 1 1 1
  0 1 1 1 1 0 0 2 1 0 0 2 1 2 2 2
  1 2 2 2 4 2 2 2
  0 0 0 0 0 0 0 0 1 1 0 1 1 2 1 1
  1 2 1 1 2 4 2 2
  0 0 0 0 0 0 0 0 1 0 1 1 1 1 2 1
  1 1 2 1 2 2 4 2
  -3 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 1 -1 1 1 1
  -1 1 1 1 2 2 2 4
  

• PROPERTIES
  INTEGRAL=1
  MODULAR=1
  

• REFERENCES
  SPLAG p. 131 etc.
  

• NOTES
  Leech lattice = LAMBDA24
  There is another version in Leech.b
  

• LAST_LINE
  

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  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe