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 13:27:35 CEST 2014

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
DIVISORS
MINIMAL_NORM
KISSING_NUMBER
GROUP_ORDER
GROUP_NAME
GROUP_GENERATORS
GRAM
PROPERTIES
REMARKS
LAST_LINE

• NAME
  Sch14
  

• DIMENSION
  14
  

• DIVISORS
  1 1 1 1 1 1 1 7 7 7 7 7 7 7
  

• MINIMAL_NORM
  6
  

• KISSING_NUMBER
  560
  

• GROUP_ORDER
  2^4 * 3^2 * 7
  

• GROUP_NAME
  C2 x PSL2(8)
  

• GROUP_GENERATORS
  2
  14 14
  1 -1 -1 0 1 0 2 0 0 0 -1 -1 0 -1
  0 0 -1 -1 0 1 1 1 1 0 0 0 -1 0
  0 0 0 0 1 1 1 0 0 0 0 0 0 0
  1 -1 1 1 1 0 0 -1 -1 1 0 0 1 -1
  -1 0 1 -1 -1 0 -1 0 0 0 0 1 -1 0
  0 -1 0 0 0 0 0 0 0 0 0 0 0 0
  1 0 -1 0 1 0 1 1 0 0 0 -1 0 0
  -1 0 1 0 0 1 -1 -1 0 0 0 1 0 0
  1 0 0 1 1 0 1 0 -1 1 0 0 1 -1
  1 0 -2 -1 0 0 1 1 1 0 0 -1 0 0
  0 0 0 1 0 -1 0 0 -1 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 -1 0 0 0
  -1 1 0 0 -1 0 -1 0 0 -1 0 0 0 1
  0 0 0 0 0 -1 0 0 0 0 0 -1 0 0
  14 14
  -1 1 1 1 0 0 -1 -1 0 0 0 0 1 1
  -1 1 1 1 -1 -1 -1 0 0 0 1 0 0 1
  -1 1 1 1 0 0 -1 -1 0 0 1 0 0 1
  1 0 -1 0 1 0 1 0 0 0 0 -1 1 0
  -1 0 0 -1 -1 1 0 1 1 0 0 1 -1 1
  1 0 0 1 1 -1 0 0 -1 1 1 0 1 -1
  0 0 1 0 0 0 -1 -1 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 0 0 0 0 -1 0 1
  0 0 1 1 0 -1 0 0 -1 0 0 0 0 0
  1 -1 -1 -1 0 0 0 0 0 0 -1 0 0 -1
  0 -1 0 -1 0 1 0 0 1 0 -1 0 0 0
  0 -1 0 -1 0 0 0 0 0 0 0 0 -1 -1
  -1 0 1 0 0 1 0 -1 0 0 -1 1 0 0
  

• GRAM
  14 14
  6 2 2 1 -2 -2 2 -3 3 1 -1 2 -3 2
  2 6 3 -2 0 -2 2 -1 2 3 -3 -1 -2 -1
  2 3 6 0 -2 0 3 1 3 0 -2 -2 0 -2
  1 -2 0 6 -1 2 -2 2 2 -2 -1 -1 -2 -1
  -2 0 -2 -1 6 -2 -3 1 -1 -1 -1 1 -1 1
  -2 -2 0 2 -2 6 -1 3 -2 -2 2 -3 2 -3
  2 2 3 -2 -3 -1 6 -2 1 1 1 1 1 1
  -3 -1 1 2 1 3 -2 6 -1 -3 -1 -2 2 -3
  3 2 3 2 -1 -2 1 -1 6 1 -2 0 -2 -1
  1 3 0 -2 -1 -2 1 -3 1 6 -2 -1 -2 1
  -1 -3 -2 -1 -1 2 1 -1 -2 -2 6 1 2 0
  2 -1 -2 -1 1 -3 1 -2 0 -1 1 6 0 3
  -3 -2 0 -2 -1 2 1 2 -2 -2 2 0 6 -1
  2 -1 -2 -1 1 -3 1 -3 -1 1 0 3 -1 6
  

• PROPERTIES
  INTEGRAL =1
  MODULAR = 7
  

• REMARKS
  Found by Rudolf Scharlau by enumerating the whole genus, which has
  class number 83006.
  This lattice is unique in its genus with minimum >=6.
  

• LAST_LINE
  

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  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe