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 Tue Feb 18 12:31:50 CET 2014

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
MINIMUM
KISSING_NUMBER
GRAM
DETERMINANT
GROUP_ORDER
GROUP_GENERATORS
MODULAR
REFERENCES
LAST_LINE

• NAME
  P48m
  

• MINIMUM
  6
  

• KISSING_NUMBER
  52416000
  

• GRAM
  48 48
  6 -2 1 2 -1 -1 -3 1 1 -1 2 -3 2
  0 1 -2 -3 -2 2 -2 -3 -2 -1 1 0 2 1 0 -2 2 -2 -2 3 2 1 -2 1 3 3 2 -3 3 0
  -3 -2 0 2 -2 -2 8 -1 -2 -2 1 0 -3 -2 3 2 2 2 -2 3 0 -2 3 -4 0 4 4 -3 1
  2 1 2 0 2 0 -1 3 -4 -1 -4 2 0 -4 -2 -3 1 0 0 -1 3 3 -4 3 1 -1 6 -2 0 -3
  0 2 -2 2 -1 -3 -2 1 -2 2 -3 -2 -2 2 -3 -1 -1 0 -1 2 1 2 -3 0 1 -1 0 -1
  -1 0 0 0 -2 2 2 -2 2 -1 0 -1 2 2 2 -2 -2 6 1 2 -3 1 0 -3 0 1 1 1 2 -3
  1 -2 4 -2 0 -3 1 2 -2 1 0 -1 2 1 1 -2 0 2 2 -2 -1 1 1 0 -1 3 -1 -1 -1
  -2 2 -1 -1 -2 0 1 6 -2 -2 2 -2 -2 1 2 -3 -1 -1 0 2 -3 0 1 -1 -3 2 -2 -3
  0 -1 2 1 -2 -1 0 0 -2 3 -1 -3 -2 1 2 1 -2 2 2 -2 -3 -1 -2 -1 1 -3 2 -2 6
  2 0 1 0 -1 2 1 2 1 0 1 1 1 -2 3 2 0 2 1 -1 1 -2 2 0 1 1 0 0 -2 0 0 1
  1 -2 1 2 -3 -1 0 1 1 1 -3 0 0 -3 -2 2 8 -1 2 3 -1 1 0 1 -3 4 2 2 -2 2
  3 3 2 1 1 -2 -2 1 -1 -1 0 0 2 -2 -2 0 2 0 -2 0 0 -2 -1 2 0 0 1 0 1 -3
  2 1 2 0 -1 6 -1 0 -1 0 -1 0 -1 -1 0 -2 2 1 -2 -3 0 1 -2 -1 -1 0 -1 -1 0
  0 1 0 2 -2 0 1 0 1 3 -2 2 0 -3 -3 2 0 1 -2 -2 0 -2 1 2 -1 6 -2 -1 0 2
  1 -1 0 1 2 3 0 1 2 2 1 0 -1 -2 0 0 2 -1 0 3 2 2 -1 1 4 2 1 -3 1 -1 0
  -1 2 2 -3 -1 3 2 -3 -2 0 3 0 -2 6 1 0 0 0 -1 1 -1 1 -3 2 1 1 -2 1 1 0
  1 1 -2 0 0 0 0 -2 -4 1 2 -2 -2 -1 1 -1 1 -1 1 1 -1 3 2 2 -1 0 1 -1 -1
  -1 -1 1 6 1 2 -3 2 -1 -1 0 -1 -1 0 0 0 0 1 0 0 2 -1 1 -3 0 0 -1 -1 0 0
  -2 1 1 -3 2 1 -1 -1 0 -3 -1 -3 2 -3 1 2 2 1 0 0 0 1 6 0 -1 1 0 3 1 0 0
  4 1 2 0 -1 -2 -2 0 3 -1 0 1 -1 -1 0 0 -1 -3 -1 -1 1 -1 0 2 0 -1 -2 0 2
  2 -2 1 -3 1 0 -1 2 0 2 0 6 -1 2 -2 -1 2 1 -2 1 2 0 3 1 -1 -1 -1 0 1 -1
  0 0 2 0 0 2 1 0 -1 -2 3 0 -1 0 2 -1 -1 0 -2 1 1 -1 2 1 0 1 0 -3 -1 -1
  6 -3 1 0 -2 1 0 0 0 0 1 -1 1 2 0 0 1 2 -2 1 0 0 0 0 2 1 1 1 2 -2 -1 0
  2 3 1 1 3 -2 2 -1 1 -3 -1 -1 -1 2 1 2 -3 6 -2 -1 2 0 -2 1 1 -2 1 1 1 0
  -1 2 0 0 2 -3 1 -1 0 0 -1 0 -2 -1 1 0 -1 1 0 -2 1 -2 0 2 -3 0 0 4 -1 0
  1 -1 0 -2 1 -2 6 0 0 -3 1 0 3 1 -1 0 0 0 1 0 -2 0 0 1 -2 -2 1 0 0 -1 1
  1 -2 -1 1 1 0 1 1 -3 -2 -3 1 2 1 2 0 1 -1 -1 3 -1 0 -1 0 6 1 2 1 1 -1
  3 -1 -1 -2 -3 -1 1 -1 1 0 1 -1 2 0 0 -1 0 -1 0 -1 0 3 0 -1 -1 -2 -2 3 -2
  -2 -3 1 2 -2 2 1 0 1 2 -2 2 0 1 6 0 1 2 4 -1 1 2 -1 -1 -1 1 0 0 3 -1 1
  -1 2 2 0 -1 -2 -1 -1 0 1 2 2 -2 1 2 -4 -2 4 0 1 -2 2 3 -3 -1 0 1 1 0 -3
  2 0 8 0 -2 -2 1 2 -2 0 -1 -1 1 3 0 -1 2 4 3 -1 1 3 1 0 -1 3 -1 0 -1 -1
  2 -2 -2 0 2 -2 1 -2 2 1 0 2 -1 0 -2 0 -2 1 1 1 0 6 1 0 0 1 -1 1 -1 3 0
  0 0 0 0 -1 1 -1 0 -1 -2 1 1 -3 2 1 0 0 1 0 -3 4 -3 0 -1 3 3 -2 1 1 0 4
  1 0 1 0 1 2 -2 1 8 2 0 1 1 -1 -1 0 3 0 0 1 -2 -1 -1 -1 0 -2 -2 -2 0 -1
  -1 1 0 1 -1 0 -2 4 -1 -3 -3 2 3 -3 2 1 0 1 2 0 1 3 -1 4 -2 0 2 8 -1 1
  2 0 0 0 2 0 -1 3 -1 0 -3 3 1 0 0 -1 0 0 -2 0 2 4 -1 2 -1 -3 -1 1 2 0 2
  0 2 -2 0 2 0 0 -2 1 3 -1 1 0 0 -1 6 0 -1 -2 -3 1 0 -1 1 -2 2 -1 2 -1 -2
  0 0 2 -1 0 0 2 -1 -2 1 -3 1 1 0 2 -2 2 1 1 1 1 0 0 3 1 1 -1 -1 1 2 1
  1 1 0 6 -1 1 0 1 1 1 0 0 0 1 0 -1 1 1 -1 0 0 2 0 -1 0 0 2 1 0 2 -1 -2
  -3 1 1 -2 0 1 1 -1 1 -1 1 0 -1 2 -2 -1 1 2 -1 -1 6 -1 1 -2 -1 1 0 0 -1
  0 -2 1 1 -1 0 -1 -1 1 -2 -1 1 2 -1 1 2 1 2 1 0 -1 -2 -1 -1 0 0 -2 -1 1
  1 0 -2 -1 0 1 -1 0 -2 1 -1 6 2 2 0 1 0 0 0 0 -1 0 -1 0 1 1 -1 1 0 -2 1
  1 1 0 1 2 1 0 -1 1 -2 -1 -2 1 0 -2 -1 2 0 0 -3 -1 -1 -1 -1 0 -3 0 1 2 6
  0 0 1 0 0 -1 0 -2 1 -1 0 1 0 1 2 -1 -3 1 2 0 2 0 0 2 -1 2 -2 1 0 0 1
  2 0 -1 0 -1 1 -1 -1 -1 3 0 0 1 1 -2 2 0 6 -1 0 -1 0 0 -2 0 -1 -2 -1 0 3
  -1 -1 2 0 -1 0 0 -1 -2 2 -3 2 1 2 -1 -1 0 -2 -1 3 0 0 2 0 1 1 1 0 3 2
  0 1 -1 0 0 -1 6 -1 0 1 -2 1 1 0 -1 -1 0 -1 1 0 -2 1 1 0 0 1 2 0 0 1 -2
  0 -1 -1 2 0 1 -1 1 1 0 -2 -1 0 3 0 0 0 -1 1 1 1 1 0 -1 6 -1 -1 0 2 0 0
  1 1 0 0 -2 3 -1 -2 0 2 1 0 -2 -1 1 1 -1 1 0 0 -1 0 -3 0 -1 2 0 0 1 0 0
  0 0 -1 1 0 0 0 0 -1 0 -1 6 -1 -2 0 -1 1 -1 0 -2 -1 2 0 0 0 2 0 1 2 -2
  3 -1 -2 0 1 0 0 0 0 0 1 0 -2 2 0 0 3 -1 0 1 3 -2 0 0 0 0 0 1 -1 -1 6
  -2 -1 -1 2 0 -1 0 -2 2 -2 1 1 1 1 -3 1 3 -4 0 0 0 0 2 1 3 0 0 -1 0 1
  -3 1 1 -1 2 0 -2 -1 2 0 -1 0 -1 0 -2 0 -2 -2 8 0 1 -2 1 4 4 2 -2 1 -1
  -1 -2 -1 3 -3 2 -1 -1 2 -2 0 -2 0 2 -2 -1 -1 2 0 1 -2 -1 1 4 -1 -1 0 -1
  1 0 0 0 -2 1 2 0 -1 0 6 1 0 2 2 0 0 -1 2 -1 0 0 0 2 0 1 -4 -1 2 3 -2
  -2 2 2 -4 -1 0 0 0 -1 -2 2 -1 3 1 -1 -3 2 0 -2 -1 -2 0 1 0 -1 -1 1 1 8
  -3 -1 2 1 2 -1 -1 2 2 -2 -1 1 -4 -2 2 0 -2 -1 0 0 -2 -1 1 0 0 0 0 0 1 0
  2 -1 -1 -1 3 -1 -1 1 0 1 -1 0 0 1 2 -2 0 -3 6 1 -1 -1 -1 1 0 -1 1 2 2
  -2 2 1 0 0 -1 -3 0 2 0 1 2 0 -1 2 0 0 0 0 2 1 0 0 1 -2 1 1 -1 -1 -2 -1
  1 -1 0 1 2 -1 1 6 1 -1 -1 -1 0 0 1 0 0 0 1 3 -4 0 1 -2 1 0 1 4 -2 -2
  -3 1 2 -1 0 -1 0 3 -1 -2 0 0 1 -1 0 0 -1 -1 1 0 -1 4 2 2 -1 1 8 3 1 -2
  1 -1 -2 -1 1 4 -2 3 -2 -2 1 1 1 -2 0 2 -2 1 -1 0 1 0 -1 0 -1 1 -2 -2 0
  0 -1 0 1 1 0 0 0 -2 0 4 0 1 -1 -1 3 8 2 -3 2 -1 -2 -2 2 1 -2 2 -3 2 0
  2 -2 0 1 1 -1 1 -1 -1 1 -2 1 -1 -2 0 1 -2 -1 2 0 -1 1 0 3 -1 0 -1 -2 2
  0 2 -1 -1 1 2 6 -2 -1 1 0 -3 -1 3 -2 -3 1 2 -1 1 1 0 3 -3 1 -3 1 -2 1
  -1 1 0 -1 -1 1 0 0 -1 0 -1 -1 1 -1 1 -2 2 2 -2 -1 -1 1 -1 -2 -3 -2 8 -2
  0 1 1 -1 0 3 3 0 -2 3 -2 2 -2 -2 1 -1 2 -1 3 2 1 -2 -1 -1 3 -3 -1 0 0 2
  1 1 2 -1 0 3 0 -2 1 2 -1 0 0 1 2 -1 -2 8 -3 -3 1 2 0 0 0 0 2 -1 2 -3
  -1 2 -1 1 1 0 0 -2 0 -1 0 0 -1 2 -1 -2 0 0 -2 0 -1 2 -2 -1 0 1 -1 -1 2
  -1 0 -1 -1 1 0 -3 6 1 -1 -1 -2 -1 -3 -1 -1 -1 2 -1 2 0 0 -1 -1 2 -1 -1 -1
  1 3 1 0 1 1 0 2 -1 -1 -2 -3 0 1 -2 0 1 -1 0 2 1 1 -2 -2 0 1 -3 1 6 0
  -2 -2 -1 -2 3 0 -1 -2 0 0 -3 -1 1 -1 0 0 0 1 1 0 2 -1 0 0 2 -1 0 1 1 1
  -1 1 0 2 1 -2 0 -2 2 0 -1 -2 -3 1 1 -1 0 6 2 -2 3 0 3 -1 -2 -3 1 0 -3 2
  1 0 -1 2 2 0 0 -1 2 -1 0 1 4 -2 0 2 1 2 0 0 2 0 1 -1 0 -1 2 0 1 2 -1
  -1 2 -1 -2 2 8 -1 0 2 -4 2 2 -1 1 1 2 2 -1 -3 -2 -1 3 -2 1 -1 -2 2 1 -1
  -1 1 2 -1 1 0 0 0 1 1 -3 3 2 1 -2 0 4 1 3 0 0 -2 -2 -2 -1 8 0 -2 3 2
  -1 -2 1 0 0 -3 3 -1 0 -1 1 1 1 -2 1 -2 0 0 2 -3 1 1 0 2 -1 1 0 2 1 -3
  0 -4 2 1 -2 -2 -2 3 0 -1 -1 3 0 0 8
  

• DETERMINANT
  1
  

• GROUP_ORDER
  1200
  

• GROUP_GENERATORS
  6
  48 48
  -4 -3 0 0 -4 0 -1 1 1 -1 2 2 1 -1 -1 0 0 -1 -2 0 -1 -1 -1 0 0 2 1
  0 1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 -6 1 0 -3 2 3 -3 0
  -1 -2 -1 2 1 1 -2 1 0 1 0 1 3 -1 -1 0 0 0 -1 2 1 1 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 1 2 -4 4 -2 -4 0 3 0 0 1 -2 -3 1 -1 1 0 0 -1 0 1 2
  1 0 0 -1 0 0 -1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 -1 2 0 3
  2 1 -2 2 1 -1 2 3 0 1 0 -2 0 0 1 -2 -2 -1 -1 1 1 0 -1 0 0 -1 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 3 -1 4 1 0 -2 2 1 -1 0 0 0 1 -1 1
  0 1 -1 0 0 -1 1 1 -1 0 0 0 -1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1 0 -1 -1 -2 0 1 0 0 -1 1 1 0 0 0 0 -1 -1 0 1 -1 -1 0 0 -1 1 0 -1 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 -1 0 -1 0 1 0 -1 -1 0 0
  -1 0 0 0 0 0 0 1 0 0 0 0 -1 -1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 1 2 1 2 -1 0 -1 2 1 0 -1 -1 0 0 0 1 0 1 -2 1 0 -1 1 1
  -1 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 -2 1 -1 -4 0 0
  0 -1 -2 2 2 0 0 0 -1 0 -1 0 1 0 0 0 0 -1 1 1 -1 0 -1 -1 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 2 2 -3 2 1 -1 1 1 -1 1 -1 -2 -1 1 0 1 -1 1 0
  0 0 0 1 -1 0 -1 -1 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1
  -1 -1 1 1 1 0 0 0 0 1 2 1 1 0 -2 1 -1 1 -2 -2 0 -1 0 1 0 0 1 1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 -2 3 1 2 -2 0 0 -1 1 1 1 2
  -1 -1 0 1 1 -1 -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 -2 -2 0 -1 1 2 0 -1 -1 0 -1 1 3 0 1 1 -2 1 0 1 -1 -2 0 -1 0 1 0
  0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 -1 1 -3 -1 0 1 1
  -1 2 0 -2 0 0 0 0 -2 0 1 0 1 0 0 -1 0 0 -1 -1 -1 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 -1 -3 0 0 -1 1 1 -2 0 -1 1 2 1 0 1 -2 1 -1 1 -1
  -1 1 -1 0 1 0 0 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 -2 0
  -3 -1 0 1 -1 -2 1 0 -2 0 -1 0 1 -1 -1 1 0 1 0 1 -1 -1 0 0 0 0 1 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 3 -2 4 3 1 -3 0 0 -2 1 1 0 1 -1
  0 1 1 0 -1 -1 -1 0 0 -1 -1 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 1 0 -2 0 -2 -1 1 1 -3 -1 0 0 0 1 0 0 -1 1 0 1 0 0 2 -1 -1 0 0 0
  0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -3 -2 5 -1 2 3 0 -3 2 1 0
  2 3 0 1 -1 -1 0 1 0 -1 -2 -1 -1 1 1 0 -1 1 -1 -2 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 3 3 -2 3 2 -3 2 1 -1 1 -1 -2 -2 2 1 0 -1 1 1 0 1 2
  2 -1 0 -2 0 0 -1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 -2 -1 0
  -2 3 1 -1 -1 0 0 -1 1 2 -1 -1 -1 1 1 0 1 1 0 -1 0 1 -1 -1 0 1 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 -3 0 -3 -1 0 1 -3 -1 0 0 0 1 0 1
  -1 0 0 2 0 0 2 -1 -1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 -1 3 -2 2 3 0 -3 1 -1 0 2 1 -1 0 -1 0 0 0 1 -1 -1 -2 1 0 0 0 -1
  0 -1 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 -4 3 1 -2 2 1 -1 1
  -1 0 1 2 1 2 -4 1 0 2 -1 -1 2 -2 0 0 0 -1 -1 1 0 2 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 -1 -1 -1 -2 0 0 1 -1 -1 1 0 0 -1 -1 0 0 0 -1 0 0
  0 0 0 -1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 -5 2
  -4 -3 1 3 -1 -1 1 1 -1 1 0 0 -2 -1 -2 2 -1 1 2 -1 -1 1 1 -1 -1 1 0 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 -3 1 -4 -2 0 3 0 -1 2 -1 -2 0
  -1 0 0 -1 -1 0 0 1 1 0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 -4 2 -2 -3 1 2 -1 0 1 0 -1 2 1 0 -2 0 -1 2 0 1 2 -1 -1 0
  1 -1 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 1 2 -1 4 1 1 -2 0
  1 -2 0 1 0 1 0 0 0 2 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 -1 1 -2 2 -1 -2 2 2 0 0 1 0 0 2 1 0 -2 0 0 1 -1 0 1
  -2 0 1 0 -1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0
  -1 0 0 0 0 0 0 0 0 -1 0 0 1 0 0 0 0 0 0 -1 -1 -1 0 0 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 1 1 -5 1 -3 -4 0 3 -3 0 0 -1 -2 2 0 1 -1 1 0 0
  1 1 3 0 -1 0 0 0 -1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -4 -1 -9
  1 -12 -2 -4 6 -3 -4 3 -2 -7 -1 -3 1 0 0 -4 -2 1 3 1 2 -4 1 -1 2 -1 1
  0 -2 2 0 1 0 2 -2 -1 2 1 0 1 -2 1 0 -1 -1 -6 -5 11 -4 3 6 -3 -5 4 2
  2 2 6 -2 1 -2 2 -2 2 -1 0 -2 -2 0 2 2 2 -1 2 -2 -2 0 0 0 0 -1 0 0 0
  -1 -1 -1 -1 1 0 0 1 0 3 -2 11 0 10 2 3 -7 2 3 -4 4 5 -1 2 -1 1 1 3 0
  0 -3 -1 0 4 -1 1 -1 1 -2 -2 1 -2 1 -1 0 -1 2 1 -1 0 0 -1 0 -1 1 -1 1
  0 1 0 -1 0 2 -1 -1 0 0 0 0 1 0 0 0 -1 0 1 1 -1 -1 0 -1 0 0 -1 0 0 0
  0 0 0 -1 0 0 0 0 0 0 0 0 0 1 0 0 1 0 -4 0 5 -2 -1 2 -3 -2 1 2 3 -1
  1 0 0 0 2 -1 3 -3 1 0 -1 0 1 0 0 1 1 -1 0 0 0 0 1 -1 0 0 1 -1 0 -1
  0 1 0 -1 2 -1 -4 -2 0 2 -6 -1 -4 1 0 0 3 0 -2 -1 -3 1 1 0 -1 -2 1 1
  0 1 0 1 0 1 0 -1 -1 0 0 0 0 -1 1 0 0 0 1 0 0 0 0 0 0 -1 -5 1 -6 -1
  -13 -2 -3 6 -2 -4 5 -2 -6 0 -1 0 1 -3 -2 -1 1 3 1 1 -4 1 0 1 -1 0 0
  -2 2 0 2 1 1 -2 0 1 0 0 1 -1 1 -1 0 -1 -2 -1 6 -1 2 2 0 -2 4 0 2 2
  2 -1 1 -2 1 -2 0 1 -1 -1 -2 0 1 0 2 -1 1 -2 0 0 0 0 0 0 0 0 0 -1 -1
  0 -1 1 0 0 1 0 3 4 -5 3 3 -3 0 2 -2 1 -3 -4 -4 1 0 2 -1 2 1 -2 2 2
  2 1 0 -2 -2 1 -2 1 1 0 1 0 0 0 1 0 -1 1 0 0 0 -1 0 1 -1 0 -3 -2 -2
  -1 -2 2 0 0 -1 -1 0 2 2 0 0 1 -3 0 -1 2 -2 -2 0 -1 -1 2 -1 -1 0 1 -1
  0 0 0 0 0 0 0 0 1 0 0 0 -1 0 0 -1 0 0 0 2 0 2 -1 1 -1 2 1 2 0 1 2
  1 -1 0 0 1 0 0 0 0 0 1 0 1 -1 0 -1 0 0 -1 0 0 0 -1 0 1 -2 0 -1 0 1
  0 -1 1 0 0 -2 14 -5 8 5 0 -7 4 3 0 2 5 -1 3 -3 4 -2 4 -1 1 -2 -2 1 3
  -1 2 -1 2 -3 -1 0 -1 1 0 0 -1 1 1 -2 -1 -1 -1 1 0 0 1 0 -1 0 -4 4 -2
  -2 -1 3 -2 2 0 -2 -1 2 0 2 -2 1 -2 1 0 1 3 -1 0 0 -1 0 0 2 0 2 1 1
  0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 3 2 -5 1 -3 -2 4 3 -2 -3 0 0 -1 2 2 0
  -2 -1 -1 4 -1 0 2 -2 -2 0 0 -1 -1 1 0 0 0 0 0 2 -1 0 0 0 0 0 0 0 0
  0 -1 1 -1 1 -4 3 -4 -1 -1 2 1 -2 1 0 -2 -1 -2 1 -1 -1 -2 1 -1 1 -1 0
  -1 0 0 0 -1 0 1 0 1 -1 0 0 1 -1 -1 1 0 0 0 0 0 0 0 0 -1 2 -4 3 -1
  -2 -3 2 -2 3 1 -5 -3 2 -1 3 -1 1 1 -2 2 2 3 0 0 -1 -2 1 -1 1 1 2 1 1
  1 -1 1 -1 0 0 0 -1 0 -1 0 0 0 -1
  48 48
  1 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 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 1 0 1 1 0 -1 0 0 0 0 1 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 0 0 0 0 0 0
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  0 1 -1 0 -1 -1 1 0 0 1 0 -1 1 1 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0
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  -1 1 1 0 0 1 -1 0 -1 -1 1 0 0 1 0 -1 1 1 -1 0 0 -1 0 0 0 0 0 0 0 0
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  0 -1 1 -1 -1 1 1 1 0 -1 1 0 0 0 0 1 -1 0 0 0 0 0 1 0 0 0 0 0 0 0 0
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  0 0 0 0 0 0 0 0 0 0 0 0 1 0 -1 -1 -1 0 0 0 -1 -1 0 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 0 0 0 0 0 0 0 1 2
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  0 0 3 0 3 1 0 -2 1 1 -1 0 1 0 1 0 0 0 1 0 0 0 0 0 1 -1 0 0 0 0 0
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  0 0 -1 -1 2 -2 -1 2 -1 -1 1 -1 1 1 0 -1 0 -1 1 -1 0 0 0 0 -1 1 0 0 0
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  48 48
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  -1 1 -1 -1 1 0 -1 0 0 -1 1 1 0 0 0 -1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0
  0 0 1
  

• MODULAR
  1
  

• REFERENCES
  G. Nebe, A fourth extremal even unimodular lattice of dimension 48. Preprint 2013
  

• LAST_LINE
  

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  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe