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 13:12:35 CEST 2014

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
GRAM
DIVISORS
MINIMAL_NORM
SUBGROUP_NAME
SUBGROUP_GENERATORS
PROPERTIES
REFERENCES
NOTES
LAST_LINE

• NAME
  L24,2.otimes.L_24,2
  

• DIMENSION
  72
  

• GRAM
  72 0
  18
  -9 18
  6 -3 18
  3 -6 9 18
  -3 12 -6 -6 18
  -12 6 -3 3 6 18
  -6 9 -3 3 12 9 18
  0 -6 -6 -6 -6 0 -9 18
  6 0 -9 -9 3 -9 -3 0 18
  -6 6 0 -3 3 -3 0 -6 3 18
  -6 -3 6 0 -6 0 -6 0 -6 9 18
  3 -3 -9 -6 6 3 3 9 3 -9 -9 18
  3 -3 -9 -3 -3 -6 -3 0 12 0 -3 0 18
  -6 9 0 0 6 6 9 -9 -3 -3 -3 -3 -3 18
  9 -3 12 3 -6 -9 -6 -6 0 -3 3 -9 0 3 18
  6 0 9 9 3 0 6 -9 -3 -3 0 -3 -3 3 9 18
  0 -9 0 6 -9 3 -6 6 -3 -6 3 0 3 -3 0 0 12
  -6 9 6 6 6 9 9 -6 -9 0 0 -3 -9 6 0 9 -3 18
  -9 9 0 -3 9 9 9 -3 -6 0 3 0 -9 9 0 6 -3 9 18
  3 -6 -3 0 -9 -9 -9 3 6 0 -3 -3 6 -3 3 -6 3 -9 -9 18
  -6 0 0 6 6 9 12 -6 -6 0 0 3 -6 6 -6 3 0 6 6 -6 18
  12 -9 9 0 -6 -9 -6 3 0 -6 0 3 -3 -3 9 3 0 -6 -3 0 -3 18
  3 0 6 3 -3 -3 -3 3 -6 0 3 -3 -3 -6 3 3 0 3 0 -3 -6 3 12
  -12 0 -9 -12 -3 3 -6 12 3 9 12 0 3 -9 -9 -12 3 -6 3 0 -3 -6 0 30
  5 -9 9 5 -6 -6 -5 -5 0 6 9 -6 -1 -5 6 4 2 -3 -4 1 3 6 -1 0 20
  1 3 1 4 5 6 6 -6 0 -7 -8 0 -1 9 3 4 1 3 3 0 6 -2 -6 -10 0 20
  6 -5 -3 0 0 -3 -1 2 3 -5 -6 6 3 -1 -1 -1 1 -4 -5 3 0 3 -2 -5 -2 1 12
  4 -3 -6 -4 -3 -3 -5 4 6 -7 -4 3 10 2 3 -2 4 -8 -3 4 -8 3 -2 -1 -7 1 3 22
  2 -2 0 -1 0 -3 0 -1 1 1 4 -1 1 1 3 3 0 -3 3 -3 -1 3 1 1 1 -5 2 0 12
  0 6 -3 -3 3 0 0 0 2 0 -3 1 3 3 -1 0 -2 2 -1 -2 -6 -3 1 -3 -5 -1 3 2 3 14
  -9 8 -11 -4 3 3 2 3 5 4 -4 -1 3 3 -8 -6 0 1 3 5 -1 -11 -3 7 -10 1 1 1 0 3 22
  -12 14 -8 -5 9 6 10 0 -2 6 -1 -1 0 4 -8 -2 -6 7 9 -4 1 -11 3 8 -12 -1 -4 2 -2 2 12 26
  5 -5 0 -4 0 -3 -2 2 1 -3 1 5 0 -1 1 -2 -1 -6 -1 -3 -1 7 0 0 4 -3 1 1 4 -2 -9 -7 14
  -7 -3 3 0 1 4 4 -2 -6 7 10 -1 -9 0 -4 -2 -1 -1 7 -4 12 2 -3 9 10 -2 -5 -10 4 -8 -4 -2 2 26
  7 2 0 -8 5 -6 -2 2 5 0 -6 6 0 -4 0 -4 -7 -4 -5 1 -4 5 1 -2 -4 0 6 1 -3 2 -2 -1 1 -4 20
  5 -6 0 11 -3 -3 3 -7 1 -2 -5 -1 6 3 0 4 3 0 -8 4 5 0 -3 -14 6 2 7 0 0 2 -2 -7 0 -4 -4 24
  -6 0 2 3 -2 6 -1 5 -8 3 5 1 -8 -4 -7 -2 2 7 1 -4 3 -3 3 5 0 -6 -2 -5 -1 3 1 1 -3 5 -3 -2 18
  -3 -3 3 6 -3 6 4 -2 -8 -6 -1 1 -2 3 0 2 3 4 1 0 6 0 -1 -4 0 6 0 2 -3 -2 -3 1 -2 3 -3 1 4 16
  -7 7 -12 -7 9 7 7 6 3 0 -6 10 0 0 -13 -5 -3 3 4 -4 3 -8 -3 7 -8 -1 2 -3 0 6 9 7 -1 1 1 -3 6 -2 20
  8 -9 -4 -4 -6 -6 -10 10 6 -8 -2 6 7 -7 3 -2 6 -9 -6 6 -9 5 1 3 -4 -6 8 9 5 2 0 -8 2 -7 5 -1 -3 -4 1 22
  0 -3 -1 2 -5 -4 -4 3 1 2 1 -3 1 -4 0 -1 2 -1 -2 7 -3 -1 2 3 -2 -5 3 0 1 -2 8 2 -5 -3 -1 2 1 -1 -2 4 12
  -2 4 3 -2 1 1 -3 1 -3 4 5 -3 -6 -1 1 0 -2 3 4 -4 -4 -1 4 3 -2 -3 0 -3 5 6 4 1 -3 2 2 -8 7 -3 2 1 1 16
  -9 3 -9 0 5 8 4 1 1 5 2 2 0 -1 -11 -2 2 3 4 -2 5 -12 -3 8 -1 2 -3 -2 -1 0 9 8 -4 4 -7 -1 7 1 7 -6 1 3 20
  5 -8 7 3 -7 -3 -8 1 0 -1 5 -2 -2 -4 6 2 4 -2 -4 2 -1 6 -1 -1 7 -1 2 -4 4 -2 -2 -14 0 5 1 0 1 -1 -4 7 2 5 -4 18
  4 6 -2 -8 5 -6 -2 -4 9 1 -5 -1 5 5 5 -2 -6 -3 -2 3 -6 1 -3 -5 -2 5 -2 5 -2 3 0 1 3 -7 6 -2 -9 -4 -3 -2 -5 -3 -4 -3 18
  11 -9 8 8 -7 -9 -5 -3 0 -3 -2 -2 -1 -2 8 4 2 -4 -7 6 0 9 1 -12 5 -2 7 -1 2 -3 -4 -14 1 -3 4 10 -3 -3 -8 7 5 0 -10 9 -4 22
  6 0 0 1 3 -3 -1 -3 5 0 -3 1 2 0 2 4 -1 0 -3 0 -2 0 -1 -7 3 5 1 3 -2 3 -2 -3 -1 -4 1 3 -1 -2 0 -1 -3 1 4 1 4 0 12
  -1 -3 6 1 -6 0 -3 -4 -3 0 6 -6 2 1 7 0 2 -3 -1 1 -1 3 -1 1 8 0 -3 -1 -1 -3 -10 -9 3 4 -1 2 -5 1 -7 0 -4 -3 -8 3 -1 3 -4 20
  -6 14 -11 -7 9 2 4 -5 8 6 -6 -2 9 7 -5 -5 -5 -1 0 1 -5 -12 -4 0 -8 3 -2 6 0 10 11 12 -3 -8 0 0 -5 -5 6 -4 -4 2 6 -9 11 -10 3 -3 30
  -13 7 -5 -6 2 10 4 5 -6 1 3 2 -2 4 -9 -9 -1 5 4 -6 3 -7 -1 11 -10 -4 -3 0 -1 3 5 11 -2 3 0 -8 8 5 7 -4 -1 2 3 -5 -2 -12 -8 -1 5 24
  6 -1 3 3 3 -3 4 0 -3 -2 -4 5 -5 -2 -1 4 -4 2 0 -4 2 6 5 -8 -2 -2 3 -1 0 -1 -3 3 2 -2 6 3 1 0 -2 -2 1 0 -2 -3 -1 5 1 -7 -4 -3 16
  2 -1 5 -3 -5 -7 -8 -1 3 8 6 -8 2 -7 5 -4 -2 -5 -5 4 -7 2 3 7 3 -4 0 -3 2 1 0 -2 -3 1 7 -7 0 -2 -7 2 4 7 -4 5 2 3 -3 3 -1 2 -1 22
  -2 -2 -4 -5 -2 -5 -1 5 3 3 2 2 2 -4 -2 -3 -1 -4 1 5 0 2 0 9 0 -8 -1 1 2 -4 5 4 1 5 2 -2 0 -1 3 4 5 -2 -2 0 -2 1 -7 0 -1 3 0 1 20
  1 5 -2 -2 3 -3 0 -1 4 3 -3 -2 2 0 1 1 -3 1 0 2 -4 -3 1 -1 -4 -3 0 -1 3 4 5 2 -1 -5 1 -1 0 -5 4 2 2 2 -2 -1 3 1 -1 -3 7 -1 -1 0 1 12
  -5 7 6 -2 1 2 2 -1 -8 0 4 -5 -8 5 5 2 -4 6 9 -3 -1 1 5 1 -4 0 -8 -1 0 -1 -2 8 -3 6 0 -10 1 3 -3 -5 -2 3 -3 -2 2 -6 -3 2 -2 5 0 2 0 -1 20
  2 -8 6 5 -7 -3 -4 2 -4 3 5 -2 -3 -9 0 -1 2 -2 -5 3 2 4 3 3 8 -5 0 -5 -1 -6 -6 -4 0 8 2 2 5 2 -5 1 2 0 -1 4 -6 5 -3 3 -9 -3 3 5 4 -3 0 16
  -9 0 5 8 -1 8 6 -8 -9 8 10 -8 -3 0 -3 1 1 5 2 -6 10 -6 0 4 6 0 -5 -9 -1 -5 -5 2 -3 11 -6 1 5 6 -4 -11 -2 0 5 0 -7 -3 -3 6 -4 6 -1 4 -6 -4 1 7 24
  10 -2 1 -4 1 -12 0 -4 8 0 -2 -1 7 1 9 4 -4 -9 -1 1 -4 10 1 -4 3 -3 5 6 10 0 -3 -3 6 0 4 3 -11 -5 -3 8 1 -2 -11 1 3 8 -1 3 2 -7 2 3 7 5 -2 -2 -8 28
  1 2 -7 1 10 3 9 -3 4 -2 -8 8 0 2 -5 5 -2 1 5 -2 7 -3 -4 -6 -4 5 2 2 1 -1 5 3 -3 1 0 3 -1 1 6 -1 1 -1 8 -3 -2 1 4 -7 1 -5 3 -8 1 1 -3 -4 -3 2 20
  -6 -4 5 4 -8 5 -2 5 -11 -2 6 -2 -6 -2 -1 -3 5 2 1 1 3 1 3 6 1 -2 -4 -6 -1 -5 -1 0 0 8 -5 -6 5 8 -2 -3 1 0 -2 4 -6 -3 -8 4 -9 8 -4 1 3 -3 6 4 6 -7 -6 20
  3 -4 -1 0 -2 -2 -1 3 1 -1 -3 4 0 -2 -4 -6 0 -5 -7 2 2 3 -2 -1 1 -1 3 -1 -3 -1 -3 -3 2 1 5 3 -1 -2 -1 1 -2 -3 -3 -1 1 3 0 0 0 2 3 1 1 -4 -4 4 0 -2 -3 0 14
  8 -9 2 7 -8 -9 -5 -5 7 5 1 -6 11 -9 3 0 3 -9 -14 7 -3 1 0 -2 8 -1 0 5 -2 -4 -3 -7 -1 -2 2 7 -4 0 -9 2 1 -3 -1 4 1 8 4 4 -1 -10 0 7 1 -2 -7 6 4 3 0 -2 3 28
  -2 2 -2 -2 3 0 -1 -3 4 6 6 -4 4 -2 1 3 0 2 2 -3 -1 -6 0 6 4 -1 -2 2 2 2 2 3 -3 0 -2 0 2 -2 0 1 1 4 8 0 -1 -4 4 0 6 0 -2 3 1 0 -2 -1 2 2 2 -8 -5 3 18
  5 -8 9 7 -6 -2 -7 3 -6 0 5 -2 -8 -9 4 4 4 0 -1 2 -1 6 6 -1 10 -3 -1 -8 1 -5 -7 -9 1 7 -4 0 4 -1 -5 3 2 3 -1 8 -7 6 1 2 -12 -11 1 1 -2 -2 1 9 1 -1 -1 6 -2 1 -1 22
  0 -3 2 -2 -5 -1 -6 3 0 0 4 -3 1 -1 3 -4 3 -5 -2 3 -3 3 -1 5 4 2 -2 4 -3 -3 -4 -2 3 0 0 -3 -2 0 -5 1 -2 -3 -3 -1 3 -2 -1 5 -3 -1 -3 3 0 -4 1 2 0 0 -7 2 2 3 -1 2 12
  4 4 5 -3 2 -6 1 -5 2 1 1 -3 0 5 8 6 -5 3 2 -3 -3 4 1 -5 5 2 0 1 0 4 -5 1 2 -4 2 2 -4 -3 -2 -3 -4 0 -5 -3 5 0 5 3 2 -5 1 -2 -1 -1 3 -2 -5 6 -3 -6 0 -2 2 -3 2 18
  1 7 -5 -2 7 -2 4 -1 4 3 -8 2 2 -1 -5 -2 -6 2 -2 1 -2 -5 2 -3 -8 0 3 1 -3 3 8 10 -4 -8 8 1 -1 -3 4 -1 3 1 2 -7 4 0 1 -9 7 0 5 0 1 5 -1 -2 -5 0 6 -5 1 3 -1 -5 -4 0 16
  -3 -3 -4 -1 1 7 2 2 -3 -7 -1 5 1 4 -2 -2 4 -3 4 -2 4 1 -4 1 0 4 4 4 0 -3 -2 -1 5 1 -3 3 -6 3 0 3 -2 -5 -2 -2 -2 -1 -4 6 0 0 -2 -8 0 -4 -4 0 1 1 0 1 1 -6 -2 0 3 -1 -4 20
  -4 -8 3 3 -5 5 0 4 -6 -3 7 1 -7 0 -1 0 6 0 5 -1 9 3 -3 7 4 1 0 -7 1 -8 -2 -6 1 12 -4 -3 3 2 -1 1 1 0 0 7 -8 3 -5 2 -18 1 -2 0 1 -6 2 5 7 -7 -2 10 2 -2 -6 5 3 -4 -7 4 24
  -7 7 4 -2 0 1 -1 1 -6 9 7 -4 -9 -1 -3 -3 -5 7 3 -4 -1 -2 5 5 -1 -8 -5 -7 -2 2 2 7 -3 2 0 -6 11 -2 1 -9 2 8 5 -2 -3 -3 0 -4 0 6 4 3 -2 0 5 3 6 -10 -4 2 -1 -7 1 2 -2 2 1 -7 -2 22
  -2 -6 -4 10 -4 3 3 -2 1 -1 -3 -2 4 -1 -4 2 7 -1 -2 7 6 -6 -4 -1 3 5 0 0 -4 -5 4 -1 -5 0 -10 10 0 4 -1 -4 5 -8 8 -4 -6 2 1 0 -2 -5 -1 -4 -2 -1 -7 3 7 -6 6 0 0 6 1 1 -1 -6 -2 3 4 -4 24
  -2 5 -5 -1 4 5 6 2 0 -8 -9 6 2 6 -3 1 0 5 2 -1 1 -3 -2 -5 -9 4 0 2 -3 5 1 5 -1 -8 -2 1 -1 3 6 -1 -3 -6 -1 -8 4 -7 -1 -3 5 5 0 -8 -2 2 2 -6 -5 -5 1 0 0 -9 -6 -6 -1 1 2 3 -3 -2 1 18
  

• DIVISORS
  1
  

• MINIMAL_NORM
  <= 6
  

• SUBGROUP_NAME
  SL_2(13) otimes SL_2(13)
  

• SUBGROUP_GENERATORS
  2
  72 72
  0 5 -10 8 15 -6 19 2 2 -14 9 -6 -5 -2 6 -7 15 5 -4 6 -8 7 -6 3 9 -8 0 1 -1 -2 2 1 1 -2 4 -1 3 1 0 -3 -1 1 0 2 1 1 0 0 0 0 -1 3 -2 0 1 -1 1 -1 0 -1 0 0 -2 1 -1 0 0 1 -2 0
  -1 -1
  -15 -8 4 3 7 -6 -13 -3 -3 -3 -7 4 0 6 -4 4 -6 0 -4 -2 -3 1 1 3 0 2 -5 0 7 -5 -2 2 -3 -2 3 1 2 -2 1 -1 -1 0 -2 0 -3 -2 -1 -1 1 -3 -2 1 -1 -1 -2 -1 0 1 0 0 1 1 1 -1 0 0 0 0 1 0
  1 1
  3 -11 11 -7 1 -1 3 4 -5 2 -2 -2 6 5 -2 0 -5 -3 5 -1 -1 -2 -2 2 -4 -1 -2 -2 1 -4 0 -1 -4 -4 1 3 4 -1 2 -2 -1 -1 1 0 -1 0 1 -1 3 -3 -1 1 0 -1 0 -1 1 -1 0 1 0 0 0 1 0 -1 0 1 -1 -2
  -1 0
  27 11 -7 -8 -31 14 -3 -4 5 19 8 2 0 -9 3 -1 -1 -5 11 -8 12 -8 0 -10 -12 7 6 -2 -15 12 2 1 7 7 -6 -1 -5 3 -2 5 2 0 3 -1 3 1 0 3 -5 3 3 -4 4 2 2 2 -1 2 -2 0 0 -2 0 2 -2 0 1 -1 -1 0
  1 1
  11 18 -10 3 -12 7 2 5 11 1 10 1 -6 -3 3 -2 3 4 0 2 6 -4 4 -7 3 -2 4 3 -4 4 0 0 5 5 0 -2 -3 2 -2 1 0 0 0 0 0 -1 -1 1 -2 0 1 2 0 0 0 0 0 1 1 0 0 0 -1 -1 -1 0 0 1 0 0
  1 0
  16 8 -3 -6 -11 11 6 -2 0 2 8 0 0 -5 4 -6 1 1 4 2 1 -2 1 -4 1 -2 3 0 -3 1 1 -1 -1 2 0 1 -1 0 0 0 -1 0 1 -1 1 0 0 -2 0 0 1 -1 1 0 0 0 -1 1 1 1 0 0 0 -1 0 -1 -1 0 1 0
  1 1
  -5 6 0 4 -7 1 -16 -1 4 7 -4 6 1 1 -2 6 -6 -1 -1 -3 5 -4 4 -3 -3 5 2 1 0 3 -1 -1 3 4 -3 -2 -4 0 -1 2 0 0 -1 -1 -2 -2 -1 1 -3 1 2 -1 1 0 0 1 -1 1 0 0 1 0 1 -1 0 0 1 0 1 1
  1 0
  -16 6 -16 12 20 -9 11 -1 -2 -15 2 -2 -7 -1 6 -2 14 10 -15 4 -13 12 -4 5 14 -5 0 2 4 -4 2 2 3 1 5 -3 1 0 -2 -1 0 2 -3 0 1 2 0 -1 0 1 -2 2 -2 0 0 -1 1 -1 1 -2 0 1 -1 0 0 0 -1 -1 0 1
  1 0
  -35 -23 2 11 33 -20 -15 -12 -9 -18 -16 -1 -2 9 -5 5 1 0 -12 0 -13 10 -5 13 5 0 -13 -2 14 -10 -4 6 -8 -8 7 1 7 -4 4 -4 -1 1 -3 2 -4 -2 -2 -1 2 -3 -3 1 -3 -2 -3 -2 0 1 -1 -1 1 1 0 -1 0 1 0 0 1 1
  -1 0
  5 -8 5 -6 -20 3 -23 -8 1 16 -8 6 2 3 -7 7 -13 -8 7 -11 10 -8 3 -3 -14 11 -3 -3 -4 5 -3 3 0 1 -3 1 -1 -1 1 4 2 -1 2 -1 -1 -1 -1 2 -2 0 1 -3 3 1 0 1 0 2 -2 1 0 -1 1 1 -1 1 0 0 0 -1
  0 1
  -2 -2 1 1 -9 -1 -5 -5 2 7 -2 7 -2 0 -2 2 -4 -1 -1 -5 3 -2 3 0 -5 6 0 1 -1 3 1 0 2 1 -1 -1 -1 -1 -1 2 2 -1 1 -1 1 1 1 2 -1 1 0 -1 2 2 1 0 1 0 -1 0 0 -1 1 2 0 1 0 0 0 -1
  0 1
  -9 10 -3 4 -4 1 -9 9 5 6 -5 3 1 1 -1 8 -4 4 -7 -2 5 -4 5 -4 2 4 5 3 0 5 0 -2 7 7 -4 -5 -5 1 -5 3 2 0 -2 -2 0 0 0 2 -3 1 2 0 1 0 0 1 0 0 1 -1 0 0 0 -1 0 0 0 -1 1 1
  1 -1
  -8 -17 0 -6 -8 -2 -27 -13 -6 13 -17 3 0 1 -9 12 -9 -6 -1 -11 8 -2 1 1 -13 14 -8 -3 -1 6 -3 6 1 1 -4 0 -2 -1 0 5 4 1 0 0 0 0 -1 4 -3 1 0 -4 2 1 -1 1 -1 3 -3 -1 0 -1 1 1 -1 2 1 -2 1 2
  0 1
  4 1 7 3 6 -1 12 -3 -1 -8 8 1 0 -4 1 -10 2 -3 7 5 -4 1 -2 3 2 -6 1 1 1 -3 2 -3 -5 -5 1 3 1 0 1 -3 -3 0 1 2 1 -1 1 -2 1 0 -1 0 -1 1 0 0 -1 0 0 1 1 0 1 0 1 0 0 0 0 0
  0 1
  -14 -16 19 0 22 -10 11 8 -5 -11 -4 -4 4 5 -4 -2 -3 -3 2 6 -6 2 -2 8 3 -6 -5 1 8 -9 0 -3 -7 -9 3 5 5 -1 2 -4 -2 0 0 2 -1 0 2 -2 5 -3 -3 3 -3 -1 -1 -2 1 -2 0 1 0 1 0 0 1 0 0 1 -1 -1
  -2 0
  -4 -10 10 -10 -10 3 -17 8 -1 15 -11 1 6 7 -4 11 -13 -2 0 -7 9 -8 4 -4 -9 7 -2 -1 0 2 -2 0 2 2 -3 0 -1 0 0 2 2 -1 0 -2 -3 -1 0 2 1 -3 1 0 1 -2 -1 0 0 1 0 0 0 0 0 0 -1 -1 1 0 1 -1
  0 0
  26 -4 -7 -20 -33 16 -16 -6 -6 29 -7 -3 5 -5 -2 8 -6 -6 9 -13 14 -7 0 -9 -18 12 2 -7 -15 12 -1 4 6 7 -9 -1 -5 3 -1 7 4 1 2 -1 3 2 -1 4 -3 3 3 -7 4 0 1 3 -2 3 -1 -1 -1 -2 1 1 -1 0 1 -3 1 1
  1 1
  19 -2 11 -17 -28 13 -12 12 4 20 -2 -1 6 4 -6 7 -16 -6 12 -7 16 -14 5 -10 -13 5 1 -2 -6 4 -3 0 1 3 -4 3 -2 2 0 3 1 -1 2 -2 -1 -1 0 1 1 -3 1 0 2 -1 -1 0 0 1 0 2 -1 0 0 0 -1 -1 0 1 0 -2
  0 0
  9 -11 20 -18 -7 8 -5 14 -5 12 -9 -6 12 7 -7 6 -14 -6 10 1 8 -8 4 -3 -7 -1 -1 -3 1 -4 -4 -4 -5 -3 -4 5 0 1 3 0 -1 0 1 0 -2 -1 0 -2 5 -2 1 0 -1 -3 -1 0 -1 -1 2 2 -1 1 1 -2 2 -1 0 1 1 -1
  -1 -1
  -5 6 7 6 3 -1 7 6 5 -3 5 2 0 -4 3 -4 -1 -1 2 2 0 -2 1 -1 2 -2 5 3 0 2 3 -4 2 1 -1 -1 -2 1 -2 0 0 -2 0 -1 1 0 2 0 0 1 0 0 0 1 0 1 0 -1 0 0 0 0 0 0 0 0 0 -1 0 0
  0 0
  19 15 -2 -8 -34 16 -17 1 6 24 0 5 3 -7 -2 7 -11 -5 9 -8 17 -12 7 -11 -12 10 9 -1 -11 12 0 -2 8 10 -10 -2 -9 3 -4 7 2 0 1 -2 2 0 0 3 -5 4 4 -5 4 1 1 3 -2 2 0 0 0 -1 1 -1 0 0 1 -2 1 1
  2 1
  -29 -20 5 7 34 -19 -3 -7 -14 -18 -13 -2 2 9 -4 3 2 2 -11 3 -15 11 -6 15 7 -3 -10 -1 14 -12 -1 2 -8 -9 6 2 7 -4 3 -5 -2 1 -3 2 -3 -1 0 -2 3 -3 -3 2 -3 -2 -2 -2 1 -1 0 -1 1 1 0 0 1 0 0 0 0 0
  -1 0
  16 -3 -11 -9 -16 4 -4 -4 -2 13 -1 -3 -2 0 -1 4 3 -1 3 -7 6 0 -2 -4 -9 5 -2 -4 -9 5 -1 5 4 2 -2 0 -1 2 1 3 2 1 1 1 1 1 -1 3 -1 1 0 -1 1 0 1 1 0 1 -1 -1 -1 -1 0 2 -1 0 1 0 -1 0
  0 0
  -7 -15 5 -2 12 -5 -2 -7 -10 -4 -9 -3 4 4 -3 0 -1 -3 0 0 -9 6 -3 7 1 -1 -4 -5 5 -8 -3 1 -8 -6 2 3 4 -2 4 -1 -1 1 0 0 0 1 0 -3 4 1 -1 -2 -1 -1 0 0 -1 -1 1 1 -1 1 1 -1 2 0 -2 0 1 0
  -1 0
  22 -28 18 -30 -22 10 -18 -5 -14 25 -18 -7 14 3 -15 10 -18 -14 18 -9 15 -10 0 -1 -23 12 -7 -8 -7 5 -5 2 -6 -4 -9 6 1 -1 3 4 2 0 5 1 1 1 0 2 1 0 2 -5 3 0 0 1 -1 2 -2 2 -1 -1 1 1 0 1 0 0 0 0
  -3 0
  -6 1 -12 5 22 -5 16 -9 -10 -20 6 -6 -5 -7 6 -9 15 8 -8 9 -15 13 -7 7 11 -8 -3 1 6 -6 3 2 -3 -2 6 0 4 -1 0 -5 -3 1 -2 3 1 1 0 -2 1 -1 -3 1 -3 -1 -2 -2 -1 1 1 -2 2 1 0 -1 0 0 0 -1 1 2
  1 2
  15 19 1 -10 -16 15 6 26 10 11 7 -5 4 -2 4 4 -4 7 0 4 12 -10 7 -12 1 -3 10 3 -3 6 2 -6 8 9 -5 -4 -5 5 -5 1 1 -2 -1 -3 0 1 1 2 1 -1 3 1 0 -3 0 1 0 -1 3 -1 -1 0 -2 -2 0 -2 1 0 1 -1
  1 -2
  -3 9 -9 13 17 -4 19 -7 1 -21 12 0 -6 -5 7 -13 14 4 -4 9 -13 9 -4 5 13 -10 1 2 6 -6 2 -1 -5 -3 6 -1 3 -1 1 -5 -2 0 -1 1 2 1 0 -3 0 1 -1 1 -2 1 0 -1 0 -2 0 0 0 0 0 0 1 1 -1 0 -1 0
  0 0
  -17 -16 19 1 22 -11 9 12 2 -12 -3 -2 1 8 -5 0 -5 -1 -1 6 -2 -1 1 6 5 -5 -8 4 8 -7 0 -2 -5 -9 4 5 5 -1 1 -3 -1 0 0 2 -3 -1 1 -1 5 -4 -3 5 -3 -1 -1 -3 2 -1 -1 1 0 1 -2 1 0 0 0 2 -1 -1
  -2 -1
  10 -24 1 -23 -10 3 -12 -6 -15 14 -13 -6 3 4 -8 8 -6 -2 2 -8 8 -1 -3 0 -14 8 -12 -4 -4 4 -2 7 -1 -3 -2 3 2 -1 1 2 2 1 2 2 -1 0 -1 3 1 -4 -2 -1 1 -1 -2 0 0 4 -2 -1 0 -1 0 2 -2 0 1 -1 1 0
  0 1
  2 -8 14 -10 -2 4 -4 7 -2 2 -1 -2 6 5 0 0 -10 -3 5 -1 2 -5 1 -2 -2 -2 -2 -2 3 -5 -2 0 -5 -3 2 4 3 0 3 -1 -1 -1 0 -1 -3 -2 -1 -3 5 -4 -1 0 -1 -3 -2 -1 -1 0 1 1 0 1 -1 -1 0 -2 -1 0 1 -2
  1 0
  -17 8 11 7 -17 0 -28 13 16 14 -6 15 1 9 -7 13 -22 -1 -3 -9 12 -14 13 -8 -5 10 4 5 6 2 -2 -3 5 7 -2 -3 -5 1 -4 4 2 -3 -3 -5 -4 -2 0 2 -1 -2 1 1 2 0 -1 0 1 -1 0 1 0 0 1 0 0 0 0 0 1 -2
  2 0
  -11 -5 14 14 20 -12 16 3 7 -18 6 3 -1 1 -5 -9 0 -4 5 7 -7 0 -1 7 6 -6 -1 4 6 -5 2 -4 -7 -8 3 3 4 -1 -1 -4 -3 -1 1 2 1 0 2 -1 1 0 -2 3 -1 3 1 -2 2 -2 -2 2 0 0 0 2 1 2 -1 2 -2 0
  -3 -1
  -13 10 3 18 13 -8 8 0 10 -13 6 7 -3 0 1 -5 3 1 -3 8 -5 1 4 4 10 -4 3 6 6 -3 1 -5 -1 -2 2 -2 1 -2 0 -3 -1 -1 -1 1 0 -1 0 -1 -1 2 1 2 -1 1 1 -1 1 -2 0 1 1 0 0 0 1 1 0 2 -1 0
  -1 -1
  6 1 -9 -9 17 1 29 6 -12 -14 8 -11 -3 -2 11 -8 16 12 -9 10 -10 12 -6 4 13 -12 -2 1 1 -5 4 0 0 -3 5 2 3 -1 1 -3 -1 1 0 1 0 1 2 -3 5 -3 -4 5 -3 -2 0 -1 1 -1 3 -2 0 2 -3 -1 0 -3 -1 0 0 0
  1 0
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  -3 -9 -1 -3 0 -2 -6 -7 -9 8 -8 -1 4 -3 0 3 0 -4 1 -6 -3 3 -4 1 -8 4 0 -5 -3 1 0 1 0 1 -3 -1 0 1 0 1 0 1 1 1 2 2 -1 1 -1 2 0 -5 0 0 0 1 -2 1 -1 -1 1 -1 3 0 1 1 1 -2 1
  1 1 1
  1 -3 3 0 11 -3 14 12 3 -10 5 -8 0 5 1 -4 4 3 1 6 -4 1 -2 1 6 -9 -2 0 2 -6 -2 0 -3 -4 5 2 5 1 2 -4 -1 0 0 2 -1 0 -1 -2 5 -3 -1 4 -3 -2 -1 -2 1 -1 2 1 -1 1 -2 0 0 0 -1 2 -1
  -2 -1 -1
  -3 17 0 18 -2 -4 5 0 17 -11 15 11 -8 -2 0 -8 0 2 0 3 1 -5 4 -1 6 -2 4 8 2 2 3 -2 2 1 3 -2 -1 0 -3 -2 -1 -2 -1 0 0 -2 0 1 -3 -1 0 3 1 3 0 -1 2 0 -1 1 1 -1 0 2 -1 1 0 1 -1
  -1 0 1
  40 -8 2 -27 -33 18 -11 -12 -12 28 -5 -4 10 -4 -6 2 -6 -10 18 -7 15 -7 -1 -6 -21 9 0 -8 -15 10 -2 1 -1 0 -11 2 -4 1 3 4 1 1 5 2 2 -1 -2 2 -3 3 4 -7 4 1 2 4 -3 3 -1 0 0 -2 2 1 0 0 1 -1 0
  1 0 0
  -1 10 1 0 -5 4 4 7 9 -3 8 4 -4 1 5 -2 -2 5 -5 2 3 -4 5 -4 6 -2 1 5 3 0 1 -1 2 2 3 0 0 -1 -1 0 1 -1 -1 -3 -2 -1 1 -1 1 -3 0 3 0 -1 -1 -1 1 -1 1 1 0 0 -2 -1 -1 -2 -1 1 0
  -2 1 0
  4 -9 10 -6 24 -4 34 8 -9 -20 8 -9 1 3 2 -12 9 4 1 15 -11 9 -4 8 12 -15 -4 2 6 -11 2 -4 -9 -11 5 6 6 -2 4 -6 -3 0 1 3 0 0 2 -5 8 -3 -4 6 -4 0 0 -2 2 -3 2 1 -1 2 -1 0 2 -1 -1 2 -1
  -1 -2 -1
  -13 -1 -3 6 22 -8 13 -2 -4 -19 3 -2 -6 0 3 -5 8 7 -9 9 -9 10 -2 8 13 -7 -5 4 8 -6 2 0 -3 -5 6 2 2 -3 1 -3 -1 1 -1 0 -1 0 2 -3 2 -1 -3 4 -3 0 -1 -1 1 -1 1 0 0 2 -2 -1 0 -1 -2 1 0
  0 -1 0
  12 -24 16 -29 -7 11 -13 9 -15 18 -20 -14 16 6 -10 12 -14 -8 11 -3 9 -6 0 -2 -12 4 -5 -8 -2 -1 -6 0 -5 -2 -7 5 1 1 3 3 1 1 1 1 -1 1 -1 -1 5 -1 2 -3 0 -4 -1 0 -1 1 1 1 -2 1 0 -2 2 0 1 -1 1
  1 -1 -1
  -7 4 6 2 7 0 3 13 1 -1 -1 -1 5 6 4 2 -2 3 -4 4 -3 0 3 -1 6 -5 5 1 4 -4 0 -5 0 1 0 -2 0 0 1 -2 -1 -2 -1 -2 -2 -1 0 -2 3 -1 1 2 -1 -2 0 0 0 -3 3 0 0 1 0 -2 1 -2 0 1 1
  -1 0 -2
  -38 -6 -7 24 44 -20 16 -14 -7 -34 3 2 -9 -5 10 -11 15 5 -15 6 -30 19 -8 15 19 -9 -3 0 15 -15 2 2 -8 -6 12 1 8 -3 1 -6 -3 1 -3 1 1 3 2 -5 4 0 -5 1 -4 0 -1 -3 -1 -1 0 -1 1 2 0 -2 2 0 -2 -1 1
  1 1 3
  -43 -6 -18 26 49 -26 15 -7 -3 -36 1 1 -13 7 7 -5 22 17 -28 10 -27 22 -6 13 23 -10 -9 5 18 -13 2 4 -3 -5 15 -5 9 -5 1 -9 -2 0 -5 2 -3 0 -1 -2 2 -4 -6 7 -5 -1 -2 -4 2 -1 0 -3 2 2 -1 0 0 0 0 2 0
  1 0 -1
  -26 -14 12 12 11 -15 -11 -6 5 -9 -5 11 -4 5 -9 2 -9 -3 -4 -4 -1 -3 2 6 -3 6 -7 5 9 -1 1 2 -3 -4 3 0 3 -3 -2 -2 0 -2 -1 1 -2 -2 1 3 -2 -4 -3 2 1 3 -2 -2 2 1 -4 0 2 -1 1 3 -1 2 1 0 -1
  0 -1 1
  12 -3 8 -13 -15 9 -15 3 -4 17 -11 -3 11 5 -7 8 -10 -6 8 -3 10 -7 3 -4 -8 5 2 -4 -3 2 -4 -2 -1 1 -7 0 -3 0 2 3 1 0 1 -1 -1 -1 -1 0 -1 2 4 -3 2 -1 1 2 -1 -1 1 1 -1 0 1 -1 1 0 0 0 0
  0 -1 -2
  21 -8 -16 -9 -12 4 -4 -30 -12 2 2 -1 -6 -9 -1 -6 8 -4 6 -6 2 5 -8 3 -10 6 -8 -4 -9 8 1 8 -2 -3 -1 2 0 -2 2 1 1 1 3 4 2 -1 -1 2 -5 1 0 -4 3 3 0 2 -1 5 -4 -1 1 -2 0 3 -2 1 1 -2 -1
  2 0 2
  -3 -4 8 12 37 -14 51 3 0 -36 19 -7 -5 -2 6 -23 17 1 3 17 -21 12 -8 13 19 -21 -3 4 7 -16 3 -5 -13 -14 11 8 10 -2 4 -8 -5 2 3 4 3 3 3 -7 7 -1 -5 7 -5 2 1 -4 2 -5 0 4 -1 1 -2 1 3 1 -3 4 -4
  -2 -3 0
  6 -24 4 -11 -2 -2 -15 -16 -15 9 -14 -3 5 3 -9 4 -5 -9 7 -7 2 2 -5 5 -13 6 -10 -7 -3 0 -3 6 -6 -6 -2 4 2 -1 4 1 0 2 2 3 0 -1 -2 1 0 0 -1 -4 0 0 -1 1 -2 3 -2 0 0 -1 2 1 0 1 0 -1 1
  1 -1 1
  -28 17 1 17 34 -9 26 26 11 -28 9 -3 -5 2 7 -4 9 15 -17 17 -12 6 3 3 27 -15 5 10 15 -10 3 -7 2 1 7 -3 2 0 -5 -5 -1 0 -5 -2 -1 2 3 -3 4 -3 -2 8 -5 -2 -1 -3 3 -5 3 0 0 3 -3 -3 1 -1 -1 1 -1
  -1 0 -2
  -11 -29 20 -21 -14 0 -42 2 -12 26 -30 1 14 15 -17 24 -29 -8 2 -15 13 -10 6 0 -19 17 -8 -6 5 -1 -7 2 -3 -1 -6 3 0 -2 2 5 3 -1 -1 -3 -5 -1 0 2 3 -3 1 -3 2 -3 -2 1 -1 1 0 1 -1 0 1 -1 1 -1 0 -1 2
  -1 0 0
  -40 -16 17 11 -4 -13 -49 -11 3 9 -22 19 3 8 -15 17 -28 -9 -4 -17 4 -10 8 3 -13 20 -4 0 13 0 -4 3 -2 2 -2 -2 0 -3 -3 3 2 -4 -4 -3 -4 -2 1 4 -3 -2 0 -4 3 1 -3 0 -1 2 -3 0 2 -1 3 0 0 1 1 -2 2
  0 1 2
  -18 13 -21 16 24 -6 9 4 1 -19 4 -6 -7 -2 7 -1 17 16 -17 11 -16 14 -3 3 17 -9 2 1 8 -7 1 1 4 5 7 -5 1 1 -2 -4 -3 1 -6 0 -1 2 -1 -2 1 0 -1 3 -5 -3 -2 -1 0 0 4 -2 0 2 0 -4 1 0 0 0 1
  2 1 0
  -3 -3 5 -1 4 0 3 -4 -6 -2 -1 1 2 -5 0 -3 -1 -4 3 0 -3 1 -2 2 -1 0 0 0 1 -1 2 -1 -2 -1 -1 2 -1 0 -1 0 -1 1 0 1 2 1 1 -1 -1 1 -1 -2 0 1 -1 0 -1 0 -1 0 1 0 2 0 1 1 0 -2 0
  1 1 2
  -1 -6 -1 -7 -2 1 -8 -2 -4 2 -7 -1 0 1 -6 7 -3 2 -4 0 4 0 1 1 -3 4 -5 0 3 1 -1 3 0 1 -1 0 0 -1 -1 1 1 1 -1 0 0 1 0 2 -1 -1 -1 0 0 0 -1 -1 1 1 -1 -1 0 0 0 0 0 1 1 0 0
  1 0 0
  -4 -16 15 -15 -2 1 -15 18 -6 17 -19 -8 16 14 -8 16 -12 -1 1 -3 6 -6 2 -3 -9 4 0 -5 3 -2 -5 -3 -1 1 -5 -2 2 0 2 0 1 -2 0 -2 -3 0 -1 1 3 -2 3 0 0 -4 0 0 0 -2 2 0 -1 1 0 -1 1 -1 1 2 0
  -1 -2 -4
  43 -28 25 -48 -22 23 -6 2 -26 28 -18 -18 26 5 -11 6 -17 -16 26 -2 13 -7 -2 -2 -20 3 -4 -13 -8 -1 -6 -3 -12 -7 -11 10 1 -1 8 3 0 1 6 0 0 1 0 -4 6 1 4 -6 2 -3 1 3 -2 -2 2 4 -3 0 1 -2 3 -1 -1 0 0
  -1 -3 -2
  -34 12 -15 26 12 -13 -12 -5 13 -15 3 14 -15 2 3 3 2 11 -21 0 -6 4 6 2 11 3 -3 9 12 -1 2 3 6 5 8 -6 0 -2 -4 -2 1 -2 -6 -1 -4 -2 -1 2 -3 -3 -2 4 -1 0 -3 -2 2 1 -1 -2 2 0 0 0 -2 1 1 0 1
  0 2 2
  -6 17 -16 6 -24 6 -30 4 12 20 -6 9 -4 1 -2 16 -7 6 -10 -10 13 -7 9 -11 -6 13 6 2 -3 11 -1 2 14 14 -5 -9 -9 3 -6 6 4 -1 -4 -4 -1 0 -2 6 -6 2 3 -2 3 0 0 2 0 2 0 -3 0 -1 1 0 -2 1 2 -2 2
  1 3 0
  17 7 -1 -8 -9 8 6 7 -1 9 2 -6 6 -1 3 1 2 -1 6 2 3 -1 0 -4 -2 -2 6 -3 -6 1 -1 -4 1 2 -4 0 -2 2 2 1 0 0 2 -1 1 1 0 -1 1 3 3 -1 0 -1 2 2 -1 -2 2 1 -1 0 0 -1 1 -1 0 1 0
  0 -1 -2
  21 18 -16 -2 -6 10 19 0 -3 5 10 -7 1 -9 14 -7 16 2 3 3 -6 7 -4 -4 5 -7 12 -5 -11 1 1 -4 3 4 -3 -2 -4 3 2 1 -1 2 3 -1 4 3 0 -3 0 7 3 -3 0 0 4 3 -3 -2 3 0 -1 1 0 -2 2 -2 -1 0 0
  1 1 -1
  38 -16 23 -42 -56 25 -40 5 -7 52 -21 0 19 6 -19 20 -34 -17 24 -18 37 -25 9 -14 -35 21 -2 -6 -15 16 -5 0 3 4 -17 4 -9 2 0 10 5 0 5 -2 -1 -2 -1 5 -3 0 5 -7 7 0 0 4 -1 3 -2 2 -1 -2 2 2 -1 0 1 -2 1
  -1 0 0
  -44 -8 6 26 24 -23 -11 -6 5 -16 -4 15 -6 8 0 1 -5 2 -13 -4 -14 4 1 9 7 3 -4 4 14 -9 0 1 -3 -4 9 -1 5 -4 0 -3 -1 -2 -3 -1 -4 -2 0 -1 1 -3 -4 3 -1 1 -1 -3 1 0 -1 0 2 1 1 1 0 0 -1 1 1
  -1 1 2
  47 -6 21 -33 -42 23 -11 1 -7 35 -6 -5 18 -3 -8 3 -18 -20 30 -10 23 -17 1 -9 -25 8 5 -9 -18 10 -4 -3 -3 -1 -15 6 -5 3 3 7 2 1 8 0 3 0 0 1 -1 4 6 -8 5 1 3 4 -2 0 -1 3 -2 -2 1 1 1 0 0 -1 -1
  -2 -1 -1
  -2 22 -6 16 0 0 10 4 17 -8 13 5 -7 -5 4 -6 6 2 -1 5 -1 -2 5 -3 11 -4 9 5 1 0 0 -4 2 3 0 -3 -3 2 -2 0 0 0 -1 -1 2 1 1 0 -2 4 2 1 0 2 2 0 -1 -2 0 1 0 0 -1 -1 1 0 0 1 -1
  1 0 -1
  20 -1 2 -13 -37 14 -27 -13 -2 29 -8 6 5 -7 -5 7 -14 -13 13 -16 18 -13 2 -8 -21 16 2 -4 -14 15 -1 3 5 6 -10 0 -7 1 -2 8 3 0 3 -1 2 -1 -1 4 -7 3 4 -8 6 2 1 3 -2 4 -3 0 0 -3 2 1 -2 1 1 -3 1
  1 1 2
  -4 -4 0 9 2 -7 -3 -4 6 -1 0 2 -2 1 -1 -1 1 -6 4 -5 -1 -2 -2 1 -3 1 -1 -2 -2 0 -2 2 -2 -2 1 0 2 1 1 0 0 0 1 1 1 0 -1 1 -1 1 0 -1 0 1 1 0 -1 0 -2 1 0 -1 0 1 0 1 0 1 -1
  0 -1 -1
  

• PROPERTIES
  Uniodular=1
  

• REFERENCES
  G. Nebe, Some cyclo-quaternionic lattices, J. Alg. 199 (1998), 472-498.
  

• NOTES
  CycloQuaternionic lattice of type Delta2 otimes Delta2
  

• LAST_LINE
  

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  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe