The Lattice L_56,2(M)

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 Mon Nov 2 22:06:07 EST 1998

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
GRAM
DIVISORS
MINIMAL_NORM
KISSING_NUMBER
HERMITE_NUMBER
SUBGROUP_ORDER
SUBGROUP_NAME
SUBGROUP_GENERATORS
PROPERTIES
REFERENCES
NOTES
LAST_LINE

• NAME
  L_56,2(M)
  
• DIMENSION
  56
  
• GRAM
  56 0
  14
  -7 14
  7 -7 14
  7 -7 0 14
  -4 7 -5 -3 14
  4 3 1 -1 -4 14
  1 3 -4 -2 7 -3 14
  -4 5 -7 -1 -2 0 -3 14
  9 -2 0 5 3 1 2 -1 18
  -4 7 -5 -2 3 0 5 0 -6 14
  -3 -2 -3 4 0 0 0 0 -7 0 14
  -2 0 -1 -3 -6 1 1 1 -1 -1 -4 14
  2 -5 -2 4 2 -2 4 -5 0 -1 7 -3 14
  7 -1 5 -1 -1 2 -1 1 7 -2 -5 -3 -5 14
  -6 3 -1 -6 -2 3 -2 1 -5 -1 0 4 0 -6 12
  5 3 -2 3 -1 3 0 3 8 0 -3 1 -4 7 -3 14
  -6 -1 3 -3 -6 0 -9 2 -9 -2 1 1 -2 -4 7 -7 18
  3 -4 5 -1 1 -5 1 -1 4 -5 -1 -2 -2 6 -3 2 -5 14
  -7 4 0 -4 1 0 -6 0 -7 3 2 -4 -1 -3 5 -1 4 -2 16
  -6 -1 3 -3 -6 0 -9 2 -6 0 -1 3 -6 1 3 -2 6 -1 6 18
  4 -5 2 3 -10 2 -3 1 2 -2 -3 7 -2 2 -1 4 1 -2 -2 5 14
  3 -3 3 -1 -7 3 0 4 -1 -4 -1 4 -2 2 3 1 2 0 -2 1 7 14
  -2 4 -4 3 4 -5 2 4 -2 6 1 -4 0 0 -3 4 -2 -2 2 0 -2 -2 14
  4 -2 7 -1 -7 5 -3 -2 0 -2 -3 6 -3 1 4 0 3 0 -1 1 4 4 -7 14
  -3 2 -7 0 7 -3 4 2 -1 2 4 -6 7 -2 0 -1 -2 -2 2 -4 -5 -2 7 -10 14
  -7 4 -4 -5 4 -2 -3 4 -2 1 0 -5 0 -1 2 -2 3 -2 8 5 -2 -2 4 -7 7 14
  5 -5 0 2 -6 6 -1 -3 2 -2 0 4 5 -2 2 1 -1 -4 0 -3 7 3 -6 5 -2 -2 16
  -2 1 2 -5 -2 0 0 0 -7 3 -3 0 -2 1 3 -3 7 -3 0 4 1 2 2 -1 2 2 -1 14
  -4 5 -6 2 7 -4 2 2 4 2 -1 -2 0 -3 1 1 0 -4 2 -3 -3 -3 4 -2 3 2 -2 -3 14
  0 0 -5 2 -2 4 -4 3 4 -4 0 0 1 -1 1 2 2 -3 1 0 4 0 -4 -3 2 3 6 0 2 14
  -2 -1 -1 -1 -5 3 -2 3 -3 -3 3 4 3 -6 7 -4 3 -1 1 2 1 4 -5 4 -2 -1 4 -1 -2 3 12
  -7 -1 -5 -4 5 -3 1 0 2 -6 1 3 1 -2 5 -3 -3 4 0 4 -5 -1 -6 -3 3 2 -2 -3 2 2 3 24
  -3 2 2 -7 -2 1 -1 1 -6 2 -4 1 -4 -1 4 -6 6 -2 3 4 0 1 -4 2 -3 2 2 7 -2 1 3 -1 14
  6 -4 -3 9 -3 3 0 1 1 1 3 -1 3 -1 -7 1 -3 -5 -4 -5 4 0 1 -3 2 -3 7 -3 -1 4 -2 -6 0 18
  -5 2 -2 -2 -3 -1 -1 3 -2 1 -2 5 -3 -4 3 -3 2 -2 0 8 4 2 -2 1 -6 2 0 1 1 1 6 2 5 -3 16
  2 3 0 -1 2 6 0 -2 -1 1 0 -3 0 0 1 3 -1 -4 5 -3 -2 0 1 -2 5 3 3 1 0 4 -3 -2 1 5 -8 16
  2 0 0 -1 5 -4 3 0 3 -2 -1 -3 4 -1 -3 -3 -3 1 0 -6 -2 -3 -2 1 2 2 3 -2 4 2 0 -2 3 2 -2 2 18
  5 -2 5 4 1 -2 0 -4 1 -1 -2 -1 2 -2 -1 1 -3 1 -1 -3 -1 -1 3 4 -2 -5 0 -1 1 -6 -1 -5 -3 0 -1 -1 4 16
  0 3 3 -1 -1 5 -6 2 -6 2 2 -8 -5 1 -1 0 6 -1 6 1 -1 1 1 -2 0 4 -1 5 -3 3 -2 -10 5 3 -2 7 1 0 20
  -7 4 3 -4 3 -6 -1 0 -3 3 0 -1 -7 2 0 -2 2 4 5 8 -2 -2 0 4 -7 1 -10 -1 4 -7 -2 3 1 -12 6 -9 0 -1 -1 24
  4 4 4 -2 5 4 -2 -1 10 -2 -8 -3 -7 10 -4 6 -2 1 -1 0 -3 0 -1 0 -2 1 -5 -3 4 0 -7 1 -2 -2 -4 6 -1 -2 3 2 24
  5 -9 8 3 -4 -4 -5 -4 5 -5 -2 -2 1 5 -3 0 3 4 0 1 2 0 -1 3 -4 -1 0 -3 -1 -3 -3 -3 -4 -4 -4 -5 -2 2 -4 3 3 20
  -7 3 -8 3 -2 -3 0 7 -5 4 4 4 -1 -6 0 -1 1 -6 0 6 4 0 6 -4 1 3 -3 -1 2 0 2 0 0 4 8 -5 -4 -3 -4 3 -9 -5 18
  -6 5 -1 -5 6 -3 -2 0 0 -2 -4 1 -3 -2 2 -2 0 2 5 3 -3 -5 -2 0 0 4 -2 0 4 3 0 7 3 -5 2 1 7 1 0 6 2 -6 -1 16
  0 5 -3 -1 3 3 4 1 3 3 0 1 0 0 -1 3 -3 -2 -1 -7 -1 1 2 0 0 0 1 -4 1 -2 -1 -5 -4 0 -2 -1 -3 -3 -1 0 3 1 1 -3 14
  5 -2 3 2 4 -4 6 -6 8 -1 -4 0 -1 5 -5 3 -6 5 -7 -4 -1 -3 -1 1 -4 -6 -1 0 4 -2 -5 1 -2 -3 1 -4 2 3 -5 4 5 4 -6 0 -1 16
  -5 0 -3 -1 3 -6 3 -4 1 2 -3 5 1 -4 0 -3 2 -4 0 1 2 -2 -1 -2 -1 0 1 0 7 1 -2 4 1 -1 5 -4 0 -2 -6 4 2 2 2 2 1 6 16
  7 -4 3 8 -1 -3 3 -4 4 -2 1 1 3 1 -7 3 -2 1 -7 -6 4 -1 3 0 -1 -7 -1 -2 0 -1 -4 -9 -6 6 -4 -1 2 5 -2 -3 -1 2 1 -3 1 5 1 16
  -5 4 4 -5 4 -1 -2 -5 -5 1 -1 0 -4 -3 1 -3 2 1 6 3 -4 -5 1 0 -3 2 -5 0 0 -4 -3 -2 0 -6 1 1 -2 5 3 5 1 3 -1 5 1 1 2 0 18
  -2 1 4 -6 1 -6 6 -4 -8 6 0 2 4 -4 2 -6 2 -1 4 -2 -3 -1 3 3 0 -1 -2 2 0 -9 1 -8 4 -5 -1 0 6 5 -3 3 -5 5 -2 -3 0 1 4 2 7 26
  6 -8 4 9 1 -2 -2 -6 5 -4 2 -7 3 0 -4 -1 1 -1 -2 -5 -3 -3 0 -1 0 -2 1 -2 3 -1 -5 -1 -4 4 -5 1 0 4 1 -2 3 10 -5 -6 -1 6 2 3 0 -2 20
  -7 7 -6 -3 4 0 1 2 -1 4 -2 1 -2 -5 4 -1 0 -6 2 5 -2 -3 2 -3 1 5 -3 3 6 2 2 4 2 -5 9 -1 -1 1 -1 3 0 -5 6 4 -2 1 4 -6 4 -1 -2 16
  -4 1 -2 3 6 -7 2 -1 -4 4 6 -6 4 -4 0 -2 1 1 3 -1 -7 -4 8 -4 5 1 -6 -2 6 -5 -2 0 -3 -2 -2 -1 0 4 0 5 -2 1 2 -1 -1 1 2 1 2 6 3 0 16
  -4 4 -4 1 3 -5 -2 8 1 -2 3 -3 -1 1 0 5 0 1 5 1 0 1 8 -4 5 5 -5 -3 6 0 -1 -1 -3 -2 -2 -1 3 0 1 5 0 0 6 3 2 -4 -2 1 -2 -1 -3 0 5 18
  -6 -3 -4 3 1 -3 -6 -1 1 -4 4 -1 3 -4 2 -4 7 -3 1 4 -1 -5 -4 -1 0 3 1 -2 6 6 1 10 -2 -2 3 -5 -1 -4 -4 5 -1 4 3 4 -3 1 7 -3 -1 -9 6 4 3 0 20
  -4 -3 -3 1 4 -9 4 1 -2 -1 5 0 3 -1 -3 -5 -3 7 -4 -1 -5 -3 0 -3 3 -2 -6 -3 2 -3 0 10 -4 -2 0 -7 2 -1 -8 5 -5 0 2 3 -4 4 2 1 0 1 -1 -1 5 0 5 18
  
• DIVISORS
  1
  
• MINIMAL_NORM
  6
  
• KISSING_NUMBER
  15590400
  
• HERMITE_NUMBER
  6
  
• SUBGROUP_ORDER
  2^6 * 3^2 * 5 * 7 * 29
  
• SUBGROUP_NAME
  SL_2(29) o SL_2(3).2
  
• SUBGROUP_GENERATORS
  3
  56 56
  -4 1 5 0 0 -1 2 3 -1 -1 -5 -1 2 1 1 0 -3 -3 0 0 1 -1 -2 -1 -2 0 1 -1 -1 0 1 -1 -2 1 -1 0 -1 -2 1 0 -1 -1 -1 -1 -1 0 -1 1 0 0 1 1 2 1 1 1
  -8 0 3 2 -3 4 4 -1 -1 -2 -1 -5 -2 -3 -4 4 2 1 -1 0 0 -1 0 2 4 -1 0 0 0 1 -1 1 1 0 2 -1 1 2 -2 -1 1 1 0 0 1 0 0 -1 -1 1 -1 -1 -1 0 0 0
  -9 -2 5 0 -1 3 3 4 1 -1 -4 -2 3 -1 -3 1 0 -1 1 0 2 -1 0 0 -1 -1 0 -2 -1 0 0 -1 1 -1 -2 1 0 0 -1 0 -1 -2 -1 -2 0 1 0 0 0 -1 1 1 1 0 0 1
  5 1 -2 -2 2 -4 -2 -1 -2 0 -3 2 2 2 4 -1 -3 -2 -1 1 -2 1 -1 0 -2 1 1 0 0 0 2 -1 -3 2 -1 -1 -1 -3 3 1 0 0 1 0 -2 0 -1 1 1 0 1 0 1 1 0 0
  3 -5 -1 -4 2 2 -5 2 2 4 5 1 1 -1 -1 0 2 3 0 -2 1 0 3 1 2 -1 -2 0 1 1 -1 2 3 -1 2 2 0 2 -1 1 0 0 1 1 2 1 1 1 0 0 0 0 -2 -1 -1 -1
  -12 5 12 2 -3 -1 8 3 1 -3 -5 -6 -2 -2 -4 2 0 -5 1 0 2 -3 -3 1 2 -2 3 -1 -3 2 0 1 -3 1 0 -2 -1 0 -1 -2 0 -1 -1 -2 -1 0 -2 -1 -1 1 0 0 2 1 1 1
  12 -2 -8 -3 2 -1 -5 -2 -1 2 4 4 0 1 3 -2 0 3 0 0 -1 1 1 -1 -1 1 -2 1 2 -1 0 0 1 0 1 1 0 0 1 1 0 1 1 2 1 0 1 1 0 0 0 0 -1 0 0 -1
  -1 1 -3 6 1 1 2 -4 -5 -3 -3 1 -1 2 3 2 -2 0 -2 1 -2 1 -2 -1 0 2 0 1 1 -1 1 -2 -1 1 0 -2 1 -1 1 0 1 2 0 1 -1 -1 -1 -1 0 1 -1 -1 0 0 1 0
  1 0 -2 -5 -5 -1 -5 -3 3 1 2 -1 1 -2 0 -1 -3 0 -1 -2 -2 2 3 2 -1 1 -2 2 1 1 -1 1 0 2 1 0 0 -1 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 -1 0
  -8 8 1 2 -9 1 5 -4 -1 -5 -6 -7 -1 -4 -3 2 -2 0 -2 3 -3 1 -1 2 2 -1 3 1 -1 0 -1 0 -2 2 0 -3 1 -1 0 -1 1 1 -1 -1 -1 -1 0 0 0 1 0 -1 1 2 1 1
  19 -4 -1 -4 12 -7 -5 5 3 9 10 9 -2 5 6 -5 3 -1 2 -1 1 -1 -1 -2 -2 1 0 0 0 1 1 2 -1 -1 1 2 -3 1 2 0 -1 0 2 2 0 0 0 1 1 0 0 0 -1 0 0 -2
  6 7 -2 0 -3 -5 0 -3 2 -1 3 2 -2 0 0 -3 0 -1 1 1 -1 1 0 -1 -2 1 1 1 0 -1 0 0 -1 0 -1 -1 0 -1 0 -1 0 0 -1 0 -1 -1 0 -1 0 -1 0 0 1 0 0 0
  21 -3 -7 -4 9 -6 -9 2 -1 6 6 10 1 7 8 -6 -1 0 1 -1 1 0 -1 -4 -4 2 -2 0 2 -2 2 0 0 -1 0 3 -2 -1 3 1 -2 0 1 2 1 0 1 2 1 -1 1 1 0 0 0 -1
  -16 1 6 5 -5 5 5 0 -1 -3 -7 -5 2 -2 -2 4 -3 -1 -2 0 -1 1 -1 1 0 1 0 0 -1 1 -1 -1 0 2 -1 -2 1 -1 -1 0 0 0 -2 -1 -1 0 -1 0 0 1 0 0 1 1 1 1
  1 -2 -10 2 -2 4 -1 -7 -3 -4 0 0 -1 0 -1 1 1 3 0 0 -1 1 1 0 0 1 -3 1 2 -2 0 -2 2 -1 0 0 2 1 -1 0 1 1 1 1 1 0 1 -2 -1 0 -1 -1 -1 -1 -1 0
  -6 1 4 1 -3 0 2 -1 2 1 1 -4 -2 -1 0 2 -1 -2 -2 -1 -2 1 0 2 0 1 0 1 -1 2 -1 1 -1 2 2 -1 0 0 -1 -1 0 1 -1 1 -1 -1 0 0 0 1 -1 -1 0 1 0 0
  4 1 -1 2 3 -2 0 1 0 0 2 4 -1 3 1 -3 2 0 2 0 2 -1 -1 -3 -1 0 1 -1 0 -2 1 -1 0 -2 -2 1 0 1 0 0 0 -1 0 -1 0 0 0 -1 0 -1 0 1 0 -1 0 0
  -2 -7 -4 -2 0 5 -2 0 1 1 1 0 3 -1 -1 1 1 3 0 -1 0 1 3 1 -1 0 -3 0 1 0 -1 -1 3 -1 0 2 1 1 -1 1 0 0 1 1 1 1 1 0 0 -1 0 0 -1 -1 -1 0
  -14 0 3 3 -5 6 4 -2 -1 -3 -6 -6 1 -3 -4 5 -1 0 -2 1 -2 1 0 3 2 0 0 0 0 1 -1 0 1 1 0 -2 1 0 -1 -1 0 0 -1 -1 0 0 0 0 0 1 0 -1 0 1 0 1
  -19 1 6 5 -6 7 7 -1 0 -5 -6 -9 -1 -6 -7 6 1 0 -1 1 0 0 0 3 4 -2 1 0 -2 1 -2 0 1 0 0 -2 2 1 -3 -1 1 0 -1 -2 0 0 0 -2 -1 1 -1 -1 0 0 0 1
  -3 1 3 0 -2 0 2 -1 1 -1 0 -4 -3 -3 -2 2 1 -1 0 0 0 0 0 2 2 -1 0 0 -1 1 -1 1 -1 1 1 -1 0 0 -1 -1 0 0 0 0 0 0 0 -1 -1 1 -1 0 0 0 0 0
  -2 -3 -7 5 0 5 0 -5 -7 -4 -6 1 2 2 3 3 -3 2 -2 1 -2 2 -1 -1 -1 2 -3 0 2 -2 1 -3 1 1 -1 -1 2 -2 1 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 1 0
  -8 -1 3 4 0 3 3 0 -2 -1 -2 -4 -1 -1 -1 4 1 0 -2 0 0 0 0 1 3 -1 1 -1 -1 1 0 0 1 0 1 -1 1 1 -1 0 1 1 0 0 0 0 0 -1 0 1 -1 -1 -1 0 0 0
  -6 2 -3 3 -4 3 3 -4 -5 -6 -9 -1 3 0 0 2 -4 0 -1 2 -2 1 -2 0 -2 2 -1 0 1 -2 1 -3 -1 2 -2 -2 1 -3 1 0 0 0 -1 -1 -1 0 -1 0 0 0 1 0 2 1 1 1
  15 -4 -5 -3 7 -2 -8 2 0 5 7 7 0 4 4 -4 1 2 1 -2 2 0 1 -3 -1 0 -2 0 2 -1 0 1 2 -2 1 3 -1 1 1 1 -1 0 1 2 2 0 1 1 0 0 0 1 -1 -1 0 -1
  -9 -6 2 3 1 8 2 1 -3 -2 -3 -3 0 -2 -4 5 2 2 0 -1 2 -1 0 1 4 -1 -2 -1 1 0 -1 0 3 -1 1 0 1 2 -2 0 0 0 0 0 2 1 0 -1 -1 1 -1 0 -1 -1 0 0
  3 6 3 1 2 -5 2 1 -1 -2 -4 2 0 2 2 -2 -2 -4 2 1 1 -1 -4 -2 -3 1 2 0 -1 -1 2 -1 -4 2 -2 -2 -2 -3 2 -1 -1 -1 -1 -1 -2 0 -2 0 0 0 1 1 3 1 1 1
  -5 0 -2 6 1 4 4 0 -5 -5 -6 0 1 2 0 1 0 1 1 1 2 -1 -3 -3 -1 0 0 -1 0 -3 1 -3 0 -1 -2 0 1 0 0 0 0 0 -1 -1 0 0 0 -1 -1 0 0 1 1 0 1 1
  16 1 -13 -7 -2 -5 -11 -8 2 3 7 4 0 0 4 -4 -2 3 -2 0 -5 4 4 2 -1 2 -2 3 3 0 0 1 0 2 1 0 0 -1 2 2 1 1 2 2 0 0 1 1 1 0 0 -1 -2 0 -2 -1
  -2 3 5 -1 -1 -2 2 2 2 -1 -1 -2 -1 -1 -2 -1 1 -2 2 0 2 -2 -1 0 1 -2 2 0 -1 0 0 1 -2 0 0 0 -1 0 0 -1 0 -1 0 -1 0 0 -1 0 -1 0 0 1 1 0 0 1
  10 1 -8 -2 -1 -3 0 -3 -1 -2 1 3 -1 2 3 -4 -1 0 2 1 -1 -1 0 -1 -2 0 0 2 1 -2 1 -1 -2 0 0 0 0 -1 2 0 1 1 1 1 0 -1 0 0 0 -1 0 0 1 0 0 0
  10 -2 -16 -1 -2 1 -7 -8 -1 -1 3 6 2 2 3 -3 -2 4 0 0 -4 4 3 -1 -3 3 -4 3 3 -2 0 -2 2 0 -1 0 2 -1 1 2 1 1 1 2 0 0 1 0 1 -1 0 -1 -1 -1 -1 -1
  -13 3 -1 7 -5 6 9 -3 -5 -10 -11 -4 1 -2 -4 4 -1 0 1 3 0 -1 -3 -1 0 0 1 0 0 -3 1 -4 -1 0 -3 -3 2 -1 0 -1 1 0 -1 -2 -1 0 -1 -2 -1 0 0 0 2 0 1 2
  5 4 10 -2 7 -8 3 8 2 2 1 2 -2 2 2 -3 1 -5 3 0 4 -4 -3 -2 0 -3 5 -1 -3 1 2 1 -5 0 0 0 -3 -1 2 -1 0 -1 1 -1 -2 0 -2 0 0 0 1 1 2 0 1 0
  -9 -3 -3 3 -3 7 3 -6 -5 -5 -6 -5 0 -4 -4 7 1 2 -2 1 -2 1 0 3 3 1 -2 0 1 0 0 -1 1 1 0 -3 2 0 -1 0 1 1 1 0 0 1 0 -2 -1 1 -1 -1 -1 0 -1 0
  -4 -2 3 2 3 2 1 4 -3 -1 -4 0 2 3 1 1 -1 -1 0 0 3 -2 -2 -2 0 -1 0 -2 0 -1 1 -1 1 -1 0 2 0 0 0 0 -1 -1 -1 -1 1 0 0 1 0 0 1 1 1 0 1 1
  12 0 5 -4 7 -4 -3 9 5 7 7 7 0 2 1 -6 2 0 4 -1 4 -2 -1 -4 -3 0 1 0 0 -1 0 2 0 -2 0 3 -3 1 0 -1 -2 -2 -1 0 1 0 0 2 0 -1 1 2 1 0 1 0
  -4 -7 4 -2 4 4 0 5 -1 2 1 -3 0 -1 -2 3 3 1 0 -2 4 -3 1 1 3 -3 -1 -2 -1 1 0 1 2 -2 3 3 0 2 -2 0 0 0 1 0 2 1 1 0 -1 0 0 0 -1 -1 -1 0
  -17 -2 15 2 1 4 7 8 2 0 -4 -6 0 -2 -5 4 2 -3 1 -1 4 -3 -2 1 3 -3 2 -3 -3 2 -1 1 0 -1 0 0 -1 2 -2 -2 -1 -2 -1 -2 0 1 -1 0 -1 1 0 1 1 0 1 1
  -2 -6 -3 -3 -2 6 0 -1 2 1 2 -2 0 -5 -4 2 3 4 0 0 -2 1 3 3 2 0 -2 1 1 1 -2 1 2 0 1 0 1 2 -2 1 1 0 1 0 1 1 1 0 0 0 -1 -1 -2 0 -1 -1
  -11 4 -1 0 -11 3 0 -5 -1 -5 -7 -5 4 -3 -2 2 -6 0 -3 1 -4 3 2 3 0 1 -1 1 1 0 -1 -1 0 3 -1 -2 2 -3 0 1 0 0 -2 -1 -1 0 0 1 1 0 1 0 1 1 0 1
  -1 5 0 -1 -6 -4 -4 -2 4 2 0 1 2 1 2 -3 -5 -2 -2 0 -3 3 1 0 -3 2 1 1 0 0 0 0 0 1 -2 0 0 -2 1 1 -1 -1 -2 -1 -1 -1 0 2 2 -1 1 0 1 1 0 1
  1 0 -5 3 0 1 3 -5 -4 -3 -2 0 -2 -1 0 3 1 1 -1 2 -3 1 -1 1 2 1 0 1 1 0 1 -1 -1 1 0 -3 1 0 1 0 2 2 2 1 -1 0 -1 -2 0 1 -1 -2 -1 0 0 -1
  -1 -6 4 -2 6 4 1 6 0 1 1 0 1 -2 -4 2 6 2 3 -1 5 -3 1 0 3 -3 -1 -2 0 0 0 1 2 -2 1 2 0 2 -2 0 0 -1 1 -1 2 2 0 -1 -1 -1 0 1 -1 -2 -1 0
  -4 5 2 0 -6 -1 2 -1 0 -2 -4 -2 2 -1 0 0 -3 -1 -1 1 -2 1 0 1 0 0 1 0 0 0 0 0 -1 2 -1 -2 0 -2 1 0 0 0 -1 0 -1 0 -1 1 1 0 1 0 1 1 1 0
  -3 3 -6 3 -3 3 0 -6 -4 -5 -7 1 4 -1 -1 2 -3 2 -1 2 -3 3 -1 0 -3 4 -1 1 2 -2 1 -3 0 2 -3 -3 1 -3 1 1 0 0 -1 -1 -2 0 -1 0 0 0 1 0 1 1 0 1
  16 6 -1 -9 0 -9 -8 0 9 6 11 7 -1 -1 -1 -8 1 0 3 -1 -1 2 3 0 -3 1 1 2 1 1 -1 3 -1 0 -1 0 -3 0 1 0 -1 -2 0 0 -1 0 0 1 0 -1 1 1 0 0 -1 -1
  11 2 6 -4 5 -8 0 7 5 6 9 3 -4 1 2 -5 3 -2 3 -1 3 -3 0 -1 0 -2 3 0 -2 1 0 3 -2 -1 2 2 -2 1 0 -1 0 0 0 0 0 -1 0 1 0 -1 0 1 0 0 0 -1
  -2 -6 7 -5 4 0 -3 5 4 7 6 -2 0 -2 -3 3 5 0 -1 -2 2 -1 3 4 4 -2 -1 -3 -1 4 -1 4 3 -1 2 2 -1 3 -2 0 -1 -1 1 0 2 2 1 0 0 0 0 0 -3 -1 -2 -1
  15 4 -2 -3 3 -7 -6 2 3 6 7 7 0 3 4 -6 -1 0 0 1 0 1 0 -3 -4 2 1 0 1 -1 0 1 1 -1 -1 2 -2 0 1 0 -2 -1 -2 0 1 -1 1 2 1 -1 1 1 0 1 1 0
  8 -3 1 -7 4 -4 -8 3 4 7 5 4 2 1 2 -3 0 0 0 -2 0 1 2 0 -1 0 0 -1 0 2 0 2 0 0 0 2 -2 0 1 2 -1 -2 1 0 0 1 0 2 1 0 1 1 -1 0 -1 -1
  -6 -3 0 0 -1 4 2 -2 -3 -2 -3 -5 -1 -3 -3 5 2 1 -1 0 0 -1 0 3 4 -1 -1 0 0 1 0 1 0 1 2 -1 1 1 -1 0 1 1 1 0 1 1 0 -1 -1 1 -1 -1 -1 0 -1 0
  6 0 -5 -2 1 0 -3 0 1 1 1 4 3 1 0 -3 1 2 1 1 0 1 1 -2 -2 0 0 0 1 -2 1 -1 1 -1 -2 1 0 0 1 1 0 -1 1 0 0 1 0 0 1 -1 1 0 0 0 0 0
  5 -6 -6 1 3 2 -4 -2 -1 3 4 3 0 2 3 1 1 2 -2 -1 -2 2 2 0 0 2 -3 0 2 0 0 0 3 -1 1 1 1 1 0 1 0 1 1 2 1 0 1 0 1 0 -1 -1 -2 -1 -1 -1
  9 -3 -8 -3 2 0 -5 -3 1 1 4 5 0 1 1 -3 1 3 2 -1 -1 1 2 0 -1 1 -2 2 2 -1 0 0 0 0 0 0 0 0 1 1 1 0 2 1 0 0 0 0 0 0 0 0 -1 -1 -1 -1
  23 -5 -13 -5 8 -4 -11 -2 2 7 11 12 1 4 6 -6 1 4 1 -1 -2 3 3 -2 -4 3 -3 2 3 -1 0 0 2 -1 0 2 -1 0 2 2 0 1 2 3 0 0 1 1 1 -1 0 0 -2 -1 -1 -2
  56 56
  32 -4 -2 -10 14 -12 -10 7 9 15 23 12 -6 5 6 -11 7 1 4 -3 3 -2 3 -2 -2 -1 0 1 0 2 -1 5 0 -3 4 6 -4 4 0 0 -1 0 2 3 2 -1 2 1 0 -1 -1 1 -3 -1 -1 -3
  -22 -2 -1 3 -10 9 7 -8 -4 -10 -12 -11 2 -7 -7 10 -1 0 -2 1 -3 1 1 6 4 0 -2 0 0 1 0 -2 0 3 -1 -5 3 -1 -1 0 2 1 1 -1 -1 2 -1 -3 -1 1 -1 -2 0 0 -2 1
  20 12 0 -5 -2 -15 -4 0 9 7 12 7 -4 3 5 -11 -2 -4 1 1 -4 2 0 -2 -5 2 4 3 -1 1 -1 3 -4 1 0 0 -3 -1 2 -1 -1 0 -2 1 -2 -3 0 2 2 -1 0 0 1 2 1 -1
  26 -6 -4 -7 15 -7 -9 8 4 10 15 14 -1 7 6 -10 4 2 5 -3 5 -2 2 -5 -4 -1 -1 0 1 -1 1 1 1 -4 1 6 -3 2 1 1 -1 -1 2 2 1 0 1 1 0 -2 1 2 -1 -2 0 -2
  -7 -2 -3 6 0 5 3 -3 -8 -6 -10 -1 3 1 1 5 -2 0 -1 1 0 0 -3 -1 0 2 -2 -1 1 -2 2 -3 0 1 -2 -2 2 -2 1 1 0 1 0 -1 0 1 -1 -1 0 0 0 0 1 0 0 1
  7 -2 4 -9 0 -5 -1 2 9 6 13 -2 -6 -5 -4 -2 6 0 2 -2 0 -2 5 5 4 -3 1 1 -1 5 -3 5 0 -1 4 1 -2 4 -2 -1 1 0 2 1 1 0 1 -1 -1 0 -2 -1 -3 -1 -2 -2
  9 -8 -11 1 7 4 -5 -2 -6 0 -1 5 2 3 4 1 1 4 0 0 1 0 -1 -2 -1 2 -4 0 3 -3 2 -2 2 -1 0 2 1 0 1 2 0 1 2 1 2 1 1 0 0 0 0 0 -1 -1 -1 0
  -22 -6 1 3 -5 13 6 -2 -5 -8 -10 -10 3 -6 -8 9 2 4 -1 0 2 -1 2 4 5 -3 -2 -2 0 0 -1 -2 3 0 0 -1 3 1 -3 0 2 0 1 -1 1 2 0 -2 -2 1 0 0 -1 -1 -1 1
  11 -6 4 -5 11 -4 -4 6 3 8 10 3 -3 2 2 -2 6 0 2 -3 5 -3 1 0 1 -2 -1 -1 -1 2 0 3 0 -1 3 4 -2 3 -1 0 -1 0 2 1 2 1 1 -1 -1 0 -1 1 -2 -1 -1 -1
  -6 -3 -5 1 -3 4 -1 -4 -3 -4 -5 -2 2 -1 -1 3 -2 1 -1 0 -1 1 1 1 1 0 -2 0 1 -1 1 -2 1 0 -1 -1 2 -1 0 1 1 0 1 0 0 1 0 -1 0 0 0 -1 0 -1 -1 0
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  56 56
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  -76 9 7 21 -39 25 31 -14 -23 -36 -54 -36 14 -13 -15 25 -13 -4 -11 11 -7 0 -3 11 9 -2 1 -7 -2 -2 1 -9 0 6 -8 -12 9 -8 0 -1 3 0 -5 -7 -2 4 -2 -3 1 0 1 -3 5 4 1 6
  -12 30 -19 1 -40 -7 12 -26 0 -22 -15 -15 2 -12 -2 -2 -12 -2 -3 12 -15 8 4 8 -2 2 3 7 0 -2 0 -4 -8 13 -8 -13 5 -8 4 0 6 5 -3 -1 -6 1 -3 -3 3 -2 -1 -4 3 3 -1 2
  -25 -17 -16 15 -6 34 -1 -8 -20 -15 -16 -11 7 -5 -8 15 1 18 -5 1 5 2 4 -1 6 -1 -13 -5 6 -7 -6 -7 16 -7 0 3 10 3 -9 1 0 -1 -2 0 9 1 5 -2 -4 3 -1 2 -4 -4 2 0
  1 6 4 -5 -5 -2 2 6 2 -2 -7 3 5 1 1 -7 -9 -4 4 1 0 -1 -3 -5 -9 0 4 2 1 -4 0 -2 -4 -1 -4 -1 -3 -5 4 -2 -1 -3 -2 -1 -3 -2 -2 5 0 -1 4 2 6 3 4 3
  -15 11 -6 18 -6 6 15 -12 -16 -18 -23 0 5 3 2 8 -3 -2 -1 8 -4 3 -5 -4 -3 6 -1 -3 1 -5 5 -8 -3 6 -9 -10 6 -6 3 0 0 2 -3 -3 -4 2 -4 -5 1 -1 0 -1 3 0 2 2
  -34 10 -23 20 -19 18 17 -28 -24 -35 -43 -5 12 0 -2 14 -15 1 -4 10 -12 8 -7 -1 -8 10 -3 4 5 -9 8 -18 -5 11 -13 -15 7 -12 5 2 3 3 -2 -2 -8 0 -6 -5 0 1 3 -2 8 3 2 6
  14 -22 -7 0 26 4 -22 6 -7 11 4 21 10 15 12 -1 -2 4 -2 -8 4 3 -1 -8 -5 5 -8 -5 6 -2 1 -3 8 -5 -1 6 -2 0 3 5 -4 -3 4 2 2 3 -1 3 0 1 2 3 -2 -4 0 -3
  -1 -8 -11 5 8 3 1 -3 -11 -7 -8 0 3 5 7 5 3 1 -1 0 1 -1 0 -2 3 -2 0 -4 -1 -4 6 -7 -1 0 -3 0 4 -2 1 5 3 2 6 0 -3 4 1 -4 2 -3 -1 -1 -2 -4 -3 -1
  
• PROPERTIES
  Unimodular=1
  
• REFERENCES
  G. Nebe, Some cyclo-quaternionic lattices, J. Alg. 199 (1998), 472-498.
  
• NOTES
  CycloQuaternionic lattice of type Delta2
  The first two generators are the same as for L_56,2^(7)(M)
  
• LAST_LINE
  

INDEX FILE | ABBREVIATIONS

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