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 13:16:43 CEST 2014

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
DET
GRAM
DIVISORS
MINIMAL_NORM
GROUP_NAME
GROUP_GENERATORS
PROPERTIES
REFERENCES
NOTES
LAST_LINE

• NAME
  J2dim14
  

• DIMENSION
  28
  

• DET
  5^14
  

• GRAM
  28 0
  8
  -4 8
  -4 0 8
  3 1 -4 8
  -1 3 2 2 8
  3 -1 -4 0 -4 8
  2 0 -4 4 2 2 8
  2 2 -4 2 2 0 4 8
  -3 -1 0 1 -3 -1 -2 -4 10
  -4 2 1 -1 -2 -2 -2 -2 5 8
  2 -4 1 -1 1 -1 -1 -1 -2 -4 8
  -2 4 0 2 0 -2 -1 0 1 4 -2 8
  -4 2 1 0 -1 -3 -1 0 2 2 0 4 8
  -4 2 0 1 -1 -1 0 0 3 4 -2 2 4 8
  2 -2 1 2 -1 -1 -1 0 -1 0 0 0 -1 0 8
  -4 4 2 -3 3 -1 0 2 -2 1 -2 0 1 2 -2 8
  -4 2 2 -2 2 -4 0 2 -1 2 -1 2 2 2 -1 2 8
  -1 3 2 2 2 -2 -2 0 -1 -1 0 3 1 -1 3 -1 0 8
  4 -2 -2 4 -2 0 -1 1 0 -2 0 0 1 1 5 -3 -2 1 10
  2 -4 0 -3 -4 4 -2 -1 1 -2 1 -3 -2 -3 1 -2 -3 0 0 10
  -4 4 1 1 1 -2 -1 0 3 4 -4 4 2 2 1 2 2 2 -1 -2 8
  3 -1 -2 4 2 -1 1 2 1 -2 1 -2 -2 -1 2 -1 -2 0 4 0 0 8
  -4 2 2 1 3 -1 2 -2 3 0 -2 0 2 1 -2 3 0 0 -2 -2 3 0 10
  -2 -2 2 -4 -4 2 -4 -4 2 1 0 -1 0 0 0 0 0 0 -1 4 0 -2 0 8
  0 -1 0 -1 -3 3 -1 -3 3 0 -2 -3 -2 0 0 0 -3 -1 1 3 -2 1 1 3 8
  -1 -1 0 0 -2 2 2 -2 0 1 1 1 1 2 1 -1 -1 -1 -2 1 0 -3 0 0 0 8
  -2 4 0 -1 3 1 0 0 -1 0 -2 0 -2 0 -4 4 0 0 -4 -2 1 -2 3 0 0 -1 8
  2 -4 -1 -1 -2 2 1 -2 0 -2 4 -1 -1 -2 -2 -2 -2 -2 -1 2 -4 -1 -1 2 1 2 0 8
  

• DIVISORS
  5^14
  

• MINIMAL_NORM
  8
  

• GROUP_NAME
  C2xJ2
  

• GROUP_GENERATORS
  4
  28 28
  -2 -2 -2 -5 5 2 -3 2 3 -5 -5 3 0 1 3 -2 -2 -1 -2 -3 -2 1 0 0 -1 1 -2 1
  -2 -1 0 2 -1 0 1 -1 -1 1 1 0 0 -1 -1 1 0 0 1 1 0 0 -1 0 0 0 1 -1
  3 3 1 -1 -1 -1 3 -1 1 1 2 0 0 0 0 0 1 0 1 1 0 0 0 1 0 0 1 -1
  -4 -2 -1 -3 3 2 -1 1 2 -4 -3 3 0 0 2 -1 -2 -1 -1 -2 -2 1 -1 0 -1 0 -1 0
  0 -1 0 0 2 3 -2 1 1 0 -1 0 2 -1 1 0 1 0 -1 -1 -1 1 0 0 0 1 0 0
  -1 -1 -1 -1 2 0 -2 1 0 -1 -2 0 0 0 0 -1 -1 0 0 -1 0 0 0 0 0 1 -1 1
  -2 -2 -1 -2 3 2 -3 2 1 -2 -3 1 1 0 1 -1 -1 0 -1 -2 -1 1 0 0 0 1 -1 1
  -2 -2 -1 2 -1 0 -2 0 -1 -1 -1 0 0 0 0 1 0 0 -1 0 0 0 0 -1 0 0 0 0
  0 0 2 3 -3 0 1 -1 -2 3 2 -2 0 -1 -2 1 1 1 1 1 1 0 0 -1 0 -1 1 0
  1 1 1 2 -3 -1 2 -2 -2 3 2 -2 0 0 -2 1 1 1 1 2 1 0 0 -1 0 -1 1 0
  2 1 1 1 -1 0 0 1 0 1 2 -1 0 0 0 0 1 0 0 0 1 -1 1 0 1 0 0 0
  -2 0 0 -1 -1 -1 3 -1 0 -1 1 2 -1 0 0 0 -1 -1 1 1 0 0 -1 0 0 -1 1 -1
  -1 1 1 4 -6 -4 4 -2 -3 2 5 0 -3 0 -3 2 0 0 2 3 2 -2 0 0 1 -2 1 -2
  0 1 1 5 -6 -3 3 -3 -4 3 4 -2 -1 0 -3 2 1 1 1 3 2 -1 0 -1 1 -2 1 -1
  0 1 -2 -8 5 1 1 0 5 -6 -4 4 0 2 4 -2 -2 -1 -1 -2 -3 1 -1 1 -2 0 -1 0
  1 -1 0 3 -1 1 -1 -1 -2 3 1 -2 2 -1 -1 1 2 1 0 1 1 0 0 -1 1 0 1 0
  1 1 1 3 -4 -2 2 -1 -2 2 3 -1 0 0 -1 1 1 0 0 2 1 0 0 0 1 -1 2 -1
  -1 1 0 -2 1 0 2 0 2 -2 0 2 -1 0 1 0 -1 -1 1 0 -1 0 -1 1 -1 0 0 -1
  -3 -1 -2 -3 1 -1 1 -1 2 -5 -2 4 -2 1 2 0 -2 -1 -1 -1 -2 0 -1 0 -1 -1 -1 -1
  1 1 0 1 -1 -2 0 0 -1 1 1 -1 -1 0 -1 0 0 0 1 1 1 -1 1 0 0 0 0 0
  0 0 0 -2 1 1 1 -1 1 -1 -1 1 1 0 1 0 0 0 0 0 -1 1 -1 0 -1 0 1 0
  -2 -2 0 1 1 2 -2 1 0 0 -1 0 1 -1 1 0 0 0 -1 -1 -1 0 0 -1 0 0 0 0
  0 -1 0 -3 4 3 -1 1 2 -1 -2 1 2 -1 1 -1 0 0 0 -2 -1 1 -1 1 0 1 0 0
  2 2 1 2 -2 -2 2 -1 -2 3 3 -2 0 0 -1 0 1 0 1 2 2 -1 0 0 1 -1 1 0
  -1 -1 0 1 0 0 0 0 -1 2 0 -1 0 -1 -1 0 0 1 1 0 0 0 0 0 0 0 0 0
  1 1 0 -3 1 -1 2 0 1 -1 0 1 0 1 0 -1 -1 0 1 0 0 0 0 1 0 0 0 0
  1 -1 0 0 3 3 -2 0 1 0 -2 -1 3 -1 1 0 1 0 -1 -1 0 1 -1 0 0 1 0 1
  1 0 0 -2 2 1 0 1 1 0 0 0 1 0 1 -1 0 0 0 -1 1 0 0 0 1 0 0 1
  28 28
  0 -2 -1 -6 5 3 -2 1 4 -5 -5 3 1 1 3 -1 -1 0 -2 -3 -2 2 -1 0 -1 1 -1 1
  -1 -1 0 3 -1 0 -1 0 -2 2 1 -1 1 -1 -1 0 1 0 0 1 1 0 0 -1 1 0 1 0
  0 2 2 6 -6 -3 3 -1 -4 6 6 -3 -2 -1 -4 2 1 1 3 3 2 -2 1 0 1 -1 1 -1
  0 -2 -1 -4 4 2 -1 1 3 -3 -3 2 1 0 2 -1 0 0 -1 -2 -1 1 -1 0 0 1 0 0
  -2 -2 1 4 -2 -1 0 1 -2 2 2 0 -1 -1 -2 1 0 0 1 1 1 -1 0 0 1 0 1 -1
  0 0 -1 -5 4 2 -2 1 3 -4 -4 2 1 1 3 -2 -1 -1 -2 -2 -2 2 0 0 -1 1 -1 1
  -2 -2 -2 -6 6 2 -2 2 5 -7 -5 5 0 1 4 -2 -2 -2 -2 -3 -3 1 -1 1 -1 1 -1 0
  -2 -3 -1 -2 3 2 -2 1 2 -4 -3 3 1 0 2 -1 -1 -1 -2 -2 -1 1 -1 0 0 0 0 0
  2 3 0 -1 -1 -2 3 -1 0 1 2 -1 -1 0 -1 0 0 0 2 1 1 -1 0 1 0 0 0 -1
  1 2 0 2 -2 -1 1 -1 -1 2 2 -2 0 -1 -1 1 1 0 1 1 1 -1 0 0 0 0 0 0
  0 -1 1 2 -1 0 0 0 -1 1 0 -1 0 0 -1 1 0 1 0 0 0 0 0 0 0 0 0 0
  1 0 0 3 -2 0 0 -1 -2 3 2 -2 1 -1 -1 1 2 1 0 1 1 0 0 -1 1 0 1 0
  1 0 -1 0 1 1 0 -1 0 1 0 -1 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0
  0 0 0 1 0 1 0 0 0 1 0 -1 1 -1 0 0 1 0 0 0 0 0 0 0 0 0 0 0
  1 0 0 -2 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 -1 0 0 0 0 0 0 0 0
  -1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 -1 -1 -1 0 0 0 0 0 1 0 0 0 0
  -2 0 1 8 -7 -3 1 -1 -5 4 5 -2 -2 -1 -3 2 1 0 1 3 2 -2 1 -1 1 -2 1 -1
  0 0 1 4 -4 -2 2 -1 -3 4 4 -2 0 -1 -2 1 1 1 1 2 2 -1 0 -1 2 -1 2 -1
  1 -1 -1 -6 3 2 1 -1 3 -3 -3 2 1 1 2 -1 0 1 -1 -2 -1 2 -1 0 -1 0 0 0
  2 2 1 0 -1 0 0 0 0 1 1 -1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
  1 1 0 3 -4 -3 2 -1 -3 4 4 -2 -1 -1 -3 1 1 1 2 2 2 -1 1 0 1 0 1 -1
  0 -1 0 -4 3 1 0 1 3 -3 -3 2 0 0 1 -1 -1 0 0 -2 -1 1 -1 1 -1 1 0 0
  -1 0 -1 -5 4 0 1 2 2 -2 -1 3 -1 1 1 -3 -2 -1 1 -1 -1 0 0 2 0 1 0 -1
  1 3 1 2 -3 -2 2 -1 -2 3 3 -2 -1 0 -1 0 0 0 1 2 1 -1 1 0 0 -1 0 0
  1 3 0 -3 1 -1 1 0 2 -2 -1 1 -1 1 1 -1 -1 -1 0 0 -1 0 0 1 -1 0 -1 0
  2 1 0 0 1 1 -2 1 1 0 -1 -1 1 0 1 0 1 0 -1 -1 -1 0 1 0 0 1 -1 1
  0 0 1 1 0 0 0 1 -1 1 1 0 1 0 0 -1 0 -1 0 1 1 0 0 0 1 0 1 0
  1 1 0 -4 3 1 1 0 3 -3 -2 2 1 1 3 -1 -1 -1 -1 -1 -2 1 -1 1 -1 0 0 0
  28 28
  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 1 0
  -1 -1 0 1 2 2 -3 2 0 1 -1 -1 1 -1 0 0 0 0 0 -1 0 0 0 0 0 1 -1 1
  2 2 1 1 -2 -1 2 -1 -1 2 2 -1 1 0 0 0 1 0 0 1 1 0 0 0 1 -1 1 0
  -1 0 0 2 -1 -1 0 0 -1 1 1 -1 -1 0 -1 1 0 0 1 1 0 -1 0 0 0 0 0 0
  1 0 0 0 2 2 -2 1 1 1 -1 -1 2 -1 1 0 1 0 0 -1 -1 0 0 0 0 1 0 1
  0 0 0 3 -2 -2 -1 0 -2 1 1 -1 -2 0 -2 1 0 0 0 1 1 -1 1 0 0 0 -1 0
  -1 0 -1 -2 2 0 -1 1 2 -3 -2 2 -1 0 1 0 -1 -1 0 -1 -2 0 0 1 -1 1 -1 0
  -2 -3 -2 -8 9 5 -3 3 5 -5 -6 4 2 0 4 -3 -2 -1 -1 -4 -3 2 -1 1 -1 2 -1 1
  -1 1 0 1 -4 -4 4 -2 -2 1 3 0 -3 1 -3 1 -1 1 2 2 1 -1 0 0 0 -1 0 -2
  0 1 0 1 -3 -2 2 -1 -1 1 2 -1 -1 0 -2 1 0 1 1 1 1 0 0 0 0 0 0 -1
  1 0 -1 -5 5 3 -1 0 4 -4 -4 2 2 1 4 -2 0 -1 -2 -2 -2 1 -1 0 -1 0 0 1
  0 0 -1 -4 4 2 -1 1 3 -3 -3 1 1 1 2 -1 -1 0 -1 -2 -1 1 -1 1 -1 1 -1 1
  -2 0 -1 -5 4 2 0 1 3 -4 -3 3 0 1 3 -2 -2 -1 -1 -2 -2 1 -1 1 -1 0 -1 0
  0 1 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
  0 0 1 3 -3 -1 1 -1 -2 2 2 -1 0 0 -1 1 1 0 0 2 1 0 0 -1 1 -1 1 0
  0 -1 0 -1 3 3 -3 2 1 0 -2 0 2 -1 1 -1 0 0 -1 -2 -1 1 0 0 0 1 -1 1
  0 -1 -1 -3 4 3 -2 1 2 -2 -3 1 2 0 2 -1 0 0 -1 -2 -1 1 0 0 0 1 -1 1
  0 0 0 -1 2 1 0 0 1 0 -1 0 1 0 1 0 0 0 0 0 0 0 -1 0 0 0 0 1
  -2 -2 1 3 -2 0 0 0 -3 2 1 -1 0 0 -1 0 0 0 0 1 1 0 0 -1 1 -1 1 0
  1 0 0 -3 1 -1 2 0 1 -1 0 2 -1 1 0 -1 -1 0 0 0 0 0 0 1 0 0 0 -1
  -1 0 -1 -1 0 -1 0 0 0 -1 0 1 -1 1 0 0 -1 0 0 0 0 0 0 0 0 0 -1 0
  -1 -2 0 0 1 1 -1 1 -1 1 0 0 1 0 0 -1 0 0 0 0 0 0 0 -1 1 0 1 0
  0 2 1 3 -3 -2 0 0 -2 2 2 -1 -2 0 -2 1 0 0 1 1 0 -1 1 0 0 0 -1 0
  1 1 1 4 -4 -2 1 -1 -3 3 3 -2 -1 0 -2 1 1 1 0 2 2 -1 1 -1 1 -1 0 0
  0 0 2 7 -6 -3 1 -1 -5 5 4 -3 -1 -1 -4 2 1 1 1 3 2 -1 1 -1 1 -1 1 -1
  1 2 0 -1 0 -1 0 0 2 -3 -1 1 -1 1 1 0 0 -1 -1 0 -1 0 0 1 -1 0 -1 0
  2 1 1 3 -1 0 -2 1 -1 3 1 -3 0 -1 -2 1 1 1 1 0 1 -1 1 0 0 1 -1 1
  1 1 0 -3 2 0 1 0 3 -4 -2 2 0 1 2 -1 -1 -1 -1 -1 -1 0 -1 1 -1 0 0 0
  28 28
  2 2 1 2 -3 -2 1 0 -1 2 2 -2 -1 0 -2 1 0 1 1 1 1 -1 1 0 0 0 0 0
  0 -2 -1 -4 6 4 -3 2 2 -1 -3 1 2 0 2 -2 0 0 -1 -2 -1 1 0 0 0 1 -1 1
  -2 -1 0 2 -1 0 -1 0 -1 0 0 0 -1 0 -1 1 0 0 0 0 0 0 0 0 0 0 -1 0
  1 0 0 -3 3 1 1 1 2 -1 -1 1 1 0 1 -1 -1 0 0 -1 0 0 -1 1 0 0 0 0
  1 -1 0 -1 2 1 -1 1 1 0 -1 0 0 0 -1 0 0 1 0 -1 0 0 0 1 0 1 -1 0
  0 0 0 2 -2 -1 0 0 -2 2 2 -1 0 0 0 0 0 0 0 1 1 -1 1 -1 1 -1 1 0
  1 -1 0 0 -1 -1 1 0 -1 1 1 0 0 0 -1 0 0 1 0 0 1 0 0 0 1 0 1 -1
  2 0 0 0 0 0 -1 1 0 1 0 -1 0 0 -1 0 1 1 0 0 0 0 1 0 0 1 0 0
  -2 -1 0 -3 3 2 1 0 2 -3 -2 3 2 0 3 -2 -1 -2 -1 -1 -1 1 -2 0 0 -1 1 0
  -2 -1 0 -2 3 2 -1 1 1 -2 -2 2 1 0 2 -2 -1 -2 -1 -1 -1 1 -1 0 0 0 0 0
  1 2 0 1 -3 -3 3 -2 0 1 2 -1 -2 0 -2 2 0 1 2 1 0 -1 0 1 -1 0 0 -1
  -2 -1 -1 -5 5 2 -1 2 3 -3 -3 3 0 0 2 -2 -2 -1 0 -2 -2 1 -1 1 -1 1 -1 0
  -1 0 -1 -2 1 0 1 -1 1 -1 -1 1 0 0 1 0 0 0 0 0 -1 1 -1 0 -1 0 0 0
  -1 0 0 0 0 0 2 -1 0 0 1 1 0 0 1 0 0 -1 0 1 0 0 -1 0 0 -1 1 -1
  -1 1 0 1 0 -1 0 1 0 -1 0 0 -1 0 0 0 -1 -1 0 0 0 -1 0 1 0 0 -1 0
  -1 -2 -1 -2 3 2 -2 1 1 -1 -2 1 1 0 1 -1 0 0 -1 -1 -1 1 0 0 0 1 0 0
  0 0 0 2 -2 -1 0 -1 -1 0 1 0 -1 0 -1 1 1 0 0 1 0 0 0 0 0 0 0 -1
  -1 -1 -1 -3 4 2 -2 2 2 -2 -3 1 0 0 1 -1 -1 0 0 -2 -1 0 0 1 -1 1 -2 1
  0 2 0 2 -2 -2 2 -1 -1 1 2 -1 -1 0 -1 1 0 0 1 2 1 -1 0 0 0 -1 0 0
  -1 1 0 1 -3 -3 1 0 -1 -1 1 1 -2 1 0 0 -1 -1 0 1 0 -1 1 0 0 -1 0 0
  -1 -1 -1 -5 7 4 -3 3 4 -4 -4 3 2 0 4 -3 -1 -2 -2 -3 -2 1 -1 1 0 1 -1 1
  2 1 0 -1 1 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
  -2 -3 0 0 2 2 -1 1 0 0 -1 1 2 -1 1 -1 0 0 -1 -1 0 1 -1 0 1 0 1 0
  -1 1 0 1 -2 -1 1 -1 -1 0 1 0 0 0 1 0 0 -1 0 1 0 0 0 0 0 -1 1 0
  -1 -1 0 1 -1 0 1 -1 -2 1 1 0 1 0 0 0 0 0 0 1 1 0 0 -1 1 -1 1 0
  -1 0 -1 -4 2 -1 2 0 2 -3 -1 3 -1 1 2 -1 -2 -1 0 -1 -1 0 -1 1 0 0 0 -1
  0 -2 0 -3 5 4 -3 2 2 -1 -3 1 2 0 2 -2 0 0 -1 -2 -1 1 0 0 0 1 0 1
  -1 0 -1 -5 1 -1 3 -1 2 -3 -1 3 -1 1 1 -1 -2 0 1 -1 -1 1 -1 1 -1 0 1 -1
  

• PROPERTIES
  MODULAR = 5
  5-modular extremal.
  

• REFERENCES
  Constructed by Gabriele Nebe <gabi@momo.math.rwth-aachen.de>
  

• NOTES
  Superlattice of the lattice of the maximal finite group [ +-J2:2 ]_{28}
  of index 3, not invariant under the outer automorphism.
  The endomorphism ring as a ZJ2-lattice is only a suborder of index 3 in the
  maximal order of Q[sqrt{5}].
  

• LAST_LINE
  

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  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe