Output of /home/aschiem/Pgm/Hn/hn --invar -t --shells-6 -D5

&K=Q(sqrt(-2))
&Hdim=6      V=K^6
&HNeighbourhood at <3,-1+w> contains 5 classes:
mass of the neighbourhood is 19/368640
  Steinitz class <1,w>:
&Hlattice (#1 <- #1)
       2 
      -w        2 
      -w        1        2 
      -w        1        1        2 
      -w        1        1        1        2 
     1-w      1+w      1+w      1+w      1+w        4 
  |Aut| = 2^10*3^2*5
  #short vectors:
    0   72    0 1800    0 17568


&Hlattice (#2 <- #2)
       2 
       0        2 
     1-w        0        2 
       0       -w        0        2 
       0        0        0       -1        2 
       0       -1        0        0        0        2 
  |Aut| = 2^12*3^3
  #short vectors:
    0   72    0 1800    0 17568


&Hlattice (#3 <- #3)
       2 
       0        2 
       0        1        2 
       0        1        1        2 
       0        1        1        1        2 
     1-w     -1+w     -1+w     -1+w     -1+w        4 
  |Aut| = 2^8*3^4*5
  #short vectors:
    0   72    0 1800    0 17568


&Hlattice (#4 <- #4)
       2 
       0        2 
       0        1        2 
       0        1        1        2 
       0        1        1        1        2 
     1+w     -1-w     -1-w     -1-w     -1-w        4 
  |Aut| = 2^8*3^4*5
  #short vectors:
    0   72    0 1800    0 17568


&Hlattice (#5 <- #5)
       2 
       0        2 
       0      1-w        2 
     1-w        0        0        2 
       0        0        0        0        2 
       0        0        0        0      1-w        2 
  |Aut| = 2^13*3^4
  #short vectors:
    0   72    0 1800    0 17568



&Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}):
156  80  96  32   0 
192  28   0 128  16 
 72 120  36 136   0 
216   0  72  36  40 
  0  96 256   0  12 


classes of Z-lattices with respect to the trace form (scaled by 1/2)
&Dim=12      V=Q^12

&Genus of the trace-forms:
det= 64 = 2^6
   2-adic symbol:  1^-6_II 2^-6_II 
  -1-adic symbol:  +^12 -^0 
level=2, weight=6
a_0,..,a_2 determine modular form

&Gram (#1 <- H1)
  2 
  0   2 
  0   1   2 
  0   1   1   2 
  0   1   0   1   2 
  0  -1  -1  -1   0   2 
  0   1   1   1   0  -1   2 
  0   0   0   0   0   0   0   2 
  0   0   0   0   0   0   0   0   2 
  0   0   0   0   0   0   0   0   0   2 
  0   0   0   0   0   0   0   0   0   0   2 
  1  -1  -1  -1   0   1  -1  -1  -1  -1  -1   4 
  |Aut| = 2^20*3^4*5^2
  #short vectors:
    0   72

&Gram (#2 <- H2,H5)
  2 
  1   2 
  1   1   2 
  1   0   1   2 
  0   0   0   0   2 
  0   0   0   0  -1   2 
  0   0   0   0  -1   0   2 
  0   0   0   0   1   0   0   2 
  0   0   0   0   0   0   0   0   2 
  0   0   0   0   0   0   0   0   1   2 
  0   0   0   0   0   0   0   0  -1  -1   2 
  0   0   0   0   0   0   0   0   1   1   0   2 
  |Aut| = 2^22*3^7
  #short vectors:
    0   72

&Gram (#3 <- H3,H4)
  2 
  1   2 
  1   0   2 
  1   0   0   2 
  1   1   0   0   2 
  1   1   0   1   0   2 
  1   1   0   1   0   1   4 
  1   0   1   0   0   0  -1   4 
  1   1   0   1   0   1   2  -1   4 
  1   0   0   1   0   1   0   0   0   4 
  1   0   0   1   0   1   0   0   0   2   4 
  1   0   0   1   0   1   0   0   0   2   2   4 
  |Aut| = 2^15*3^8*5^2
  #short vectors:
    0   72

<end>