Output of /home/aschiem/Pgm/Hn/hn --invar -t --shells-5

&K=Q(sqrt(-19))
&Hdim=3      V=K^3
&HNeighbourhood at <2,2w> contains 3 classes:
mass of the neighbourhood is 11/48
  Steinitz class <1,w>:
&Hlattice (#1 <-- #3)
       2 
       1        3 
      -1     -1-w        3 
  |Aut| = 2^2*3
  #short vectors:
    0    6   14   12   60


&Hlattice (#2 <-- #1)
       1 
       0        1 
       0        0        1 
  |Aut| = 2^4*3
  #short vectors:
    6   12    8    6   36


&Hlattice (#3 <-- #2)
       1 
       0        2 
       0       -w        3 
  |Aut| = 2^3
  #short vectors:
    2    4   16   30   32



&Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}):
 12   0   6 
  0   0  18 
  4   3  11 


classes of Z-lattices with respect to the trace form
&Dim=6      V=Q^6

&Genus of the trace-forms:
det= 6859 = 19^3
   2-adic symbol:  1^-6_II 
  19-adic symbol:  1^-3 19^-3 
  -1-adic symbol:  +^6 -^0 
level=19, weight=3
a_0,..,a_10 determine modular form

&Gram (#1 <- H1)
  4 
  2   4 
  2   2   6 
  2   2   3   6 
  1  -1  -1   1   8 
  1   2   2   0   2   8 
  |Aut| = 2^3*3
  #short vectors:
    0    0    0    6    0   14    0   12    0   60

&Gram (#2 <- H2)
  2 
  0   2 
  0   0   2 
  1   0   0  10 
  0   1   0   0  10 
  0   0   1   0   0  10 
  |Aut| = 2^7*3
  #short vectors:
    0    6    0   12    0    8    0    6    0   36

&Gram (#3 <- H3)
  2 
  0   4 
  0   0   4 
  0  -1   2   6 
  0   2  -1  -1   6 
  1   0   0   0   0  10 
  |Aut| = 2^5
  #short vectors:
    0    2    0    4    0   16    0   30    0   32

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