Output of /home/aschiem/Pgm/Hn/hn --invar -t --shells-4 -D5

&K=Q(sqrt(-1))
&Hdim=6      V=K^6
&HNeighbourhood at <2,-1+w> contains 3 classes:
mass of the neighbourhood is 1/589824
  Steinitz class <1,w>:
&Hlattice (#1 <-- #2)
       2 
     1+w        2 
     1+w        1        2 
     1+w        1        1        2 
     1+w        1        1        1        2 
       1        0        0        0        0        3 
  |Aut| = 2^15*3^2*5
  #short vectors:
    0  264 2048 7944


&Hlattice (#2 <-- #1)
       1 
       0        1 
       0        0        1 
       0        0        0        1 
       0        0        0        0        1 
       0        0        0        0        0        1 
  |Aut| = 2^16*3^2*5
  #short vectors:
   24  264 1760 7944


&Hlattice (#3 <-- #3)
       1 
       0        1 
       0        0        2 
       0        0        1        2 
       0        0        0        0        2 
       0        0      1-w      1-w        1        2 
  |Aut| = 2^15*3^2*5
  #short vectors:
    8  264 1952 7944



&Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}):
 31   1  30 
  2  30  30 
 30  15  17 


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= 1 = 1 
   2-adic symbol:  1^12_4 
  -1-adic symbol:  +^12 -^0 
level(of 2-scaled form)=4, weight=6
a_0,..,a_3 determine modular form

&Gram (#1 <- H1)
  2 
  1   2 
  1   1   2 
  1   0   1   2 
  1   1   1   0   2 
  1   1   1   0   1   2 
  1   1   1   0   1   1   2 
  1   1   1   0   1   1   1   2 
  1   1   1   0   1   1   1   1   2 
  0   0   0   0   0   0   0   0   0   2 
  1   0   0   0   1   0   0   1   1   0   3 
  1   0   1   1   0   0   0   0   0  -1   0   3 
  |Aut| = 2^21*3^5*5^2*7*11
  #short vectors:
    0  264 2048

&Gram (#2 <- H2)
  1 
  0   1 
  0   0   1 
  0   0   0   1 
  0   0   0   0   1 
  0   0   0   0   0   1 
  0   0   0   0   0   0   1 
  0   0   0   0   0   0   0   1 
  0   0   0   0   0   0   0   0   1 
  0   0   0   0   0   0   0   0   0   1 
  0   0   0   0   0   0   0   0   0   0   1 
  0   0   0   0   0   0   0   0   0   0   0   1 
  |Aut| = 2^22*3^5*5^2*7*11
  #short vectors:
   24  264 1760

&Gram (#3 <- H3)
  1 
  0   1 
  0   0   1 
  0   0   0   1 
  0   0   0   0   2 
  0   0   0   0   1   2 
  0   0   0   0   1   1   2 
  0   0   0   0  -1  -1   0   2 
  0   0   0   0   1   0   0  -1   2 
  0   0   0   0   1   1   1  -1   0   2 
  0   0   0   0   1   0   0   0   1   0   2 
  0   0   0   0  -1   0   0   0  -1   0  -1   2 
  |Aut| = 2^21*3^6*5^2*7
  #short vectors:
    8  264 1952

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