Output of hn -T10 -A100000 --graph_max2500 --herm_lll3 0.8 -t

&K=Q(sqrt(-14))
&Hdim=2      V=K^2
&HNeighbourhood at <3,-1+w> contains 4 classes:
mass of the neighbourhood is 1/3
  Steinitz class <3,1+w>:
&Hlattice (#1 <- #3)
   <2,w> <3,-1+w> 
       1 
1/3-1/6w      2/3 
  |Aut| = 2^2*3
  #short vectors:
    0    0    0    6    0   18


&Hlattice (#2 <- #2)
     <1>  <3,1+w> 
       2 
       1      2/3 
  |Aut| = 2^2*3
  #short vectors:
    0    6    0    0    0    6


  Steinitz class <3,-1+w>:
&Hlattice (#3 <- #1)
   <2,w>  <3,1+w> 
       1 
-1/3-1/6w      2/3 
  |Aut| = 2^2*3
  #short vectors:
    0    0    0    6    0   18


&Hlattice (#4 <- #4)
     <1> <3,-1+w> 
       2 
       1      2/3 
  |Aut| = 2^2*3
  #short vectors:
    0    6    0    0    0    6



&Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}):
  0   0   3   1 
  0   0   1   3 
  1   3   0   0 
  3   1   0   0 

computing the invariants of the trace forms and testing them for isometries:


classes of Z-lattices with respect to the trace form (scaled by 1/2)
one representative of each class
&Dim=4      V=Q^4

&Genus of the trace-forms:
det= 196 = 2^2 *7^2
   2-adic symbol:  1^-2_II 2^-2_II 
   7-adic symbol:  1^-2 7^-2 
  -1-adic symbol:  +^4 -^0 
level=14, weight=2
a_0,..,a_8 determine modular form

2 classes of trace forms

&begin_block

&Gram (#1 <- H1,H3)
  4 
  2   4 
  2   0   6 
  2   0  -1   6 
  |Aut| = 2^3*3^2
  #short vectors:
    0    0    0    6    0   18    0    0

&Gram (#2 <- H2,H4)
  2 
  1   2 
  1   1  10 
  1   0   5  10 
  |Aut| = 2^3*3^2
  #short vectors:
    0    6    0    0    0    6    0    6

&end_block
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