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 8 classes:
mass of the neighbourhood is 2
  Steinitz class <3,1+w>:
&Hlattice (#1 <- #8)
   <2,w> <3,-1+w> 
       1 
-2/3-1/6w        1 
  |Aut| = 2^2
  #short vectors:
    0    0    0    6    4    6    8    0    8


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


&Hlattice (#3 <- #4)
     <1>  <3,1+w> 
       2 
1/3-1/3w        1 
  |Aut| = 2^2
  #short vectors:
    0    2    4    0    0    2    8    6    8


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


  Steinitz class <3,-1+w>:
&Hlattice (#5 <- #7)
   <2,w>  <3,1+w> 
       1 
2/3-1/6w        1 
  |Aut| = 2^2
  #short vectors:
    0    0    0    6    4    6    8    0    8


&Hlattice (#6 <- #5)
   <2,w>  <3,1+w> 
     1/2 
       0      1/3 
  |Aut| = 2^2
  #short vectors:
    0    2    2


&Hlattice (#7 <- #6)
     <1> <3,-1+w> 
       2 
-1/3-1/3w        1 
  |Aut| = 2^2
  #short vectors:
    0    2    4    0    0    2    8    6    8


&Hlattice (#8 <- #1)
     <1> <3,-1+w> 
       1 
       0      1/3 
  |Aut| = 2^2
  #short vectors:
    2    0    2



&Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}):
  0   0   0   0   1   0   1   2 
  0   0   0   0   0   1   2   1 
  0   0   0   0   1   2   1   0 
  0   0   0   0   2   1   0   1 
  1   2   1   0   0   0   0   0 
  2   1   0   1   0   0   0   0 
  1   0   1   2   0   0   0   0 
  0   1   2   1   0   0   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 2^2]_4 
   7-adic symbol:  1^-2 7^-2 
  -1-adic symbol:  +^4 -^0 
level(of 2-scaled form)=56, weight=2
a_0,..,a_16 determine modular form

4 classes of trace forms

&begin_block

&Gram (#1 <- H1,H5)
  4 
  2   4 
  0  -1   5 
  0  -1  -2   5 
  |Aut| = 2^3
  #short vectors:
    0    0    0    6    4    6    8    0    8    6    8    6    4   14   16    6

&Gram (#2 <- H2,H6)
  2 
  0   3 
  0  -1   5 
  0   0   0   7 
  |Aut| = 2^3
  #short vectors:
    0    2    2    0    6    2    6    6    4    6    4   18   10   16   16    0

&Gram (#3 <- H3,H7)
  2 
  1   3 
  0  -1   6 
  1   1  -3   9 
  |Aut| = 2^3
  #short vectors:
    0    2    4    0    0    2    8    6    8    6    8   18    8   16    8    0

&Gram (#4 <- H4,H8)
  1 
  0   3 
  0  -1   5 
  0   0   0  14 
  |Aut| = 2^3
  #short vectors:
    2    0    2    6    2    6    8    0    6    6    4    6    6   14    8    6

&end_block
<end>