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:
(every Steinitz class is a special genus, since it is a neighbourhood at 2 and at 11)
mass of the neighbourhood is 3/4
  Steinitz class <1,w>:
&Hlattice (#1 <- #1)
       4 
     1+w        4 
  |Aut| = 2^2
  #short vectors:
    0    0    0    8


&Hlattice (#2 <- #4)
       2 
     1-w        8 
  |Aut| = 2^3
  #short vectors:
    0    4    0    4    0    0    0   20


  Steinitz class <2,w>:
&Hlattice (#3 <- #2)
     <1>    <2,w> 
       4 
  2+1/2w        2 
  |Aut| = 2^3
  #short vectors:
    0    0    0    8    0    8    0   16


&Hlattice (#4 <- #3)
     <1>    <2,w> 
       2 
   -1/2w        2 
  |Aut| = 2^2
  #short vectors:
    0    2    0    6    0    4    0   18



&Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}):
  0   0   2   2 
  0   0   0   4 
  4   0   0   0 
  2   2   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

3 classes of trace forms

&begin_block

&Gram (#1 <- H1,H3)
  4 
  1   4 
  0   1   4 
  1   0  -1   4 
  |Aut| = 2^4
  #short vectors:
    0    0    0    8    0    8    0   16

&Gram (#2 <- H2)
  2 
  0   2 
  1   1   8 
  1  -1   0   8 
  |Aut| = 2^6
  #short vectors:
    0    4    0    4    0    0    0   20

&Gram (#3 <- H4)
  2 
  1   4 
  0   0   4 
  0   0  -2   8 
  |Aut| = 2^4
  #short vectors:
    0    2    0    6    0    4    0   18

&end_block
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