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


&Hlattice (#2 <- #6)
       3 
       w        5 
  |Aut| = 2^2
  #short vectors:
    0    0    4    0    4


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


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


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


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


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


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



&Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}):
  0   0   0   0   1   1   0   2 
  0   0   0   0   1   1   2   0 
  0   0   0   0   0   0   2   2 
  0   0   0   0   0   0   2   2 
  2   2   0   0   0   0   0   0 
  2   2   0   0   0   0   0   0 
  0   2   1   1   0   0   0   0 
  2   0   1   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]_0 
   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

5 classes of trace forms

&begin_block

&Gram (#1 <- H1,H2,H5,H6)
  3 
  0   3 
  0  -1   5 
  1   0   0   5 
  |Aut| = 2^3
  #short vectors:
    0    0    4    0    4    8    0    8    8    8    8    8   12    0   16   16

&Gram (#2 <- H3)
  2 
  0   2 
  0   0   7 
  0   0   0   7 
  |Aut| = 2^6
  #short vectors:
    0    4    0    4    0    0    4    4   16    8   16    0    0    4   16   20

&Gram (#3 <- H4)
  1 
  0   1 
  0   0  14 
  0   0   0  14 
  |Aut| = 2^6
  #short vectors:
    4    4    0    4    8    0    0    4    4    8    0    0    8    4   16   20

&Gram (#4 <- H7)
  2 
  0   4 
  1  -2   5 
  0  -2   1   8 
  |Aut| = 2^4
  #short vectors:
    0    2    0    2    8    4    0    6    8    8    8    4    8    2   24   18

&Gram (#5 <- H8)
  1 
  0   2 
  0   0   7 
  0   0   0  14 
  |Aut| = 2^4
  #short vectors:
    2    2    4    2    0    4    2    6   10    8    8    4    8    2    8   18

&end_block
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