Output of /home/aschiem/bin/hn --invar -t --shells-12 --herm_lll3 0.8

&K=Q(sqrt(-10))
&Hdim=2      V=K^2
&HNeighbourhood at <3,3w> contains 3 classes:
mass of the neighbourhood is 3/4
  Steinitz class <1,w>:
&Hlattice (#1 <- #4)
       3 
     1+w        4 
  |Aut| = 2
  #short vectors:
    0    0    4    4    8    8    4    4    8   16    8   16


&Hlattice (#2 <- #2)
   <2,w>    <2,w> 
     1/2 
       0      1/2 
  |Aut| = 2^3
  #short vectors:
    0    4    0    4    4    0   16    4   16   12    0   16


&Hlattice (#3 <- #1)
       1 
       0        1 
  |Aut| = 2^3
  #short vectors:
    4    4    0    4    8    0    0    4    4   12   16   16





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= 100 = 2^2 *5^2
   2-adic symbol:  [1^2 2^2]_4 
   5-adic symbol:  1^2 5^2 
  -1-adic symbol:  +^4 -^0 
level(of 2-scaled form)=40, weight=2
a_0,..,a_12 determine modular form

3-classes of trace forms

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

&Gram (#2 <- H2)
  2 
  0   2 
  0   0   5 
  0   0   0   5 
  |Aut| = 2^6
  #short vectors:
    0    4    0    4    4    0   16    4   16   12    0   16

&Gram (#3 <- H3)
  1 
  0   1 
  0   0  10 
  0   0   0  10 
  |Aut| = 2^6
  #short vectors:
    4    4    0    4    8    0    0    4    4   12   16   16

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