Output of /home/aschiem/bin/hn --invar -t --shells-18 --herm_lll3 0.8 &K=Q(sqrt(-10)) &Hdim=3 V=K^3 &HNeighbourhood at <2,w> contains 12 classes: mass of the neighbourhood is 79/48 Steinitz class <2,w>: &Hlattice (#1 <- #7) <1> <1> <2,w> 3 0 4 1 1/2w 1 |Aut| = 2^2*3 #short vectors: 0 0 6 12 0 8 42 42 48 54 48 48 84 96 74 108 204 204 &Hlattice (#2 <- #8) <1> <1> <2,w> 3 1-w 5 1/2w -1 3/2 |Aut| = 2^2 #short vectors: 0 0 6 8 8 12 34 42 32 58 56 64 92 84 74 100 204 188 &Hlattice (#3 <- #2) <2,w> <2,w> <2,w> 1/2 0 1/2 0 0 1/2 |Aut| = 2^4*3 #short vectors: 0 6 0 12 6 8 36 6 72 36 48 96 36 144 152 108 192 102 &Hlattice (#4 <- #3) <1> <2,w> <1> 2 0 1/2 1-w 0 6 |Aut| = 2^4 #short vectors: 0 6 0 12 2 24 12 38 24 60 48 112 76 96 120 76 224 150 &Hlattice (#5 <- #10) <1> <1> <2,w> 2 1 2 1-1/2w 1-1/2w 5/2 |Aut| = 2^2*3 #short vectors: 0 6 6 0 12 8 18 42 36 48 72 84 96 96 98 108 180 174 &Hlattice (#6 <- #12) <1> <1> <2,w> 2 1 3 0 -1-1/2w 3/2 |Aut| = 2^2*3 #short vectors: 0 6 6 0 12 8 18 42 36 48 72 84 96 96 98 108 180 174 &Hlattice (#7 <- #6) <2,w> <1> <1> 1/2 0 3 0 1-w 4 |Aut| = 2^2 #short vectors: 0 2 4 4 18 16 24 30 24 56 64 96 84 88 100 92 200 138 &Hlattice (#8 <- #9) <1> <1> <2,w> 3 -1 3 -1+1/2w 1 3/2 |Aut| = 2^2 #short vectors: 0 2 6 4 12 12 26 42 28 56 64 76 96 84 82 100 196 178 &Hlattice (#9 <- #11) <1> <1> <2,w> 3 -1 3 -1-1/2w 1 3/2 |Aut| = 2^2 #short vectors: 0 2 6 4 12 12 26 42 28 56 64 76 96 84 82 100 196 178 &Hlattice (#10 <- #1) <1> <1> <2,w> 1 0 1 0 0 1/2 |Aut| = 2^4 #short vectors: 4 6 8 12 10 16 28 22 36 44 40 80 68 72 104 92 176 166 &Hlattice (#11 <- #4) <1> <1> <2,w> 1 0 2 0 -1/2w 3/2 |Aut| = 2^3 #short vectors: 2 2 8 12 4 12 36 38 38 52 44 56 84 76 76 100 192 202 &Hlattice (#12 <- #5) <1> <1> <2,w> 1 0 2 0 1-1/2w 2 |Aut| = 2^3 #short vectors: 2 2 4 12 20 12 16 46 54 20 12 96 108 44 88 164 200 154 &Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}): 0 3 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 2 2 0 1 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 1 0 0 0 4 0 0 1 0 0 0 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0 0 0 3 0 3 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 2 0 0 1 0 1 0 2 0 0 0 0 2 0 0 0 1 1 2 0 0 0 0 0 0 1 1 0 0 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 1 4 classes of Z-lattices with respect to the trace form (scaled by 1/2) one representative of each class &Dim=6 V=Q^6 &Genus of the trace-forms: det= 1000 = 2^3 *5^3 2-adic symbol: [1^-3 2^3]_2 5-adic symbol: 1^-3 5^3 -1-adic symbol: +^6 -^0 level(of 2-scaled form)=40, weight=3 a_0,..,a_18 determine modular form 10-classes of trace forms &Gram (#1 <- H1) 3 1 3 1 1 3 0 0 0 4 0 0 0 -1 4 0 0 0 -1 -1 4 |Aut| = 2^4*3^2 #short vectors: 0 0 6 12 0 8 42 42 48 54 48 48 84 96 74 108 204 204 &Gram (#2 <- H2) 3 1 3 1 1 3 0 0 0 4 1 -1 0 1 5 1 -1 0 -1 2 5 |Aut| = 2^4 #short vectors: 0 0 6 8 8 12 34 42 32 58 56 64 92 84 74 100 204 188 &Gram (#3 <- H3) 2 0 2 0 0 2 0 0 0 5 0 0 0 0 5 0 0 0 0 0 5 |Aut| = 2^8*3^2 #short vectors: 0 6 0 12 6 8 36 6 72 36 48 96 36 144 152 108 192 102 &Gram (#4 <- H4) 2 0 2 0 0 2 0 0 0 5 1 0 1 0 6 1 0 -1 0 0 6 |Aut| = 2^8 #short vectors: 0 6 0 12 2 24 12 38 24 60 48 112 76 96 120 76 224 150 &Gram (#5 <- H5,H6) 2 1 2 1 1 3 1 0 0 5 1 0 1 2 8 1 1 0 -1 3 8 |Aut| = 2^3*3^2 #short vectors: 0 6 6 0 12 8 18 42 36 48 72 84 96 96 98 108 180 174 &Gram (#6 <- H7) 2 0 3 0 0 3 0 1 1 4 0 -1 1 0 4 0 0 0 0 0 5 |Aut| = 2^5 #short vectors: 0 2 4 4 18 16 24 30 24 56 64 96 84 88 100 92 200 138 &Gram (#7 <- H8,H9) 2 1 3 0 1 3 1 0 1 5 0 0 -1 -2 5 1 1 1 0 2 7 |Aut| = 2^3 #short vectors: 0 2 6 4 12 12 26 42 28 56 64 76 96 84 82 100 196 178 &Gram (#8 <- H10) 1 0 1 0 0 2 0 0 0 5 0 0 0 0 10 0 0 0 0 0 10 |Aut| = 2^8 #short vectors: 4 6 8 12 10 16 28 22 36 44 40 80 68 72 104 92 176 166 &Gram (#9 <- H11) 1 0 2 0 1 3 0 0 0 4 0 0 0 2 6 0 0 0 0 0 10 |Aut| = 2^6 #short vectors: 2 2 8 12 4 12 36 38 38 52 44 56 84 76 76 100 192 202 &Gram (#10 <- H12) 1 0 2 0 -1 4 0 -1 -1 4 0 0 1 1 6 0 0 0 0 0 10 |Aut| = 2^6 #short vectors: 2 2 4 12 20 12 16 46 54 20 12 96 108 44 88 164 200 154