Output of /home/aschiem/bin/hn --invar -t --shells-17 --herm_lll3 0.8 &K=Q(sqrt(-67)) &Hdim=3 V=K^3 &HNeighbourhood at <2,2w> contains 17 classes: mass of the neighbourhood is 251/48 Steinitz class <1,w>: &Hlattice (#1 <- #5) 5 -1-w 5 -w 2 6 |Aut| = 2 #short vectors: 0 0 0 4 6 8 16 6 26 20 40 22 46 38 40 58 64 &Hlattice (#2 <- #6) 5 2-w 5 -1+w -2 6 |Aut| = 2 #short vectors: 0 0 0 4 6 8 16 6 26 20 40 22 46 38 40 58 64 &Hlattice (#3 <- #11) 5 -2+w 6 -1-w -2 7 |Aut| = 2 #short vectors: 0 0 0 2 10 6 10 22 24 12 26 32 48 34 54 54 78 &Hlattice (#4 <- #9) 3 -1 4 1 -w 5 |Aut| = 2 #short vectors: 0 0 4 4 4 4 8 14 16 26 38 26 52 46 44 58 70 &Hlattice (#5 <- #10) 3 1 4 -1 -1+w 5 |Aut| = 2 #short vectors: 0 0 4 4 4 4 8 14 16 26 38 26 52 46 44 58 70 &Hlattice (#6 <- #14) 5 -1+w 5 w 2 5 |Aut| = 2 #short vectors: 0 0 2 0 8 10 12 18 10 26 28 32 46 38 38 34 106 &Hlattice (#7 <- #12) 2 0 3 -1 -2+w 7 |Aut| = 2^2*3 #short vectors: 0 6 2 0 12 6 12 6 24 0 36 14 36 36 60 36 96 &Hlattice (#8 <- #4) 3 -1 4 -2+w 0 7 |Aut| = 2^2 #short vectors: 0 2 2 4 8 2 8 14 28 8 36 22 48 40 60 64 60 &Hlattice (#9 <- #7) 3 1 4 -2+w -1 7 |Aut| = 2^2 #short vectors: 0 2 2 4 8 2 8 14 28 8 36 22 48 40 60 64 60 &Hlattice (#10 <- #13) 2 -1 4 0 -1+w 5 |Aut| = 2^2 #short vectors: 0 2 4 4 4 0 16 18 14 8 26 36 42 32 86 64 84 &Hlattice (#11 <- #15) 5 w 6 -2 2+w 6 |Aut| = 2^2 #short vectors: 0 2 0 0 8 12 24 6 14 16 30 28 34 28 50 32 112 &Hlattice (#12 <- #16) 2 -1 4 0 -w 5 |Aut| = 2^2 #short vectors: 0 2 4 4 4 0 16 18 14 8 26 36 42 32 86 64 84 &Hlattice (#13 <- #17) 3 1 5 -1 -3+w 5 |Aut| = 2^2 #short vectors: 0 2 4 0 6 8 16 14 4 22 28 32 40 36 54 32 118 &Hlattice (#14 <- #1) 1 0 1 0 0 1 |Aut| = 2^4*3 #short vectors: 6 12 8 6 24 24 0 12 30 24 24 8 24 48 0 6 60 &Hlattice (#15 <- #2) 1 0 4 0 2-w 5 |Aut| = 2^2 #short vectors: 2 0 0 6 12 12 12 24 30 20 20 36 44 32 40 58 52 &Hlattice (#16 <- #3) 1 0 2 0 -w 9 |Aut| = 2^3 #short vectors: 2 4 8 6 8 8 0 12 18 32 40 16 48 56 24 46 56 &Hlattice (#17 <- #8) 1 0 3 0 1-w 6 |Aut| = 2^2 #short vectors: 2 0 4 10 0 8 28 12 14 28 24 44 36 28 68 74 56 &Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}): 2 3 3 1 3 1 0 1 1 0 1 0 0 0 2 0 0 3 2 3 3 1 1 0 1 1 0 1 0 0 0 2 0 0 3 3 1 1 1 1 1 1 1 1 2 1 0 0 0 1 0 1 3 1 2 1 3 0 1 1 1 0 1 1 0 0 1 1 3 1 1 1 2 3 0 1 1 1 0 1 1 0 0 1 1 1 1 1 3 3 2 1 0 0 0 3 0 3 0 0 0 0 0 0 6 0 0 6 0 3 3 0 0 0 0 0 0 0 0 2 2 2 2 2 0 1 2 1 2 0 0 0 0 2 0 0 2 2 2 2 2 0 1 1 2 0 0 2 0 0 2 0 0 0 0 2 2 2 0 0 2 0 2 1 3 2 0 0 0 2 2 2 4 0 0 6 0 0 0 1 0 1 2 0 0 0 0 0 0 2 2 2 0 0 0 2 3 1 2 2 0 0 0 2 0 0 0 2 2 6 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 6 0 4 4 0 0 0 0 0 2 2 0 0 0 0 1 1 1 3 0 0 4 4 4 0 0 0 0 0 0 0 0 1 2 1 2 0 0 0 2 2 0 0 0 0 2 0 2 0 0 3 1 6 classes of Z-lattices with respect to the trace form one representative of each class &Dim=6 V=Q^6 &Genus of the trace-forms: det= 300763 = 67^3 2-adic symbol: 1^-6_II 67-adic symbol: 1^-3 67^-3 -1-adic symbol: +^6 -^0 level=67, weight=3 a_0,..,a_34 determine modular form 13-classes of trace forms &Gram (#1 <- H1,H2) 8 2 8 4 0 10 0 2 -3 10 1 -2 -1 4 12 4 3 0 0 2 12 |Aut| = 2 #short vectors: 0 0 0 0 0 0 0 4 0 6 0 8 0 16 0 6 0 26 0 20 0 40 0 22 0 46 0 38 0 40 0 58 0 64 &Gram (#2 <- H3) 8 4 10 2 4 10 4 2 1 10 2 5 2 4 12 3 -1 4 5 5 16 |Aut| = 2^2 #short vectors: 0 0 0 0 0 0 0 2 0 10 0 6 0 10 0 22 0 24 0 12 0 26 0 32 0 48 0 34 0 54 0 54 0 78 &Gram (#3 <- H4,H5) 6 2 6 2 0 8 2 0 1 10 2 -1 0 2 14 1 -2 -2 4 6 16 |Aut| = 2 #short vectors: 0 0 0 0 0 4 0 4 0 4 0 4 0 8 0 14 0 16 0 26 0 38 0 26 0 52 0 46 0 44 0 58 0 70 &Gram (#4 <- H6) 6 2 10 2 -4 10 0 -1 2 10 2 1 -3 4 12 1 -1 4 -4 -6 16 |Aut| = 2^2 #short vectors: 0 0 0 0 0 2 0 0 0 8 0 10 0 12 0 18 0 10 0 26 0 28 0 32 0 46 0 38 0 38 0 34 0 106 &Gram (#5 <- H7) 4 2 4 0 0 6 2 2 3 14 1 -1 -2 -1 24 2 1 -2 0 -10 24 |Aut| = 2^3*3 #short vectors: 0 0 0 6 0 2 0 0 0 12 0 6 0 12 0 6 0 24 0 0 0 36 0 14 0 36 0 36 0 60 0 36 0 96 &Gram (#6 <- H8,H9) 4 0 6 2 2 8 0 0 -3 12 0 -3 0 -4 14 1 0 -1 6 -2 20 |Aut| = 2^2 #short vectors: 0 0 0 2 0 2 0 4 0 8 0 2 0 8 0 14 0 28 0 8 0 36 0 22 0 48 0 40 0 60 0 64 0 60 &Gram (#7 <- H10,H12) 4 2 6 2 0 8 0 0 -1 10 0 1 0 -2 14 1 1 0 4 6 22 |Aut| = 2^2 #short vectors: 0 0 0 2 0 4 0 4 0 4 0 0 0 16 0 18 0 14 0 8 0 26 0 36 0 42 0 32 0 86 0 64 0 84 &Gram (#8 <- H11) 4 2 10 0 -4 10 0 -4 1 10 2 1 -4 4 12 1 5 -4 0 6 22 |Aut| = 2^3 #short vectors: 0 0 0 2 0 0 0 0 0 8 0 12 0 24 0 6 0 14 0 16 0 30 0 28 0 34 0 28 0 50 0 32 0 112 &Gram (#9 <- H13) 4 2 6 0 2 10 0 -2 -5 10 2 1 2 2 16 1 3 2 0 8 22 |Aut| = 2^3 #short vectors: 0 0 0 2 0 4 0 0 0 6 0 8 0 16 0 14 0 4 0 22 0 28 0 32 0 40 0 36 0 54 0 32 0 118 &Gram (#10 <- H14) 2 0 2 0 0 2 1 0 0 34 0 1 0 0 34 0 0 1 0 0 34 |Aut| = 2^7*3 #short vectors: 0 6 0 12 0 8 0 6 0 24 0 24 0 0 0 12 0 30 0 24 0 24 0 8 0 24 0 48 0 0 0 6 0 60 &Gram (#11 <- H15) 2 0 8 0 0 8 0 3 2 10 0 -2 3 0 10 1 0 0 0 0 34 |Aut| = 2^4 #short vectors: 0 2 0 0 0 0 0 6 0 12 0 12 0 12 0 24 0 30 0 20 0 20 0 36 0 44 0 32 0 40 0 58 0 52 &Gram (#12 <- H16) 2 0 4 0 0 4 0 -1 2 18 0 2 -1 -1 18 1 0 0 0 0 34 |Aut| = 2^5 #short vectors: 0 2 0 4 0 8 0 6 0 8 0 8 0 0 0 12 0 18 0 32 0 40 0 16 0 48 0 56 0 24 0 46 0 56 &Gram (#13 <- H17) 2 0 6 0 0 6 0 1 2 12 0 -2 1 0 12 1 0 0 0 0 34 |Aut| = 2^4 #short vectors: 0 2 0 0 0 4 0 10 0 0 0 8 0 28 0 12 0 14 0 28 0 24 0 44 0 36 0 28 0 68 0 74 0 56