// Magma code for the lmfdb family of higher genus curves 7.27-4.0.3-9-9 // The results are stored in a list of records called 'data' RecFormat:=recformat; data:=[]; // Create group as a permutation group, and generate data which is the same for all entries. gp_id:=[27,4]; H:=SmallGroup(gp_id[1],gp_id[2]); n:=#H; LP:=[]; LG:=[g : g in H]; for i in [1..n] do x:=LG[i]; Tx:=[LG[j]*x : j in [1..n]]; permL:=[]; for j in [1..n] do for k in [1..n] do if Tx[j] eq LG[k] then permL[j]:=k; break; end if; end for; end for; Append(~LP,permL); end for; G:=PermutationGroup; signature:=[0,3,9,9]; genus:=7; r:=#signature-1; g0:=signature[1]; dim:=3*g0-3+r; S:=Sym(gp_id[1]); // Here we add an action to data. gen_vectors:=[[4, 5, 6, 7, 8, 9, 1, 2, 3, 13, 14, 15, 16, 17, 18, 10, 11, 12, 22, 23, 24, 25, 26, 27, 19, 20, 21], [10, 11, 12, 14, 15, 13, 18, 16, 17, 19, 20, 21, 23, 24, 22, 27, 25, 26, 2, 3, 1, 6, 4, 5, 7, 8, 9], [27, 25, 26, 20, 21, 19, 22, 23, 24, 7, 8, 9, 3, 1, 2, 5, 6, 4, 16, 17, 18, 12, 10, 11, 14, 15, 13]]; cc:=[4,6,9]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=1; gen_vect_label:=1; braid_class:=1; topological_class:=[1, 1]; full_auto:=[54,6]; full_sign:=[0,2,6,9]; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[4, 5, 6, 7, 8, 9, 1, 2, 3, 13, 14, 15, 16, 17, 18, 10, 11, 12, 22, 23, 24, 25, 26, 27, 19, 20, 21], [19, 20, 21, 24, 22, 23, 26, 27, 25, 2, 3, 1, 4, 5, 6, 9, 7, 8, 11, 12, 10, 13, 14, 15, 18, 16, 17], [18, 16, 17, 10, 11, 12, 14, 15, 13, 27, 25, 26, 19, 20, 21, 23, 24, 22, 7, 8, 9, 2, 3, 1, 6, 4, 5]]; cc:=[4,7,10]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=2; gen_vect_label:=1; braid_class:=1; topological_class:=[1, 1]; full_auto:=[54,6]; full_sign:=[0,2,6,9]; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[4, 5, 6, 7, 8, 9, 1, 2, 3, 13, 14, 15, 16, 17, 18, 10, 11, 12, 22, 23, 24, 25, 26, 27, 19, 20, 21], [13, 14, 15, 17, 18, 16, 12, 10, 11, 22, 23, 24, 26, 27, 25, 21, 19, 20, 5, 6, 4, 9, 7, 8, 1, 2, 3], [22, 23, 24, 27, 25, 26, 20, 21, 19, 5, 6, 4, 7, 8, 9, 3, 1, 2, 14, 15, 13, 16, 17, 18, 12, 10, 11]]; cc:=[4,8,11]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=3; gen_vect_label:=1; braid_class:=1; topological_class:=[1, 1]; full_auto:=[54,6]; full_sign:=[0,2,6,9]; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[7, 8, 9, 1, 2, 3, 4, 5, 6, 16, 17, 18, 10, 11, 12, 13, 14, 15, 25, 26, 27, 19, 20, 21, 22, 23, 24], [10, 11, 12, 14, 15, 13, 18, 16, 17, 19, 20, 21, 23, 24, 22, 27, 25, 26, 2, 3, 1, 6, 4, 5, 7, 8, 9], [24, 22, 23, 26, 27, 25, 19, 20, 21, 4, 5, 6, 9, 7, 8, 2, 3, 1, 13, 14, 15, 18, 16, 17, 11, 12, 10]]; cc:=[5,6,11]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=4; gen_vect_label:=1; braid_class:=1; topological_class:=[4, 1]; full_auto:=[54,6]; full_sign:=[0,2,6,9]; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[7, 8, 9, 1, 2, 3, 4, 5, 6, 16, 17, 18, 10, 11, 12, 13, 14, 15, 25, 26, 27, 19, 20, 21, 22, 23, 24], [19, 20, 21, 24, 22, 23, 26, 27, 25, 2, 3, 1, 4, 5, 6, 9, 7, 8, 11, 12, 10, 13, 14, 15, 18, 16, 17], [15, 13, 14, 16, 17, 18, 11, 12, 10, 24, 22, 23, 25, 26, 27, 20, 21, 19, 4, 5, 6, 8, 9, 7, 3, 1, 2]]; cc:=[5,7,8]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=5; gen_vect_label:=1; braid_class:=1; topological_class:=[4, 1]; full_auto:=[54,6]; full_sign:=[0,2,6,9]; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[7, 8, 9, 1, 2, 3, 4, 5, 6, 16, 17, 18, 10, 11, 12, 13, 14, 15, 25, 26, 27, 19, 20, 21, 22, 23, 24], [26, 27, 25, 19, 20, 21, 24, 22, 23, 9, 7, 8, 2, 3, 1, 4, 5, 6, 18, 16, 17, 11, 12, 10, 13, 14, 15], [18, 16, 17, 10, 11, 12, 14, 15, 13, 27, 25, 26, 19, 20, 21, 23, 24, 22, 7, 8, 9, 2, 3, 1, 6, 4, 5]]; cc:=[5,9,10]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=6; gen_vect_label:=1; braid_class:=1; topological_class:=[4, 1]; full_auto:=[54,6]; full_sign:=[0,2,6,9]; Append(~data, rec);