// Magma code for the lmfdb family of higher genus curves 4.18-3.0.3-6-6.2 // 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:=[18,3]; 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:=[0,3,6,6]; genus:=4; 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:=[[5, 6, 4, 8, 9, 7, 2, 3, 1, 14, 15, 13, 17, 18, 16, 11, 12, 10], [13, 15, 14, 16, 18, 17, 10, 12, 11, 4, 6, 5, 7, 9, 8, 1, 3, 2], [15, 14, 13, 18, 17, 16, 12, 11, 10, 6, 5, 4, 9, 8, 7, 3, 2, 1]]; cc:=[6,8,8]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=2; gen_vect_label:=1; braid_class:=1; topological_class:=[2, 1]; full_auto:=[36,12]; full_sign:=[0,2,6,6]; Append(~data, rec);