// Magma code for the lmfdb family of higher genus curves 3.16-2.0.4-4-4.1 // 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:=[16,2]; 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:=[0,4,4,4]; genus:=3; 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, 7, 8, 2, 1, 4, 3, 13, 14, 15, 16, 10, 9, 12, 11], [9, 10, 11, 12, 13, 14, 15, 16, 3, 4, 1, 2, 7, 8, 5, 6], [16, 15, 14, 13, 11, 12, 9, 10, 6, 5, 8, 7, 1, 2, 3, 4]]; cc:=[5,9,14]; 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:=[96,64]; full_sign:=[0,2,3,8]; Append(~data, rec);