// Magma code for the lmfdb family of higher genus curves 4.15-1.0.3-5-15.5 // 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:=[15,1]; 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:=[0,3,5,15]; 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:=[[11, 12, 13, 14, 15, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [2, 3, 4, 5, 1, 7, 8, 9, 10, 6, 12, 13, 14, 15, 11], [10, 6, 7, 8, 9, 15, 11, 12, 13, 14, 5, 1, 2, 3, 4]]; cc:=[3,4,10]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=5; gen_vect_label:=1; braid_class:=1; topological_class:=[1, 1]; is_hyperelliptic:=false; is_cyclic_trigonal:=true; cyc_auto:=S![6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 1, 2, 3, 4, 5]; Append(~data, rec);