// Magma code for the lmfdb family of higher genus curves 13.36-2.0.4-18-36.1 // 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:=[36,2]; 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:=[0,4,18,36]; genus:=13; 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:=[[19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 4, 5, 6, 1, 2, 3, 10, 11, 12, 7, 8, 9, 16, 17, 18, 13, 14, 15], [10, 11, 12, 7, 8, 9, 16, 17, 18, 13, 14, 15, 5, 6, 4, 2, 3, 1, 28, 29, 30, 25, 26, 27, 34, 35, 36, 31, 32, 33, 23, 24, 22, 20, 21, 19], [33, 31, 32, 36, 34, 35, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 18, 16, 17, 15, 13, 14, 4, 5, 6, 1, 2, 3, 10, 11, 12, 7, 8, 9]]; cc:=[5,19,30]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=1; gen_vect_label:=1; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Append(~data, rec);