// Magma code for the lmfdb family of higher genus curves 13.72-47.0.3-6-6.1 // 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:=[72,47]; 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:=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:=[[13, 16, 14, 15, 17, 20, 18, 19, 21, 24, 22, 23, 25, 28, 26, 27, 29, 32, 30, 31, 33, 36, 34, 35, 1, 4, 2, 3, 5, 8, 6, 7, 9, 12, 10, 11, 49, 52, 50, 51, 53, 56, 54, 55, 57, 60, 58, 59, 61, 64, 62, 63, 65, 68, 66, 67, 69, 72, 70, 71, 37, 40, 38, 39, 41, 44, 42, 43, 45, 48, 46, 47], [42, 41, 44, 43, 46, 45, 48, 47, 38, 37, 40, 39, 54, 53, 56, 55, 58, 57, 60, 59, 50, 49, 52, 51, 66, 65, 68, 67, 70, 69, 72, 71, 62, 61, 64, 63, 6, 5, 8, 7, 10, 9, 12, 11, 2, 1, 4, 3, 18, 17, 20, 19, 22, 21, 24, 23, 14, 13, 16, 15, 30, 29, 32, 31, 34, 33, 36, 35, 26, 25, 28, 27], [71, 69, 70, 72, 63, 61, 62, 64, 67, 65, 66, 68, 47, 45, 46, 48, 39, 37, 38, 40, 43, 41, 42, 44, 59, 57, 58, 60, 51, 49, 50, 52, 55, 53, 54, 56, 35, 33, 34, 36, 27, 25, 26, 28, 31, 29, 30, 32, 11, 9, 10, 12, 3, 1, 2, 4, 7, 5, 6, 8, 23, 21, 22, 24, 15, 13, 14, 16, 19, 17, 18, 20]]; cc:=[7,17,22]; 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);