// Magma code for the lmfdb family of higher genus curves 13.96-3.0.3-4-6.1 // 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:=[96,3]; 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:=[0,3,4,6]; 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:=[[33, 34, 40, 39, 36, 35, 37, 38, 59, 60, 62, 61, 58, 57, 63, 64, 41, 42, 48, 47, 44, 43, 45, 46, 56, 55, 49, 50, 53, 54, 52, 51, 65, 66, 72, 71, 68, 67, 69, 70, 91, 92, 94, 93, 90, 89, 95, 96, 73, 74, 80, 79, 76, 75, 77, 78, 88, 87, 81, 82, 85, 86, 84, 83, 1, 2, 8, 7, 4, 3, 5, 6, 27, 28, 30, 29, 26, 25, 31, 32, 9, 10, 16, 15, 12, 11, 13, 14, 24, 23, 17, 18, 21, 22, 20, 19], [10, 9, 12, 11, 14, 13, 16, 15, 6, 5, 8, 7, 2, 1, 4, 3, 26, 25, 28, 27, 30, 29, 32, 31, 22, 21, 24, 23, 18, 17, 20, 19, 42, 41, 44, 43, 46, 45, 48, 47, 38, 37, 40, 39, 34, 33, 36, 35, 58, 57, 60, 59, 62, 61, 64, 63, 54, 53, 56, 55, 50, 49, 52, 51, 74, 73, 76, 75, 78, 77, 80, 79, 70, 69, 72, 71, 66, 65, 68, 67, 90, 89, 92, 91, 94, 93, 96, 95, 86, 85, 88, 87, 82, 81, 84, 83], [88, 87, 83, 84, 82, 81, 85, 86, 66, 65, 69, 70, 72, 71, 67, 68, 75, 76, 80, 79, 77, 78, 74, 73, 92, 91, 95, 96, 94, 93, 89, 90, 24, 23, 19, 20, 18, 17, 21, 22, 2, 1, 5, 6, 8, 7, 3, 4, 11, 12, 16, 15, 13, 14, 10, 9, 28, 27, 31, 32, 30, 29, 25, 26, 56, 55, 51, 52, 50, 49, 53, 54, 34, 33, 37, 38, 40, 39, 35, 36, 43, 44, 48, 47, 45, 46, 42, 41, 60, 59, 63, 64, 62, 61, 57, 58]]; cc:=[5,7,12]; 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);