// Magma code for the lmfdb family of higher genus curves 14.40-1.0.8-8-10 // 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:=[40,1]; 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:=[0,8,8,10]; genus:=14; 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:=[[21, 25, 24, 23, 22, 26, 30, 29, 28, 27, 31, 35, 34, 33, 32, 36, 40, 39, 38, 37, 11, 15, 14, 13, 12, 16, 20, 19, 18, 17, 6, 10, 9, 8, 7, 1, 5, 4, 3, 2], [35, 34, 33, 32, 31, 40, 39, 38, 37, 36, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11], [7, 8, 9, 10, 6, 2, 3, 4, 5, 1, 17, 18, 19, 20, 16, 12, 13, 14, 15, 11, 27, 28, 29, 30, 26, 22, 23, 24, 25, 21, 37, 38, 39, 40, 36, 32, 33, 34, 35, 31]]; cc:=[7,8,11]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=1; gen_vect_label:=1; full_auto:=[80,17]; full_sign:=[0,2,8,20]; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[21, 25, 24, 23, 22, 26, 30, 29, 28, 27, 31, 35, 34, 33, 32, 36, 40, 39, 38, 37, 11, 15, 14, 13, 12, 16, 20, 19, 18, 17, 6, 10, 9, 8, 7, 1, 5, 4, 3, 2], [33, 32, 31, 35, 34, 38, 37, 36, 40, 39, 28, 27, 26, 30, 29, 23, 22, 21, 25, 24, 8, 7, 6, 10, 9, 3, 2, 1, 5, 4, 18, 17, 16, 20, 19, 13, 12, 11, 15, 14], [9, 10, 6, 7, 8, 4, 5, 1, 2, 3, 19, 20, 16, 17, 18, 14, 15, 11, 12, 13, 29, 30, 26, 27, 28, 24, 25, 21, 22, 23, 39, 40, 36, 37, 38, 34, 35, 31, 32, 33]]; cc:=[7,8,12]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=2; gen_vect_label:=1; full_auto:=[80,17]; full_sign:=[0,2,8,20]; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[26, 30, 29, 28, 27, 21, 25, 24, 23, 22, 36, 40, 39, 38, 37, 31, 35, 34, 33, 32, 16, 20, 19, 18, 17, 11, 15, 14, 13, 12, 1, 5, 4, 3, 2, 6, 10, 9, 8, 7], [40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 25, 24, 23, 22, 21, 30, 29, 28, 27, 26, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 15, 14, 13, 12, 11, 20, 19, 18, 17, 16], [7, 8, 9, 10, 6, 2, 3, 4, 5, 1, 17, 18, 19, 20, 16, 12, 13, 14, 15, 11, 27, 28, 29, 30, 26, 22, 23, 24, 25, 21, 37, 38, 39, 40, 36, 32, 33, 34, 35, 31]]; cc:=[9,10,11]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=3; gen_vect_label:=1; full_auto:=[80,17]; full_sign:=[0,2,8,20]; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[26, 30, 29, 28, 27, 21, 25, 24, 23, 22, 36, 40, 39, 38, 37, 31, 35, 34, 33, 32, 16, 20, 19, 18, 17, 11, 15, 14, 13, 12, 1, 5, 4, 3, 2, 6, 10, 9, 8, 7], [38, 37, 36, 40, 39, 33, 32, 31, 35, 34, 23, 22, 21, 25, 24, 28, 27, 26, 30, 29, 3, 2, 1, 5, 4, 8, 7, 6, 10, 9, 13, 12, 11, 15, 14, 18, 17, 16, 20, 19], [9, 10, 6, 7, 8, 4, 5, 1, 2, 3, 19, 20, 16, 17, 18, 14, 15, 11, 12, 13, 29, 30, 26, 27, 28, 24, 25, 21, 22, 23, 39, 40, 36, 37, 38, 34, 35, 31, 32, 33]]; cc:=[9,10,12]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=4; gen_vect_label:=1; full_auto:=[80,17]; full_sign:=[0,2,8,20]; Append(~data, rec);