// Magma code for the lmfdb family of higher genus curves 14.40-11.0.4-20-20.2 // 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:=[40,11]; 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:=[0,4,20,20]; 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:=[[11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 22, 21, 24, 23, 26, 25, 28, 27, 30, 29], [28, 27, 30, 29, 22, 21, 24, 23, 26, 25, 37, 38, 39, 40, 31, 32, 33, 34, 35, 36, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 18, 17, 20, 19, 12, 11, 14, 13, 16, 15], [36, 35, 38, 37, 40, 39, 32, 31, 34, 33, 26, 25, 28, 27, 30, 29, 22, 21, 24, 23, 15, 16, 17, 18, 19, 20, 11, 12, 13, 14, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4]]; cc:=[3,19,24]; 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);