// Magma code for the lmfdb family of higher genus curves 8.32-20.0.4-4-16.1 // 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:=[32,20]; 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:=[0,4,4,16]; genus:=8; 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:=[[9, 10, 12, 11, 15, 16, 13, 14, 2, 1, 3, 4, 8, 7, 6, 5, 25, 26, 28, 27, 31, 32, 29, 30, 18, 17, 19, 20, 24, 23, 22, 21], [17, 18, 20, 19, 23, 24, 21, 22, 29, 30, 32, 31, 25, 26, 28, 27, 2, 1, 3, 4, 8, 7, 6, 5, 14, 13, 15, 16, 10, 9, 11, 12], [25, 26, 27, 28, 29, 30, 31, 32, 24, 23, 21, 22, 18, 17, 20, 19, 10, 9, 12, 11, 14, 13, 16, 15, 7, 8, 6, 5, 1, 2, 3, 4]]; cc:=[4,5,8]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=1; gen_vect_label:=1; full_auto:=[64,53]; full_sign:=[0,2,4,32]; Append(~data, rec);