// Magma code for the lmfdb family of higher genus curves 3.48-48.0.2-4-6.2 // 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:=[48,48]; 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:=[0,2,4,6]; genus:=3; 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:=[[37, 39, 38, 40, 45, 47, 46, 48, 41, 43, 42, 44, 25, 27, 26, 28, 33, 35, 34, 36, 29, 31, 30, 32, 13, 15, 14, 16, 21, 23, 22, 24, 17, 19, 18, 20, 1, 3, 2, 4, 9, 11, 10, 12, 5, 7, 6, 8], [36, 33, 34, 35, 32, 29, 30, 31, 28, 25, 26, 27, 48, 45, 46, 47, 44, 41, 42, 43, 40, 37, 38, 39, 12, 9, 10, 11, 8, 5, 6, 7, 4, 1, 2, 3, 24, 21, 22, 23, 20, 17, 18, 19, 16, 13, 14, 15], [19, 18, 20, 17, 23, 22, 24, 21, 15, 14, 16, 13, 7, 6, 8, 5, 11, 10, 12, 9, 3, 2, 4, 1, 43, 42, 44, 41, 47, 46, 48, 45, 39, 38, 40, 37, 31, 30, 32, 29, 35, 34, 36, 33, 27, 26, 28, 25]]; cc:=[6,8,10]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=2; gen_vect_label:=1; braid_class:=1; topological_class:=[1, 1]; is_hyperelliptic:=true; hyp_involution:=S![13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36]; is_cyclic_trigonal:=false; Append(~data, rec);