// Magma code for the lmfdb family of higher genus curves 4.32-19.0.2-4-16 // 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:=[32,19]; 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:=[0,2,4,16]; genus:=4; 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, 1, 2, 4, 3, 7, 8, 5, 6, 25, 26, 28, 27, 31, 32, 29, 30, 17, 18, 20, 19, 23, 24, 21, 22], [18, 17, 19, 20, 24, 23, 22, 21, 30, 29, 31, 32, 26, 25, 27, 28, 1, 2, 4, 3, 7, 8, 5, 6, 13, 14, 16, 15, 9, 10, 12, 11], [25, 26, 27, 28, 29, 30, 31, 32, 23, 24, 22, 21, 17, 18, 19, 20, 10, 9, 12, 11, 14, 13, 16, 15, 8, 7, 5, 6, 2, 1, 4, 3]]; cc:=[3,5,8]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=1; gen_vect_label:=1; braid_class:=1; topological_class:=[1, 1]; is_hyperelliptic:=true; hyp_involution:=S![2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19, 22, 21, 24, 23, 26, 25, 28, 27, 30, 29, 32, 31]; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[9, 10, 12, 11, 15, 16, 13, 14, 1, 2, 4, 3, 7, 8, 5, 6, 25, 26, 28, 27, 31, 32, 29, 30, 17, 18, 20, 19, 23, 24, 21, 22], [19, 20, 17, 18, 22, 21, 23, 24, 31, 32, 29, 30, 27, 28, 25, 26, 4, 3, 2, 1, 5, 6, 8, 7, 16, 15, 14, 13, 12, 11, 10, 9], [27, 28, 26, 25, 31, 32, 30, 29, 22, 21, 24, 23, 19, 20, 18, 17, 12, 11, 9, 10, 16, 15, 13, 14, 5, 6, 7, 8, 4, 3, 1, 2]]; cc:=[3,5,9]; 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![2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19, 22, 21, 24, 23, 26, 25, 28, 27, 30, 29, 32, 31]; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[9, 10, 12, 11, 15, 16, 13, 14, 1, 2, 4, 3, 7, 8, 5, 6, 25, 26, 28, 27, 31, 32, 29, 30, 17, 18, 20, 19, 23, 24, 21, 22], [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], [26, 25, 28, 27, 30, 29, 32, 31, 24, 23, 21, 22, 18, 17, 20, 19, 9, 10, 11, 12, 13, 14, 15, 16, 7, 8, 6, 5, 1, 2, 3, 4]]; cc:=[3,5,10]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=3; gen_vect_label:=1; braid_class:=1; topological_class:=[1, 1]; is_hyperelliptic:=true; hyp_involution:=S![2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19, 22, 21, 24, 23, 26, 25, 28, 27, 30, 29, 32, 31]; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[9, 10, 12, 11, 15, 16, 13, 14, 1, 2, 4, 3, 7, 8, 5, 6, 25, 26, 28, 27, 31, 32, 29, 30, 17, 18, 20, 19, 23, 24, 21, 22], [20, 19, 18, 17, 21, 22, 24, 23, 32, 31, 30, 29, 28, 27, 26, 25, 3, 4, 1, 2, 6, 5, 7, 8, 15, 16, 13, 14, 11, 12, 9, 10], [28, 27, 25, 26, 32, 31, 29, 30, 21, 22, 23, 24, 20, 19, 17, 18, 11, 12, 10, 9, 15, 16, 14, 13, 6, 5, 8, 7, 3, 4, 2, 1]]; cc:=[3,5,11]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=4; gen_vect_label:=1; braid_class:=1; topological_class:=[1, 1]; is_hyperelliptic:=true; hyp_involution:=S![2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19, 22, 21, 24, 23, 26, 25, 28, 27, 30, 29, 32, 31]; is_cyclic_trigonal:=false; Append(~data, rec);