// Magma code for the lmfdb family of higher genus curves 10.216-158.0.2-4-6.1
// The results are stored in a list of records called 'data'

RecFormat:=recformat<group,gp_id, signature,gen_vectors,conj_classes,genus,dimension,r,g0, passport_label,gen_vect_label, is_hyperelliptic, hyp_involution, is_cyclic_trigonal,cyc_auto,full_auto, full_sign,topological_class,braid_class>;

data:=[];

// Create group as a permutation group, and generate data which is the same for all entries.
gp_id:=[216,158];
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<n|LP>; 
signature:=[0,2,4,6];
genus:=10;
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:=[[109, 111, 110, 118, 120, 119, 127, 129, 128, 112, 114, 113, 121, 123, 122, 130, 132, 131, 115, 117, 116, 124, 126, 125, 133, 135, 134, 136, 138, 137, 145, 147, 146, 154, 156, 155, 139, 141, 140, 148, 150, 149, 157, 159, 158, 142, 144, 143, 151, 153, 152, 160, 162, 161, 190, 192, 191, 199, 201, 200, 208, 210, 209, 193, 195, 194, 202, 204, 203, 211, 213, 212, 196, 198, 197, 205, 207, 206, 214, 216, 215, 163, 165, 164, 172, 174, 173, 181, 183, 182, 166, 168, 167, 175, 177, 176, 184, 186, 185, 169, 171, 170, 178, 180, 179, 187, 189, 188, 1, 3, 2, 10, 12, 11, 19, 21, 20, 4, 6, 5, 13, 15, 14, 22, 24, 23, 7, 9, 8, 16, 18, 17, 25, 27, 26, 28, 30, 29, 37, 39, 38, 46, 48, 47, 31, 33, 32, 40, 42, 41, 49, 51, 50, 34, 36, 35, 43, 45, 44, 52, 54, 53, 82, 84, 83, 91, 93, 92, 100, 102, 101, 85, 87, 86, 94, 96, 95, 103, 105, 104, 88, 90, 89, 97, 99, 98, 106, 108, 107, 55, 57, 56, 64, 66, 65, 73, 75, 74, 58, 60, 59, 67, 69, 68, 76, 78, 77, 61, 63, 62, 70, 72, 71, 79, 81, 80], [189, 188, 187, 180, 179, 178, 171, 170, 169, 183, 182, 181, 174, 173, 172, 165, 164, 163, 186, 185, 184, 177, 176, 175, 168, 167, 166, 216, 215, 214, 207, 206, 205, 198, 197, 196, 210, 209, 208, 201, 200, 199, 192, 191, 190, 213, 212, 211, 204, 203, 202, 195, 194, 193, 162, 161, 160, 153, 152, 151, 144, 143, 142, 156, 155, 154, 147, 146, 145, 138, 137, 136, 159, 158, 157, 150, 149, 148, 141, 140, 139, 135, 134, 133, 126, 125, 124, 117, 116, 115, 129, 128, 127, 120, 119, 118, 111, 110, 109, 132, 131, 130, 123, 122, 121, 114, 113, 112, 81, 80, 79, 72, 71, 70, 63, 62, 61, 75, 74, 73, 66, 65, 64, 57, 56, 55, 78, 77, 76, 69, 68, 67, 60, 59, 58, 108, 107, 106, 99, 98, 97, 90, 89, 88, 102, 101, 100, 93, 92, 91, 84, 83, 82, 105, 104, 103, 96, 95, 94, 87, 86, 85, 54, 53, 52, 45, 44, 43, 36, 35, 34, 48, 47, 46, 39, 38, 37, 30, 29, 28, 51, 50, 49, 42, 41, 40, 33, 32, 31, 27, 26, 25, 18, 17, 16, 9, 8, 7, 21, 20, 19, 12, 11, 10, 3, 2, 1, 24, 23, 22, 15, 14, 13, 6, 5, 4], [77, 78, 76, 80, 81, 79, 74, 75, 73, 68, 69, 67, 71, 72, 70, 65, 66, 64, 59, 60, 58, 62, 63, 61, 56, 57, 55, 104, 105, 103, 107, 108, 106, 101, 102, 100, 95, 96, 94, 98, 99, 97, 92, 93, 91, 86, 87, 85, 89, 90, 88, 83, 84, 82, 23, 24, 22, 26, 27, 25, 20, 21, 19, 14, 15, 13, 17, 18, 16, 11, 12, 10, 5, 6, 4, 8, 9, 7, 2, 3, 1, 50, 51, 49, 53, 54, 52, 47, 48, 46, 41, 42, 40, 44, 45, 43, 38, 39, 37, 32, 33, 31, 35, 36, 34, 29, 30, 28, 185, 186, 184, 188, 189, 187, 182, 183, 181, 176, 177, 175, 179, 180, 178, 173, 174, 172, 167, 168, 166, 170, 171, 169, 164, 165, 163, 212, 213, 211, 215, 216, 214, 209, 210, 208, 203, 204, 202, 206, 207, 205, 200, 201, 199, 194, 195, 193, 197, 198, 196, 191, 192, 190, 131, 132, 130, 134, 135, 133, 128, 129, 127, 122, 123, 121, 125, 126, 124, 119, 120, 118, 113, 114, 112, 116, 117, 115, 110, 111, 109, 158, 159, 157, 161, 162, 160, 155, 156, 154, 149, 150, 148, 152, 153, 151, 146, 147, 145, 140, 141, 139, 143, 144, 142, 137, 138, 136]];
cc:=[4,11,15];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
Append(~data, rec<RecFormat | group:=G, gp_id:=gp_id, signature:=signature, gen_vectors:=gen_vectors_as_perm, conj_classes:=cc, genus:=genus, dimension:=dim, r:=r, g0:=g0, passport_label:= passport_label,gen_vect_label:=gen_vect_label, braid_class:=braid_class, topological_class:=topological_class, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);
