// Magma code for the lmfdb family of higher genus curves 15.240-93.0.2-3-20.1
// 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:=[240,93];
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:=[0,2,3,20];
genus:=15;
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:=[[10, 13, 27, 88, 180, 55, 150, 214, 165, 1, 71, 173, 2, 110, 96, 76, 139, 114, 233, 92, 57, 200, 155, 87, 34, 37, 3, 64, 132, 79, 102, 238, 117, 25, 95, 125, 26, 158, 72, 52, 187, 162, 209, 68, 81, 224, 107, 63, 58, 61, 99, 40, 84, 127, 6, 190, 21, 49, 143, 77, 50, 206, 48, 28, 235, 210, 161, 44, 129, 176, 11, 39, 82, 85, 147, 16, 60, 175, 30, 142, 45, 73, 191, 53, 74, 230, 24, 4, 211, 234, 113, 20, 177, 128, 35, 15, 106, 109, 51, 136, 228, 31, 198, 166, 213, 97, 47, 221, 98, 14, 144, 124, 91, 18, 185, 140, 33, 152, 203, 135, 130, 133, 195, 112, 36, 223, 54, 94, 69, 121, 239, 29, 122, 182, 120, 100, 163, 186, 17, 116, 225, 80, 59, 111, 154, 157, 75, 184, 204, 7, 222, 118, 237, 145, 23, 197, 146, 38, 192, 172, 67, 42, 137, 188, 9, 104, 227, 183, 178, 181, 219, 160, 12, 199, 78, 70, 93, 169, 215, 5, 170, 134, 168, 148, 115, 138, 41, 164, 201, 56, 83, 159, 202, 205, 123, 232, 156, 103, 174, 22, 189, 193, 119, 149, 194, 62, 240, 220, 43, 66, 89, 236, 105, 8, 179, 231, 226, 229, 171, 208, 108, 151, 126, 46, 141, 217, 167, 101, 218, 86, 216, 196, 19, 90, 65, 212, 153, 32, 131, 207], [107, 124, 178, 44, 99, 233, 237, 132, 215, 125, 96, 138, 129, 211, 30, 206, 207, 56, 16, 194, 214, 31, 85, 217, 155, 172, 130, 20, 147, 209, 213, 180, 239, 173, 72, 186, 177, 235, 6, 230, 231, 80, 40, 218, 238, 7, 61, 193, 203, 220, 82, 116, 195, 161, 165, 228, 191, 221, 48, 234, 225, 187, 102, 182, 183, 128, 64, 170, 190, 103, 37, 145, 227, 196, 58, 164, 219, 113, 117, 204, 143, 197, 24, 210, 201, 139, 150, 134, 135, 176, 88, 122, 142, 151, 13, 97, 11, 76, 226, 68, 3, 185, 189, 84, 167, 77, 144, 90, 81, 163, 54, 158, 159, 32, 112, 146, 166, 55, 133, 169, 179, 148, 34, 212, 171, 17, 21, 156, 95, 149, 120, 162, 153, 91, 198, 86, 87, 224, 136, 74, 94, 199, 109, 1, 35, 52, 202, 92, 27, 137, 141, 60, 119, 53, 192, 66, 57, 115, 78, 110, 111, 8, 160, 98, 118, 79, 181, 121, 131, 100, 10, 236, 123, 41, 45, 108, 71, 101, 168, 114, 105, 67, 222, 62, 63, 200, 184, 50, 70, 223, 157, 25, 59, 28, 154, 140, 51, 89, 93, 36, 23, 29, 240, 42, 33, 19, 126, 14, 15, 104, 208, 2, 22, 127, 229, 73, 83, 4, 106, 188, 75, 65, 69, 12, 47, 5, 216, 18, 9, 43, 174, 38, 39, 152, 232, 26, 46, 175, 205, 49], [111, 236, 228, 229, 217, 72, 224, 42, 218, 219, 106, 46, 35, 220, 43, 233, 223, 101, 62, 64, 54, 105, 189, 191, 159, 212, 204, 205, 193, 96, 200, 18, 194, 195, 154, 22, 11, 196, 19, 209, 199, 149, 86, 88, 78, 153, 141, 143, 207, 164, 156, 157, 145, 144, 152, 114, 146, 147, 202, 118, 107, 148, 115, 161, 151, 197, 134, 136, 126, 201, 93, 95, 231, 116, 108, 109, 97, 192, 104, 162, 98, 99, 226, 166, 155, 100, 163, 113, 103, 221, 182, 184, 174, 225, 69, 71, 15, 188, 180, 181, 169, 48, 176, 66, 170, 171, 10, 70, 59, 172, 67, 185, 175, 5, 38, 40, 30, 9, 237, 239, 183, 20, 12, 13, 1, 240, 8, 210, 2, 3, 178, 214, 203, 4, 211, 17, 7, 173, 230, 232, 222, 177, 45, 47, 39, 140, 132, 133, 121, 24, 128, 90, 122, 123, 34, 94, 83, 124, 91, 137, 127, 29, 14, 16, 6, 33, 213, 215, 135, 44, 36, 37, 25, 216, 32, 234, 26, 27, 130, 238, 227, 28, 235, 41, 31, 125, 206, 208, 198, 129, 21, 23, 63, 92, 84, 85, 73, 120, 80, 138, 74, 75, 58, 142, 131, 76, 139, 89, 79, 53, 110, 112, 102, 57, 165, 167, 87, 68, 60, 61, 49, 168, 56, 186, 50, 51, 82, 190, 179, 52, 187, 65, 55, 77, 158, 160, 150, 81, 117, 119]];
cc:=[3,4,15];
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 >);
