// Magma code for the lmfdb family of higher genus curves 13.288-1024.0.2-3-12.1
// 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:=[288,1024];
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:=[0,2,3,12];
genus:=13;
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:=[[157, 159, 158, 160, 165, 167, 166, 168, 161, 163, 162, 164, 145, 147, 146, 148, 153, 155, 154, 156, 149, 151, 150, 152, 181, 183, 182, 184, 189, 191, 190, 192, 185, 187, 186, 188, 169, 171, 170, 172, 177, 179, 178, 180, 173, 175, 174, 176, 205, 207, 206, 208, 213, 215, 214, 216, 209, 211, 210, 212, 193, 195, 194, 196, 201, 203, 202, 204, 197, 199, 198, 200, 229, 231, 230, 232, 237, 239, 238, 240, 233, 235, 234, 236, 217, 219, 218, 220, 225, 227, 226, 228, 221, 223, 222, 224, 253, 255, 254, 256, 261, 263, 262, 264, 257, 259, 258, 260, 241, 243, 242, 244, 249, 251, 250, 252, 245, 247, 246, 248, 277, 279, 278, 280, 285, 287, 286, 288, 281, 283, 282, 284, 265, 267, 266, 268, 273, 275, 274, 276, 269, 271, 270, 272, 13, 15, 14, 16, 21, 23, 22, 24, 17, 19, 18, 20, 1, 3, 2, 4, 9, 11, 10, 12, 5, 7, 6, 8, 37, 39, 38, 40, 45, 47, 46, 48, 41, 43, 42, 44, 25, 27, 26, 28, 33, 35, 34, 36, 29, 31, 30, 32, 61, 63, 62, 64, 69, 71, 70, 72, 65, 67, 66, 68, 49, 51, 50, 52, 57, 59, 58, 60, 53, 55, 54, 56, 85, 87, 86, 88, 93, 95, 94, 96, 89, 91, 90, 92, 73, 75, 74, 76, 81, 83, 82, 84, 77, 79, 78, 80, 109, 111, 110, 112, 117, 119, 118, 120, 113, 115, 114, 116, 97, 99, 98, 100, 105, 107, 106, 108, 101, 103, 102, 104, 133, 135, 134, 136, 141, 143, 142, 144, 137, 139, 138, 140, 121, 123, 122, 124, 129, 131, 130, 132, 125, 127, 126, 128], [55, 54, 56, 53, 59, 58, 60, 57, 51, 50, 52, 49, 79, 78, 80, 77, 83, 82, 84, 81, 75, 74, 76, 73, 91, 90, 92, 89, 95, 94, 96, 93, 87, 86, 88, 85, 67, 66, 68, 65, 71, 70, 72, 69, 63, 62, 64, 61, 103, 102, 104, 101, 107, 106, 108, 105, 99, 98, 100, 97, 127, 126, 128, 125, 131, 130, 132, 129, 123, 122, 124, 121, 139, 138, 140, 137, 143, 142, 144, 141, 135, 134, 136, 133, 115, 114, 116, 113, 119, 118, 120, 117, 111, 110, 112, 109, 7, 6, 8, 5, 11, 10, 12, 9, 3, 2, 4, 1, 31, 30, 32, 29, 35, 34, 36, 33, 27, 26, 28, 25, 43, 42, 44, 41, 47, 46, 48, 45, 39, 38, 40, 37, 19, 18, 20, 17, 23, 22, 24, 21, 15, 14, 16, 13, 199, 198, 200, 197, 203, 202, 204, 201, 195, 194, 196, 193, 223, 222, 224, 221, 227, 226, 228, 225, 219, 218, 220, 217, 235, 234, 236, 233, 239, 238, 240, 237, 231, 230, 232, 229, 211, 210, 212, 209, 215, 214, 216, 213, 207, 206, 208, 205, 247, 246, 248, 245, 251, 250, 252, 249, 243, 242, 244, 241, 271, 270, 272, 269, 275, 274, 276, 273, 267, 266, 268, 265, 283, 282, 284, 281, 287, 286, 288, 285, 279, 278, 280, 277, 259, 258, 260, 257, 263, 262, 264, 261, 255, 254, 256, 253, 151, 150, 152, 149, 155, 154, 156, 153, 147, 146, 148, 145, 175, 174, 176, 173, 179, 178, 180, 177, 171, 170, 172, 169, 187, 186, 188, 185, 191, 190, 192, 189, 183, 182, 184, 181, 163, 162, 164, 161, 167, 166, 168, 165, 159, 158, 160, 157], [260, 259, 257, 258, 256, 255, 253, 254, 264, 263, 261, 262, 272, 271, 269, 270, 268, 267, 265, 266, 276, 275, 273, 274, 248, 247, 245, 246, 244, 243, 241, 242, 252, 251, 249, 250, 284, 283, 281, 282, 280, 279, 277, 278, 288, 287, 285, 286, 164, 163, 161, 162, 160, 159, 157, 158, 168, 167, 165, 166, 176, 175, 173, 174, 172, 171, 169, 170, 180, 179, 177, 178, 152, 151, 149, 150, 148, 147, 145, 146, 156, 155, 153, 154, 188, 187, 185, 186, 184, 183, 181, 182, 192, 191, 189, 190, 212, 211, 209, 210, 208, 207, 205, 206, 216, 215, 213, 214, 224, 223, 221, 222, 220, 219, 217, 218, 228, 227, 225, 226, 200, 199, 197, 198, 196, 195, 193, 194, 204, 203, 201, 202, 236, 235, 233, 234, 232, 231, 229, 230, 240, 239, 237, 238, 116, 115, 113, 114, 112, 111, 109, 110, 120, 119, 117, 118, 128, 127, 125, 126, 124, 123, 121, 122, 132, 131, 129, 130, 104, 103, 101, 102, 100, 99, 97, 98, 108, 107, 105, 106, 140, 139, 137, 138, 136, 135, 133, 134, 144, 143, 141, 142, 20, 19, 17, 18, 16, 15, 13, 14, 24, 23, 21, 22, 32, 31, 29, 30, 28, 27, 25, 26, 36, 35, 33, 34, 8, 7, 5, 6, 4, 3, 1, 2, 12, 11, 9, 10, 44, 43, 41, 42, 40, 39, 37, 38, 48, 47, 45, 46, 68, 67, 65, 66, 64, 63, 61, 62, 72, 71, 69, 70, 80, 79, 77, 78, 76, 75, 73, 74, 84, 83, 81, 82, 56, 55, 53, 54, 52, 51, 49, 50, 60, 59, 57, 58, 92, 91, 89, 90, 88, 87, 85, 86, 96, 95, 93, 94]];
cc:=[6,10,20];
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 >);
