// Magma code for the lmfdb family of higher genus curves 13.360-121.0.2-3-10.1
// 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:=[360,121];
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:=[0,2,3,10];
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:=[[6, 59, 7, 12, 113, 1, 3, 200, 13, 30, 176, 4, 9, 77, 25, 21, 44, 22, 27, 98, 16, 18, 185, 28, 15, 161, 19, 24, 62, 10, 36, 89, 37, 42, 173, 31, 33, 290, 43, 60, 266, 34, 39, 17, 55, 51, 74, 52, 57, 158, 46, 48, 275, 58, 45, 251, 49, 54, 2, 40, 66, 29, 67, 72, 263, 61, 63, 350, 73, 90, 116, 64, 69, 47, 85, 81, 14, 82, 87, 248, 76, 78, 335, 88, 75, 101, 79, 84, 32, 70, 96, 359, 97, 102, 203, 91, 93, 20, 103, 120, 86, 94, 99, 227, 115, 111, 344, 112, 117, 188, 106, 108, 5, 118, 105, 71, 109, 114, 212, 100, 126, 179, 127, 132, 233, 121, 123, 320, 133, 150, 296, 124, 129, 197, 145, 141, 164, 142, 147, 218, 136, 138, 305, 148, 135, 281, 139, 144, 182, 130, 156, 209, 157, 162, 293, 151, 153, 50, 163, 180, 26, 154, 159, 137, 175, 171, 194, 172, 177, 278, 166, 168, 35, 178, 165, 11, 169, 174, 122, 160, 186, 149, 187, 192, 23, 181, 183, 110, 193, 210, 236, 184, 189, 167, 205, 201, 134, 202, 207, 8, 196, 198, 95, 208, 195, 221, 199, 204, 152, 190, 216, 119, 217, 222, 323, 211, 213, 140, 223, 240, 206, 214, 219, 347, 235, 231, 104, 232, 237, 308, 226, 228, 125, 238, 225, 191, 229, 234, 332, 220, 246, 299, 247, 252, 353, 241, 243, 80, 253, 270, 56, 244, 249, 317, 265, 261, 284, 262, 267, 338, 256, 258, 65, 268, 255, 41, 259, 264, 302, 250, 276, 329, 277, 282, 53, 271, 273, 170, 283, 300, 146, 274, 279, 257, 295, 291, 314, 292, 297, 38, 286, 288, 155, 298, 285, 131, 289, 294, 242, 280, 306, 269, 307, 312, 143, 301, 303, 230, 313, 330, 356, 304, 309, 287, 325, 321, 254, 322, 327, 128, 316, 318, 215, 328, 315, 341, 319, 324, 272, 310, 336, 239, 337, 342, 83, 331, 333, 260, 343, 360, 326, 334, 339, 107, 355, 351, 224, 352, 357, 68, 346, 348, 245, 358, 345, 311, 349, 354, 92, 340], [2, 3, 1, 5, 6, 4, 8, 9, 7, 11, 12, 10, 14, 15, 13, 17, 18, 16, 20, 21, 19, 23, 24, 22, 26, 27, 25, 29, 30, 28, 32, 33, 31, 35, 36, 34, 38, 39, 37, 41, 42, 40, 44, 45, 43, 47, 48, 46, 50, 51, 49, 53, 54, 52, 56, 57, 55, 59, 60, 58, 62, 63, 61, 65, 66, 64, 68, 69, 67, 71, 72, 70, 74, 75, 73, 77, 78, 76, 80, 81, 79, 83, 84, 82, 86, 87, 85, 89, 90, 88, 92, 93, 91, 95, 96, 94, 98, 99, 97, 101, 102, 100, 104, 105, 103, 107, 108, 106, 110, 111, 109, 113, 114, 112, 116, 117, 115, 119, 120, 118, 122, 123, 121, 125, 126, 124, 128, 129, 127, 131, 132, 130, 134, 135, 133, 137, 138, 136, 140, 141, 139, 143, 144, 142, 146, 147, 145, 149, 150, 148, 152, 153, 151, 155, 156, 154, 158, 159, 157, 161, 162, 160, 164, 165, 163, 167, 168, 166, 170, 171, 169, 173, 174, 172, 176, 177, 175, 179, 180, 178, 182, 183, 181, 185, 186, 184, 188, 189, 187, 191, 192, 190, 194, 195, 193, 197, 198, 196, 200, 201, 199, 203, 204, 202, 206, 207, 205, 209, 210, 208, 212, 213, 211, 215, 216, 214, 218, 219, 217, 221, 222, 220, 224, 225, 223, 227, 228, 226, 230, 231, 229, 233, 234, 232, 236, 237, 235, 239, 240, 238, 242, 243, 241, 245, 246, 244, 248, 249, 247, 251, 252, 250, 254, 255, 253, 257, 258, 256, 260, 261, 259, 263, 264, 262, 266, 267, 265, 269, 270, 268, 272, 273, 271, 275, 276, 274, 278, 279, 277, 281, 282, 280, 284, 285, 283, 287, 288, 286, 290, 291, 289, 293, 294, 292, 296, 297, 295, 299, 300, 298, 302, 303, 301, 305, 306, 304, 308, 309, 307, 311, 312, 310, 314, 315, 313, 317, 318, 316, 320, 321, 319, 323, 324, 322, 326, 327, 325, 329, 330, 328, 332, 333, 331, 335, 336, 334, 338, 339, 337, 341, 342, 340, 344, 345, 343, 347, 348, 346, 350, 351, 349, 353, 354, 352, 356, 357, 355, 359, 360, 358], [7, 6, 59, 1, 12, 113, 13, 3, 200, 4, 30, 176, 25, 9, 77, 22, 21, 44, 16, 27, 98, 28, 18, 185, 19, 15, 161, 10, 24, 62, 37, 36, 89, 31, 42, 173, 43, 33, 290, 34, 60, 266, 55, 39, 17, 52, 51, 74, 46, 57, 158, 58, 48, 275, 49, 45, 251, 40, 54, 2, 67, 66, 29, 61, 72, 263, 73, 63, 350, 64, 90, 116, 85, 69, 47, 82, 81, 14, 76, 87, 248, 88, 78, 335, 79, 75, 101, 70, 84, 32, 97, 96, 359, 91, 102, 203, 103, 93, 20, 94, 120, 86, 115, 99, 227, 112, 111, 344, 106, 117, 188, 118, 108, 5, 109, 105, 71, 100, 114, 212, 127, 126, 179, 121, 132, 233, 133, 123, 320, 124, 150, 296, 145, 129, 197, 142, 141, 164, 136, 147, 218, 148, 138, 305, 139, 135, 281, 130, 144, 182, 157, 156, 209, 151, 162, 293, 163, 153, 50, 154, 180, 26, 175, 159, 137, 172, 171, 194, 166, 177, 278, 178, 168, 35, 169, 165, 11, 160, 174, 122, 187, 186, 149, 181, 192, 23, 193, 183, 110, 184, 210, 236, 205, 189, 167, 202, 201, 134, 196, 207, 8, 208, 198, 95, 199, 195, 221, 190, 204, 152, 217, 216, 119, 211, 222, 323, 223, 213, 140, 214, 240, 206, 235, 219, 347, 232, 231, 104, 226, 237, 308, 238, 228, 125, 229, 225, 191, 220, 234, 332, 247, 246, 299, 241, 252, 353, 253, 243, 80, 244, 270, 56, 265, 249, 317, 262, 261, 284, 256, 267, 338, 268, 258, 65, 259, 255, 41, 250, 264, 302, 277, 276, 329, 271, 282, 53, 283, 273, 170, 274, 300, 146, 295, 279, 257, 292, 291, 314, 286, 297, 38, 298, 288, 155, 289, 285, 131, 280, 294, 242, 307, 306, 269, 301, 312, 143, 313, 303, 230, 304, 330, 356, 325, 309, 287, 322, 321, 254, 316, 327, 128, 328, 318, 215, 319, 315, 341, 310, 324, 272, 337, 336, 239, 331, 342, 83, 343, 333, 260, 334, 360, 326, 355, 339, 107, 352, 351, 224, 346, 357, 68, 358, 348, 245, 349, 345, 311, 340, 354, 92]];
cc:=[4,7,12];
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 >);
