// Magma code for the lmfdb family of higher genus curves 15.504-156.0.2-3-9.1
// 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:=[504,156];
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:=[0,2,3,9];
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:=[[33, 263, 139, 165, 493, 37, 257, 153, 368, 51, 380, 301, 228, 160, 19, 374, 252, 143, 15, 155, 364, 462, 115, 55, 194, 486, 278, 60, 209, 94, 417, 268, 1, 68, 405, 305, 6, 488, 274, 120, 295, 46, 455, 135, 179, 42, 290, 472, 354, 385, 10, 320, 288, 98, 24, 110, 175, 327, 214, 28, 77, 315, 476, 429, 389, 265, 435, 34, 208, 419, 450, 341, 105, 335, 211, 237, 61, 109, 329, 225, 440, 123, 452, 373, 300, 232, 91, 446, 324, 215, 87, 227, 436, 30, 187, 127, 266, 54, 350, 132, 281, 166, 489, 340, 73, 140, 477, 377, 78, 56, 346, 192, 367, 118, 23, 207, 251, 114, 362, 40, 426, 457, 82, 392, 360, 170, 96, 182, 247, 399, 286, 100, 149, 387, 44, 501, 461, 337, 3, 106, 280, 491, 18, 413, 177, 407, 283, 309, 133, 181, 401, 297, 8, 195, 20, 445, 372, 304, 163, 14, 396, 287, 159, 299, 4, 102, 259, 199, 338, 126, 422, 204, 353, 238, 57, 412, 145, 212, 45, 449, 150, 128, 418, 264, 439, 190, 95, 279, 323, 186, 434, 112, 498, 25, 154, 464, 432, 242, 168, 254, 319, 471, 358, 172, 221, 459, 116, 69, 29, 409, 75, 178, 352, 59, 90, 485, 249, 479, 355, 381, 205, 253, 473, 369, 80, 267, 92, 13, 444, 376, 235, 86, 468, 359, 231, 371, 76, 174, 331, 271, 410, 198, 494, 276, 425, 310, 129, 484, 217, 284, 117, 17, 222, 200, 490, 336, 7, 262, 167, 351, 395, 258, 2, 184, 66, 97, 226, 32, 504, 314, 240, 326, 391, 39, 430, 244, 293, 27, 188, 141, 101, 481, 147, 250, 424, 131, 162, 53, 321, 47, 427, 453, 277, 325, 41, 441, 152, 339, 164, 85, 12, 448, 307, 158, 36, 431, 303, 443, 148, 246, 403, 343, 482, 270, 62, 348, 497, 382, 201, 52, 289, 356, 189, 89, 294, 272, 58, 408, 79, 334, 239, 423, 467, 330, 74, 256, 138, 169, 298, 104, 72, 386, 312, 398, 463, 111, 502, 316, 365, 99, 260, 213, 173, 49, 219, 322, 496, 203, 234, 125, 393, 119, 499, 21, 349, 397, 113, 9, 224, 411, 236, 157, 84, 16, 379, 230, 108, 503, 375, 11, 220, 318, 475, 415, 50, 342, 134, 420, 65, 454, 273, 124, 361, 428, 261, 161, 366, 344, 130, 480, 151, 406, 311, 495, 35, 402, 146, 328, 210, 241, 370, 176, 144, 458, 384, 470, 31, 183, 70, 388, 437, 171, 332, 285, 245, 121, 291, 394, 64, 275, 306, 197, 465, 191, 67, 93, 421, 469, 185, 81, 296, 483, 308, 229, 156, 88, 451, 302, 180, 71, 447, 83, 292, 390, 43, 487, 122, 414, 206, 492, 137, 22, 345, 196, 433, 500, 333, 233, 438, 416, 202, 48, 223, 478, 383, 63, 107, 474, 218, 400, 282, 313, 442, 248, 216, 26, 456, 38, 103, 255, 142, 460, 5, 243, 404, 357, 317, 193, 363, 466, 136, 347, 378, 269], [102, 176, 475, 360, 332, 49, 343, 335, 69, 444, 275, 178, 333, 125, 58, 100, 83, 321, 345, 473, 97, 423, 359, 31, 424, 497, 375, 183, 365, 277, 126, 467, 40, 442, 434, 78, 426, 95, 304, 234, 422, 13, 406, 389, 258, 219, 140, 367, 468, 170, 22, 181, 200, 456, 408, 302, 142, 171, 233, 4, 217, 236, 195, 93, 482, 52, 225, 152, 355, 163, 182, 276, 174, 248, 43, 432, 404, 121, 415, 407, 141, 12, 347, 250, 405, 197, 130, 172, 155, 393, 417, 41, 169, 495, 431, 103, 496, 65, 447, 255, 437, 349, 198, 35, 112, 10, 2, 150, 498, 167, 376, 306, 494, 85, 478, 461, 330, 291, 212, 439, 36, 242, 94, 253, 272, 24, 480, 374, 214, 243, 305, 76, 289, 308, 267, 165, 50, 124, 297, 224, 427, 235, 254, 348, 246, 320, 115, 504, 476, 193, 487, 479, 213, 84, 419, 322, 477, 269, 202, 244, 227, 465, 489, 113, 241, 63, 503, 175, 64, 137, 15, 327, 5, 421, 270, 107, 184, 82, 74, 222, 66, 239, 448, 378, 62, 157, 46, 29, 402, 363, 284, 7, 108, 314, 166, 325, 344, 96, 48, 446, 286, 315, 377, 148, 361, 380, 339, 237, 122, 196, 369, 296, 499, 307, 326, 420, 318, 392, 187, 72, 44, 265, 55, 47, 285, 156, 491, 394, 45, 341, 274, 316, 299, 33, 57, 185, 313, 135, 71, 247, 136, 209, 87, 399, 77, 493, 342, 179, 256, 154, 146, 294, 138, 311, 16, 450, 134, 229, 118, 101, 474, 435, 356, 79, 180, 386, 238, 397, 416, 168, 120, 14, 358, 387, 449, 220, 433, 452, 411, 309, 194, 268, 441, 368, 67, 379, 398, 492, 390, 464, 259, 144, 116, 337, 127, 119, 357, 228, 59, 466, 117, 413, 346, 388, 371, 105, 129, 257, 385, 207, 143, 319, 208, 281, 159, 471, 149, 61, 414, 251, 328, 226, 218, 366, 210, 383, 88, 18, 206, 301, 190, 173, 42, 3, 428, 151, 252, 458, 310, 469, 488, 240, 192, 86, 430, 459, 17, 292, 1, 20, 483, 381, 266, 340, 9, 440, 139, 451, 470, 60, 462, 32, 331, 216, 188, 409, 199, 191, 429, 300, 131, 34, 189, 485, 418, 460, 443, 177, 201, 329, 457, 279, 215, 391, 280, 353, 231, 39, 221, 133, 486, 323, 400, 298, 290, 438, 282, 455, 160, 90, 278, 373, 262, 245, 114, 75, 500, 223, 324, 26, 382, 37, 56, 312, 264, 158, 502, 27, 89, 364, 73, 92, 51, 453, 338, 412, 81, 8, 211, 19, 38, 132, 30, 104, 403, 288, 260, 481, 271, 263, 501, 372, 203, 106, 261, 53, 490, 28, 11, 249, 273, 401, 25, 351, 287, 463, 352, 425, 303, 111, 293, 205, 54, 395, 472, 370, 362, 6, 354, 23, 232, 162, 350, 445, 334, 317, 186, 147, 68, 295, 396, 98, 454, 109, 128, 384, 336, 230, 70, 99, 161, 436, 145, 164, 123, 21, 410, 484, 153, 80, 283, 91, 110, 204], [365, 477, 330, 28, 353, 233, 112, 394, 219, 140, 180, 123, 46, 326, 422, 490, 502, 408, 275, 99, 357, 10, 416, 170, 292, 241, 183, 302, 279, 465, 55, 119, 359, 157, 340, 426, 176, 306, 420, 1, 227, 467, 211, 205, 444, 95, 369, 168, 37, 461, 332, 265, 88, 345, 473, 144, 231, 19, 164, 125, 382, 439, 102, 338, 54, 150, 424, 218, 368, 103, 331, 381, 437, 45, 402, 100, 425, 305, 184, 466, 291, 212, 252, 195, 118, 398, 494, 58, 70, 480, 347, 171, 429, 82, 488, 242, 364, 313, 255, 374, 351, 33, 127, 191, 431, 229, 412, 498, 248, 378, 492, 73, 299, 35, 283, 277, 12, 167, 441, 240, 109, 29, 404, 337, 160, 417, 41, 216, 303, 91, 236, 197, 454, 7, 174, 410, 126, 222, 496, 290, 440, 175, 403, 453, 5, 117, 474, 172, 497, 377, 256, 34, 363, 284, 324, 267, 190, 470, 62, 130, 142, 48, 419, 243, 501, 154, 56, 314, 436, 385, 327, 446, 423, 105, 199, 263, 503, 301, 484, 66, 320, 450, 60, 145, 371, 107, 355, 349, 84, 239, 9, 312, 181, 101, 476, 409, 232, 489, 113, 288, 375, 163, 308, 269, 22, 79, 246, 482, 198, 294, 64, 362, 8, 247, 475, 21, 77, 189, 42, 244, 65, 449, 328, 106, 435, 356, 396, 339, 262, 38, 134, 202, 214, 120, 491, 315, 69, 226, 128, 386, 4, 457, 399, 14, 495, 177, 271, 335, 71, 373, 52, 138, 392, 18, 132, 217, 443, 179, 427, 421, 156, 311, 81, 384, 253, 173, 44, 481, 304, 57, 185, 360, 447, 235, 380, 341, 94, 151, 318, 50, 270, 366, 136, 434, 80, 319, 43, 93, 149, 261, 114, 316, 137, 17, 400, 178, 3, 428, 468, 411, 334, 110, 206, 274, 286, 192, 59, 387, 141, 298, 200, 458, 76, 25, 471, 86, 63, 249, 343, 407, 143, 445, 124, 210, 464, 90, 204, 289, 11, 251, 499, 493, 228, 383, 153, 456, 325, 245, 116, 49, 376, 129, 257, 432, 15, 307, 452, 413, 166, 223, 390, 122, 342, 438, 208, 2, 152, 391, 115, 165, 221, 333, 186, 388, 209, 89, 472, 250, 75, 500, 36, 483, 406, 182, 278, 346, 358, 264, 131, 459, 213, 370, 272, 26, 148, 97, 39, 158, 135, 321, 415, 479, 215, 13, 196, 282, 32, 162, 276, 361, 83, 323, 67, 61, 300, 455, 225, 24, 397, 317, 188, 121, 448, 201, 329, 504, 87, 379, 20, 485, 238, 295, 462, 194, 414, 6, 280, 74, 224, 463, 187, 237, 293, 405, 258, 460, 281, 161, 40, 322, 147, 68, 108, 51, 478, 254, 350, 418, 430, 336, 203, 27, 285, 442, 344, 98, 220, 169, 111, 230, 207, 393, 487, 47, 287, 85, 268, 354, 104, 234, 348, 433, 155, 395, 139, 133, 372, 23, 297, 96, 469, 389, 260, 193, 16, 273, 401, 72, 159, 451, 92, 53, 310, 367, 30, 266, 486, 78, 352, 146, 296, 31, 259, 309]];
cc:=[2,3,7];
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 >);
