// Magma code for the lmfdb family of higher genus curves 7.504-156.0.2-3-7.2
// 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:=[0,2,3,7];
genus:=7;
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], [499, 357, 370, 471, 234, 376, 389, 212, 8, 337, 330, 64, 174, 423, 70, 497, 293, 17, 391, 420, 253, 93, 171, 259, 236, 383, 26, 85, 123, 316, 273, 360, 322, 335, 113, 35, 238, 231, 190, 300, 468, 196, 200, 266, 44, 436, 465, 73, 363, 333, 79, 83, 491, 53, 202, 168, 451, 138, 126, 457, 434, 158, 62, 256, 222, 343, 48, 369, 349, 326, 248, 71, 67, 429, 442, 39, 306, 448, 461, 284, 80, 409, 402, 136, 246, 495, 142, 65, 365, 89, 463, 492, 325, 165, 243, 331, 308, 455, 98, 157, 195, 388, 345, 432, 394, 407, 185, 107, 310, 303, 262, 372, 36, 268, 272, 338, 116, 4, 33, 145, 435, 405, 151, 155, 59, 125, 274, 240, 19, 210, 198, 25, 2, 230, 134, 328, 294, 415, 120, 441, 421, 398, 320, 143, 139, 501, 10, 111, 378, 16, 29, 356, 152, 481, 474, 208, 318, 63, 214, 137, 437, 161, 31, 60, 397, 237, 315, 403, 380, 23, 170, 229, 267, 460, 417, 504, 466, 479, 257, 179, 382, 375, 334, 444, 108, 340, 344, 410, 188, 76, 105, 217, 3, 477, 223, 227, 131, 197, 346, 312, 91, 282, 270, 97, 74, 302, 206, 400, 366, 487, 192, 9, 493, 470, 392, 215, 211, 69, 82, 183, 450, 88, 101, 428, 224, 49, 42, 280, 390, 135, 286, 209, 5, 233, 103, 132, 469, 309, 387, 475, 452, 95, 242, 301, 339, 28, 489, 72, 34, 47, 329, 251, 454, 447, 406, 12, 180, 412, 416, 482, 260, 148, 177, 289, 75, 45, 295, 299, 203, 269, 418, 384, 163, 354, 342, 169, 146, 374, 278, 472, 438, 55, 264, 81, 61, 38, 464, 287, 283, 141, 154, 255, 18, 160, 173, 500, 296, 121, 114, 352, 462, 207, 358, 281, 77, 305, 175, 204, 37, 381, 459, 43, 20, 167, 314, 373, 411, 100, 57, 144, 106, 119, 401, 323, 22, 15, 478, 84, 252, 484, 488, 50, 332, 220, 249, 361, 147, 117, 367, 371, 275, 341, 490, 456, 235, 426, 414, 241, 218, 446, 350, 40, 6, 127, 336, 153, 133, 110, 32, 359, 355, 213, 226, 327, 90, 232, 245, 68, 368, 193, 186, 424, 30, 279, 430, 353, 149, 377, 247, 276, 109, 453, 27, 115, 92, 239, 386, 445, 483, 172, 129, 216, 178, 191, 473, 395, 94, 87, 46, 156, 324, 52, 56, 122, 404, 292, 321, 433, 219, 189, 439, 443, 347, 413, 58, 24, 307, 498, 486, 313, 290, 14, 422, 112, 78, 199, 408, 225, 205, 182, 104, 431, 427, 285, 298, 399, 162, 304, 317, 140, 440, 265, 258, 496, 102, 351, 502, 425, 221, 449, 319, 348, 181, 21, 99, 187, 164, 311, 458, 13, 51, 244, 201, 288, 250, 263, 41, 467, 166, 159, 118, 228, 396, 124, 128, 194, 476, 364, 393, 1, 291, 261, 7, 11, 419, 485, 130, 96, 379, 66, 54, 385, 362, 86, 494, 184, 150, 271, 480, 297, 277, 254, 176, 503], [400, 149, 498, 114, 468, 173, 442, 368, 178, 283, 248, 336, 492, 171, 272, 181, 143, 277, 247, 482, 390, 294, 126, 470, 100, 278, 475, 310, 401, 84, 159, 234, 362, 217, 305, 367, 148, 131, 237, 213, 333, 92, 343, 179, 97, 130, 284, 435, 267, 423, 137, 406, 98, 142, 481, 311, 201, 384, 360, 299, 424, 476, 304, 301, 446, 255, 105, 9, 479, 19, 341, 484, 472, 221, 66, 186, 36, 245, 10, 440, 250, 355, 320, 408, 60, 243, 344, 253, 215, 349, 319, 50, 462, 366, 198, 38, 172, 350, 43, 382, 473, 156, 231, 306, 434, 289, 377, 439, 220, 203, 309, 285, 405, 164, 415, 251, 169, 202, 356, 3, 339, 495, 209, 478, 170, 214, 49, 383, 273, 456, 432, 371, 496, 44, 376, 373, 14, 327, 177, 81, 47, 91, 413, 52, 40, 293, 138, 258, 108, 317, 82, 8, 322, 427, 392, 480, 132, 315, 416, 325, 287, 421, 391, 122, 30, 438, 270, 110, 244, 422, 115, 454, 41, 228, 303, 378, 2, 361, 449, 7, 292, 275, 381, 357, 477, 236, 487, 323, 241, 274, 428, 75, 411, 63, 281, 46, 242, 286, 121, 455, 345, 24, 504, 443, 64, 116, 448, 445, 86, 399, 249, 153, 119, 163, 485, 124, 112, 365, 210, 330, 180, 389, 154, 80, 394, 499, 464, 48, 204, 387, 488, 397, 359, 493, 463, 194, 102, 6, 342, 182, 316, 494, 187, 22, 113, 300, 375, 450, 74, 433, 17, 79, 364, 347, 453, 429, 45, 308, 55, 395, 313, 346, 500, 147, 483, 135, 353, 118, 314, 358, 193, 23, 417, 96, 72, 11, 136, 188, 16, 13, 158, 471, 321, 225, 191, 235, 53, 196, 184, 437, 282, 402, 252, 461, 226, 152, 466, 67, 32, 120, 276, 459, 56, 469, 431, 61, 31, 266, 174, 78, 414, 254, 388, 62, 259, 94, 185, 372, 447, 18, 146, 1, 89, 151, 436, 419, 21, 501, 117, 380, 127, 467, 385, 418, 68, 219, 51, 207, 425, 190, 386, 430, 265, 95, 489, 168, 144, 83, 208, 260, 88, 85, 230, 39, 393, 297, 263, 307, 125, 268, 256, 5, 354, 474, 324, 29, 298, 224, 34, 139, 104, 192, 348, 27, 128, 37, 503, 133, 103, 338, 246, 150, 486, 326, 460, 134, 331, 166, 257, 444, 15, 90, 218, 73, 161, 223, 4, 491, 93, 69, 189, 452, 199, 35, 457, 490, 140, 291, 123, 279, 497, 262, 458, 502, 337, 167, 57, 240, 216, 155, 280, 332, 160, 157, 302, 111, 465, 369, 335, 379, 197, 340, 328, 77, 426, 42, 396, 101, 370, 296, 106, 211, 176, 264, 420, 99, 200, 109, 71, 205, 175, 410, 318, 222, 54, 398, 28, 206, 403, 238, 329, 12, 87, 162, 290, 145, 233, 295, 76, 59, 165, 141, 261, 20, 271, 107, 25, 58, 212, 363, 195, 351, 65, 334, 26, 70, 409, 239, 129, 312, 288, 227, 352, 404, 232, 229, 374, 183, 33, 441, 407, 451, 269, 412]];
cc:=[2,3,5];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=2;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 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 >);
