// Magma code for the lmfdb family of higher genus curves 10.360-118.0.2-4-5.1
// 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:=[360,118];
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:=[0,2,4,5];
genus:=10;
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:=[[283, 71, 192, 220, 134, 357, 157, 317, 228, 274, 32, 93, 211, 245, 54, 268, 308, 279, 175, 143, 360, 322, 260, 75, 169, 209, 336, 136, 116, 351, 343, 11, 282, 130, 314, 207, 247, 227, 138, 334, 62, 153, 121, 95, 84, 118, 218, 339, 265, 323, 210, 232, 110, 15, 259, 299, 186, 316, 176, 201, 193, 41, 342, 310, 224, 297, 97, 137, 318, 184, 2, 243, 301, 155, 24, 178, 128, 189, 115, 233, 300, 142, 170, 45, 109, 359, 276, 226, 266, 291, 253, 221, 12, 160, 44, 147, 67, 287, 168, 244, 332, 183, 151, 305, 354, 328, 278, 249, 85, 53, 150, 292, 320, 225, 79, 29, 126, 46, 206, 141, 43, 191, 312, 340, 254, 117, 277, 77, 348, 34, 152, 213, 331, 5, 174, 28, 68, 39, 295, 263, 120, 82, 20, 195, 289, 329, 96, 256, 236, 111, 103, 131, 42, 250, 74, 327, 7, 347, 258, 94, 182, 273, 241, 215, 204, 238, 338, 99, 25, 83, 330, 352, 230, 135, 19, 59, 306, 76, 296, 321, 313, 161, 102, 70, 344, 57, 217, 257, 78, 304, 122, 3, 61, 275, 144, 298, 248, 309, 235, 353, 60, 262, 290, 165, 229, 119, 36, 346, 26, 51, 13, 341, 132, 280, 164, 267, 187, 47, 288, 4, 92, 303, 271, 65, 114, 88, 38, 9, 205, 173, 270, 52, 80, 345, 199, 149, 246, 166, 326, 261, 163, 311, 72, 100, 14, 237, 37, 197, 108, 154, 272, 333, 91, 125, 294, 148, 188, 159, 55, 23, 240, 202, 140, 315, 49, 89, 216, 16, 356, 231, 223, 251, 162, 10, 194, 87, 127, 107, 18, 214, 302, 33, 1, 335, 324, 358, 98, 219, 145, 203, 90, 112, 350, 255, 139, 179, 66, 196, 56, 81, 73, 281, 222, 190, 104, 177, 337, 17, 198, 64, 242, 123, 181, 35, 264, 58, 8, 69, 355, 113, 180, 22, 50, 285, 349, 239, 156, 106, 146, 171, 133, 101, 252, 40, 284, 27, 307, 167, 48, 124, 212, 63, 31, 185, 234, 208, 158, 129, 325, 293, 30, 172, 200, 105, 319, 269, 6, 286, 86, 21], [216, 135, 244, 29, 80, 7, 288, 33, 70, 131, 104, 139, 354, 309, 238, 65, 272, 1, 42, 261, 196, 203, 146, 205, 90, 117, 52, 47, 188, 313, 126, 315, 94, 59, 20, 37, 348, 63, 10, 311, 164, 319, 204, 219, 148, 5, 332, 31, 72, 111, 286, 293, 326, 295, 30, 177, 82, 77, 278, 223, 306, 225, 154, 89, 50, 67, 198, 3, 40, 221, 254, 229, 294, 129, 328, 35, 182, 61, 12, 171, 346, 353, 236, 355, 60, 267, 22, 17, 338, 133, 156, 45, 304, 119, 230, 97, 258, 333, 220, 41, 194, 49, 144, 279, 178, 215, 242, 91, 342, 321, 16, 23, 56, 25, 240, 207, 352, 347, 8, 283, 336, 255, 4, 149, 200, 127, 48, 153, 190, 251, 224, 259, 114, 69, 358, 185, 32, 121, 162, 21, 316, 323, 266, 325, 210, 237, 172, 167, 308, 73, 246, 75, 214, 179, 140, 157, 108, 183, 130, 71, 284, 79, 324, 339, 268, 125, 92, 151, 192, 231, 46, 53, 86, 55, 150, 297, 202, 197, 38, 343, 66, 345, 274, 209, 170, 187, 318, 123, 160, 341, 14, 349, 54, 249, 88, 155, 302, 181, 132, 291, 106, 113, 356, 115, 180, 27, 142, 137, 98, 253, 276, 165, 64, 239, 350, 217, 18, 93, 340, 161, 314, 169, 264, 39, 298, 335, 2, 211, 102, 81, 136, 143, 176, 145, 360, 327, 112, 107, 128, 43, 96, 15, 124, 269, 320, 247, 168, 273, 310, 11, 344, 19, 234, 189, 118, 305, 152, 241, 282, 141, 76, 83, 26, 85, 330, 357, 292, 287, 68, 193, 6, 195, 334, 299, 260, 277, 228, 303, 250, 191, 44, 199, 84, 99, 28, 245, 212, 271, 312, 351, 166, 173, 206, 175, 270, 57, 322, 317, 158, 103, 186, 105, 34, 329, 290, 307, 78, 243, 280, 101, 134, 109, 174, 9, 208, 275, 62, 301, 252, 51, 226, 233, 116, 235, 300, 147, 262, 257, 218, 13, 36, 285, 184, 359, 110, 337, 138, 213, 100, 281, 74, 289, 24, 159, 58, 95, 122, 331, 222, 201, 256, 263, 296, 265, 120, 87, 232, 227, 248, 163], [279, 38, 137, 312, 118, 223, 357, 206, 35, 138, 154, 115, 171, 122, 311, 150, 226, 187, 333, 314, 263, 276, 292, 31, 225, 140, 119, 324, 220, 259, 339, 68, 317, 222, 178, 133, 207, 296, 65, 318, 244, 175, 261, 302, 221, 330, 136, 277, 183, 224, 113, 336, 352, 61, 135, 320, 179, 234, 130, 109, 189, 8, 227, 132, 268, 313, 297, 356, 5, 228, 94, 265, 111, 212, 131, 240, 316, 337, 273, 134, 173, 186, 202, 1, 315, 230, 269, 144, 310, 169, 249, 338, 47, 282, 208, 163, 147, 26, 335, 48, 64, 205, 81, 32, 281, 60, 166, 7, 123, 284, 323, 246, 262, 331, 165, 50, 209, 294, 160, 319, 39, 158, 257, 72, 238, 343, 117, 326, 155, 258, 274, 235, 291, 242, 71, 270, 346, 307, 93, 74, 23, 36, 52, 151, 345, 260, 239, 84, 340, 19, 99, 188, 77, 342, 298, 253, 327, 56, 185, 78, 4, 295, 21, 62, 341, 90, 256, 37, 303, 344, 233, 96, 112, 181, 255, 80, 299, 354, 250, 229, 309, 128, 347, 252, 28, 73, 57, 116, 125, 348, 214, 25, 231, 332, 251, 360, 76, 97, 33, 254, 293, 306, 322, 121, 75, 350, 29, 264, 70, 289, 9, 98, 167, 42, 328, 283, 267, 146, 95, 168, 184, 325, 201, 152, 41, 180, 286, 127, 243, 44, 83, 6, 22, 91, 285, 170, 329, 54, 280, 79, 159, 278, 17, 192, 358, 103, 237, 86, 275, 18, 34, 355, 51, 2, 191, 30, 106, 67, 213, 194, 143, 156, 172, 271, 105, 20, 359, 204, 100, 139, 219, 308, 197, 102, 58, 13, 87, 176, 305, 198, 124, 55, 141, 182, 101, 210, 16, 157, 63, 104, 353, 216, 232, 301, 15, 200, 59, 114, 10, 349, 69, 248, 107, 12, 148, 193, 177, 236, 245, 108, 334, 145, 351, 92, 11, 120, 196, 217, 153, 14, 53, 66, 82, 241, 195, 110, 149, 24, 190, 49, 129, 218, 287, 162, 88, 43, 27, 266, 215, 288, 304, 85, 321, 272, 161, 300, 46, 247, 3, 164, 203, 126, 142, 211, 45, 290, 89, 174, 40, 199]];
cc:=[2,5,6];
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 >);

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