// Magma code for the lmfdb family of higher genus curves 14.156-8.0.2-6-6.1
// 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:=[156,8];
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:=[0,2,6,6];
genus:=14;
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:=[[79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 105, 117, 116, 115, 114, 113, 112, 111, 110, 109, 108, 107, 106, 118, 130, 129, 128, 127, 126, 125, 124, 123, 122, 121, 120, 119, 131, 143, 142, 141, 140, 139, 138, 137, 136, 135, 134, 133, 132, 144, 156, 155, 154, 153, 152, 151, 150, 149, 148, 147, 146, 145, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67], [64, 54, 57, 60, 63, 53, 56, 59, 62, 65, 55, 58, 61, 77, 67, 70, 73, 76, 66, 69, 72, 75, 78, 68, 71, 74, 51, 41, 44, 47, 50, 40, 43, 46, 49, 52, 42, 45, 48, 25, 15, 18, 21, 24, 14, 17, 20, 23, 26, 16, 19, 22, 38, 28, 31, 34, 37, 27, 30, 33, 36, 39, 29, 32, 35, 12, 2, 5, 8, 11, 1, 4, 7, 10, 13, 3, 6, 9, 142, 132, 135, 138, 141, 131, 134, 137, 140, 143, 133, 136, 139, 155, 145, 148, 151, 154, 144, 147, 150, 153, 156, 146, 149, 152, 129, 119, 122, 125, 128, 118, 121, 124, 127, 130, 120, 123, 126, 103, 93, 96, 99, 102, 92, 95, 98, 101, 104, 94, 97, 100, 116, 106, 109, 112, 115, 105, 108, 111, 114, 117, 107, 110, 113, 90, 80, 83, 86, 89, 79, 82, 85, 88, 91, 81, 84, 87], [152, 156, 147, 151, 155, 146, 150, 154, 145, 149, 153, 144, 148, 126, 130, 121, 125, 129, 120, 124, 128, 119, 123, 127, 118, 122, 139, 143, 134, 138, 142, 133, 137, 141, 132, 136, 140, 131, 135, 113, 117, 108, 112, 116, 107, 111, 115, 106, 110, 114, 105, 109, 87, 91, 82, 86, 90, 81, 85, 89, 80, 84, 88, 79, 83, 100, 104, 95, 99, 103, 94, 98, 102, 93, 97, 101, 92, 96, 74, 78, 69, 73, 77, 68, 72, 76, 67, 71, 75, 66, 70, 48, 52, 43, 47, 51, 42, 46, 50, 41, 45, 49, 40, 44, 61, 65, 56, 60, 64, 55, 59, 63, 54, 58, 62, 53, 57, 35, 39, 30, 34, 38, 29, 33, 37, 28, 32, 36, 27, 31, 9, 13, 4, 8, 12, 3, 7, 11, 2, 6, 10, 1, 5, 22, 26, 17, 21, 25, 16, 20, 24, 15, 19, 23, 14, 18]];
cc:=[3,7,12];
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 >);

// Here we add an action to data.
gen_vectors:=[[79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 105, 117, 116, 115, 114, 113, 112, 111, 110, 109, 108, 107, 106, 118, 130, 129, 128, 127, 126, 125, 124, 123, 122, 121, 120, 119, 131, 143, 142, 141, 140, 139, 138, 137, 136, 135, 134, 133, 132, 144, 156, 155, 154, 153, 152, 151, 150, 149, 148, 147, 146, 145, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67], [62, 65, 55, 58, 61, 64, 54, 57, 60, 63, 53, 56, 59, 75, 78, 68, 71, 74, 77, 67, 70, 73, 76, 66, 69, 72, 49, 52, 42, 45, 48, 51, 41, 44, 47, 50, 40, 43, 46, 23, 26, 16, 19, 22, 25, 15, 18, 21, 24, 14, 17, 20, 36, 39, 29, 32, 35, 38, 28, 31, 34, 37, 27, 30, 33, 10, 13, 3, 6, 9, 12, 2, 5, 8, 11, 1, 4, 7, 140, 143, 133, 136, 139, 142, 132, 135, 138, 141, 131, 134, 137, 153, 156, 146, 149, 152, 155, 145, 148, 151, 154, 144, 147, 150, 127, 130, 120, 123, 126, 129, 119, 122, 125, 128, 118, 121, 124, 101, 104, 94, 97, 100, 103, 93, 96, 99, 102, 92, 95, 98, 114, 117, 107, 110, 113, 116, 106, 109, 112, 115, 105, 108, 111, 88, 91, 81, 84, 87, 90, 80, 83, 86, 89, 79, 82, 85], [147, 151, 155, 146, 150, 154, 145, 149, 153, 144, 148, 152, 156, 121, 125, 129, 120, 124, 128, 119, 123, 127, 118, 122, 126, 130, 134, 138, 142, 133, 137, 141, 132, 136, 140, 131, 135, 139, 143, 108, 112, 116, 107, 111, 115, 106, 110, 114, 105, 109, 113, 117, 82, 86, 90, 81, 85, 89, 80, 84, 88, 79, 83, 87, 91, 95, 99, 103, 94, 98, 102, 93, 97, 101, 92, 96, 100, 104, 69, 73, 77, 68, 72, 76, 67, 71, 75, 66, 70, 74, 78, 43, 47, 51, 42, 46, 50, 41, 45, 49, 40, 44, 48, 52, 56, 60, 64, 55, 59, 63, 54, 58, 62, 53, 57, 61, 65, 30, 34, 38, 29, 33, 37, 28, 32, 36, 27, 31, 35, 39, 4, 8, 12, 3, 7, 11, 2, 6, 10, 1, 5, 9, 13, 17, 21, 25, 16, 20, 24, 15, 19, 23, 14, 18, 22, 26]];
cc:=[3,7,12];
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 >);
