// Magma code for the lmfdb family of higher genus curves 13.96-197.0.2-6-12
// 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:=[96,197];
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:=[0,2,6,12];
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:=[[26, 25, 28, 27, 30, 29, 32, 31, 34, 33, 36, 35, 38, 37, 40, 39, 42, 41, 44, 43, 46, 45, 48, 47, 2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19, 22, 21, 24, 23, 74, 73, 76, 75, 78, 77, 80, 79, 82, 81, 84, 83, 86, 85, 88, 87, 90, 89, 92, 91, 94, 93, 96, 95, 50, 49, 52, 51, 54, 53, 56, 55, 58, 57, 60, 59, 62, 61, 64, 63, 66, 65, 68, 67, 70, 69, 72, 71], [57, 60, 58, 59, 61, 64, 62, 63, 65, 68, 66, 67, 69, 72, 70, 71, 49, 52, 50, 51, 53, 56, 54, 55, 85, 88, 86, 87, 81, 84, 82, 83, 93, 96, 94, 95, 89, 92, 90, 91, 77, 80, 78, 79, 73, 76, 74, 75, 9, 12, 10, 11, 13, 16, 14, 15, 17, 20, 18, 19, 21, 24, 22, 23, 1, 4, 2, 3, 5, 8, 6, 7, 37, 40, 38, 39, 33, 36, 34, 35, 45, 48, 46, 47, 41, 44, 42, 43, 29, 32, 30, 31, 25, 28, 26, 27], [90, 92, 91, 89, 94, 96, 95, 93, 74, 76, 75, 73, 78, 80, 79, 77, 82, 84, 83, 81, 86, 88, 87, 85, 70, 72, 71, 69, 66, 68, 67, 65, 54, 56, 55, 53, 50, 52, 51, 49, 62, 64, 63, 61, 58, 60, 59, 57, 42, 44, 43, 41, 46, 48, 47, 45, 26, 28, 27, 25, 30, 32, 31, 29, 34, 36, 35, 33, 38, 40, 39, 37, 22, 24, 23, 21, 18, 20, 19, 17, 6, 8, 7, 5, 2, 4, 3, 1, 14, 16, 15, 13, 10, 12, 11, 9]];
cc:=[7,17,20];
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:=[[26, 25, 28, 27, 30, 29, 32, 31, 34, 33, 36, 35, 38, 37, 40, 39, 42, 41, 44, 43, 46, 45, 48, 47, 2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19, 22, 21, 24, 23, 74, 73, 76, 75, 78, 77, 80, 79, 82, 81, 84, 83, 86, 85, 88, 87, 90, 89, 92, 91, 94, 93, 96, 95, 50, 49, 52, 51, 54, 53, 56, 55, 58, 57, 60, 59, 62, 61, 64, 63, 66, 65, 68, 67, 70, 69, 72, 71], [65, 67, 68, 66, 69, 71, 72, 70, 49, 51, 52, 50, 53, 55, 56, 54, 57, 59, 60, 58, 61, 63, 64, 62, 93, 95, 96, 94, 89, 91, 92, 90, 77, 79, 80, 78, 73, 75, 76, 74, 85, 87, 88, 86, 81, 83, 84, 82, 17, 19, 20, 18, 21, 23, 24, 22, 1, 3, 4, 2, 5, 7, 8, 6, 9, 11, 12, 10, 13, 15, 16, 14, 45, 47, 48, 46, 41, 43, 44, 42, 29, 31, 32, 30, 25, 27, 28, 26, 37, 39, 40, 38, 33, 35, 36, 34], [82, 83, 81, 84, 86, 87, 85, 88, 90, 91, 89, 92, 94, 95, 93, 96, 74, 75, 73, 76, 78, 79, 77, 80, 62, 63, 61, 64, 58, 59, 57, 60, 70, 71, 69, 72, 66, 67, 65, 68, 54, 55, 53, 56, 50, 51, 49, 52, 34, 35, 33, 36, 38, 39, 37, 40, 42, 43, 41, 44, 46, 47, 45, 48, 26, 27, 25, 28, 30, 31, 29, 32, 14, 15, 13, 16, 10, 11, 9, 12, 22, 23, 21, 24, 18, 19, 17, 20, 6, 7, 5, 8, 2, 3, 1, 4]];
cc:=[7,18,19];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=2;
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:=[[50, 49, 52, 51, 54, 53, 56, 55, 58, 57, 60, 59, 62, 61, 64, 63, 66, 65, 68, 67, 70, 69, 72, 71, 78, 77, 80, 79, 74, 73, 76, 75, 86, 85, 88, 87, 82, 81, 84, 83, 94, 93, 96, 95, 90, 89, 92, 91, 2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19, 22, 21, 24, 23, 30, 29, 32, 31, 26, 25, 28, 27, 38, 37, 40, 39, 34, 33, 36, 35, 46, 45, 48, 47, 42, 41, 44, 43], [33, 36, 34, 35, 37, 40, 38, 39, 41, 44, 42, 43, 45, 48, 46, 47, 25, 28, 26, 27, 29, 32, 30, 31, 9, 12, 10, 11, 13, 16, 14, 15, 17, 20, 18, 19, 21, 24, 22, 23, 1, 4, 2, 3, 5, 8, 6, 7, 81, 84, 82, 83, 85, 88, 86, 87, 89, 92, 90, 91, 93, 96, 94, 95, 73, 76, 74, 75, 77, 80, 78, 79, 57, 60, 58, 59, 61, 64, 62, 63, 65, 68, 66, 67, 69, 72, 70, 71, 49, 52, 50, 51, 53, 56, 54, 55], [94, 96, 95, 93, 90, 92, 91, 89, 78, 80, 79, 77, 74, 76, 75, 73, 86, 88, 87, 85, 82, 84, 83, 81, 66, 68, 67, 65, 70, 72, 71, 69, 50, 52, 51, 49, 54, 56, 55, 53, 58, 60, 59, 57, 62, 64, 63, 61, 46, 48, 47, 45, 42, 44, 43, 41, 30, 32, 31, 29, 26, 28, 27, 25, 38, 40, 39, 37, 34, 36, 35, 33, 18, 20, 19, 17, 22, 24, 23, 21, 2, 4, 3, 1, 6, 8, 7, 5, 10, 12, 11, 9, 14, 16, 15, 13]];
cc:=[8,15,20];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=3;
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:=[[50, 49, 52, 51, 54, 53, 56, 55, 58, 57, 60, 59, 62, 61, 64, 63, 66, 65, 68, 67, 70, 69, 72, 71, 78, 77, 80, 79, 74, 73, 76, 75, 86, 85, 88, 87, 82, 81, 84, 83, 94, 93, 96, 95, 90, 89, 92, 91, 2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19, 22, 21, 24, 23, 30, 29, 32, 31, 26, 25, 28, 27, 38, 37, 40, 39, 34, 33, 36, 35, 46, 45, 48, 47, 42, 41, 44, 43], [41, 43, 44, 42, 45, 47, 48, 46, 25, 27, 28, 26, 29, 31, 32, 30, 33, 35, 36, 34, 37, 39, 40, 38, 17, 19, 20, 18, 21, 23, 24, 22, 1, 3, 4, 2, 5, 7, 8, 6, 9, 11, 12, 10, 13, 15, 16, 14, 89, 91, 92, 90, 93, 95, 96, 94, 73, 75, 76, 74, 77, 79, 80, 78, 81, 83, 84, 82, 85, 87, 88, 86, 65, 67, 68, 66, 69, 71, 72, 70, 49, 51, 52, 50, 53, 55, 56, 54, 57, 59, 60, 58, 61, 63, 64, 62], [86, 87, 85, 88, 82, 83, 81, 84, 94, 95, 93, 96, 90, 91, 89, 92, 78, 79, 77, 80, 74, 75, 73, 76, 58, 59, 57, 60, 62, 63, 61, 64, 66, 67, 65, 68, 70, 71, 69, 72, 50, 51, 49, 52, 54, 55, 53, 56, 38, 39, 37, 40, 34, 35, 33, 36, 46, 47, 45, 48, 42, 43, 41, 44, 30, 31, 29, 32, 26, 27, 25, 28, 10, 11, 9, 12, 14, 15, 13, 16, 18, 19, 17, 20, 22, 23, 21, 24, 2, 3, 1, 4, 6, 7, 5, 8]];
cc:=[8,16,19];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=4;
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 >);
