// Magma code for the lmfdb family of higher genus curves 8.84-7.0.2-6-6
// 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:=[84,7];
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:=8;
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:=[[43, 49, 48, 47, 46, 45, 44, 50, 56, 55, 54, 53, 52, 51, 57, 63, 62, 61, 60, 59, 58, 64, 70, 69, 68, 67, 66, 65, 71, 77, 76, 75, 74, 73, 72, 78, 84, 83, 82, 81, 80, 79, 1, 7, 6, 5, 4, 3, 2, 8, 14, 13, 12, 11, 10, 9, 15, 21, 20, 19, 18, 17, 16, 22, 28, 27, 26, 25, 24, 23, 29, 35, 34, 33, 32, 31, 30, 36, 42, 41, 40, 39, 38, 37], [33, 30, 34, 31, 35, 32, 29, 40, 37, 41, 38, 42, 39, 36, 26, 23, 27, 24, 28, 25, 22, 12, 9, 13, 10, 14, 11, 8, 19, 16, 20, 17, 21, 18, 15, 5, 2, 6, 3, 7, 4, 1, 75, 72, 76, 73, 77, 74, 71, 82, 79, 83, 80, 84, 81, 78, 68, 65, 69, 66, 70, 67, 64, 54, 51, 55, 52, 56, 53, 50, 61, 58, 62, 59, 63, 60, 57, 47, 44, 48, 45, 49, 46, 43], [79, 84, 82, 80, 78, 83, 81, 65, 70, 68, 66, 64, 69, 67, 72, 77, 75, 73, 71, 76, 74, 58, 63, 61, 59, 57, 62, 60, 44, 49, 47, 45, 43, 48, 46, 51, 56, 54, 52, 50, 55, 53, 37, 42, 40, 38, 36, 41, 39, 23, 28, 26, 24, 22, 27, 25, 30, 35, 33, 31, 29, 34, 32, 16, 21, 19, 17, 15, 20, 18, 2, 7, 5, 3, 1, 6, 4, 9, 14, 12, 10, 8, 13, 11]];
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:=[[43, 49, 48, 47, 46, 45, 44, 50, 56, 55, 54, 53, 52, 51, 57, 63, 62, 61, 60, 59, 58, 64, 70, 69, 68, 67, 66, 65, 71, 77, 76, 75, 74, 73, 72, 78, 84, 83, 82, 81, 80, 79, 1, 7, 6, 5, 4, 3, 2, 8, 14, 13, 12, 11, 10, 9, 15, 21, 20, 19, 18, 17, 16, 22, 28, 27, 26, 25, 24, 23, 29, 35, 34, 33, 32, 31, 30, 36, 42, 41, 40, 39, 38, 37], [42, 37, 39, 41, 36, 38, 40, 28, 23, 25, 27, 22, 24, 26, 35, 30, 32, 34, 29, 31, 33, 21, 16, 18, 20, 15, 17, 19, 7, 2, 4, 6, 1, 3, 5, 14, 9, 11, 13, 8, 10, 12, 84, 79, 81, 83, 78, 80, 82, 70, 65, 67, 69, 64, 66, 68, 77, 72, 74, 76, 71, 73, 75, 63, 58, 60, 62, 57, 59, 61, 49, 44, 46, 48, 43, 45, 47, 56, 51, 53, 55, 50, 52, 54], [74, 77, 73, 76, 72, 75, 71, 81, 84, 80, 83, 79, 82, 78, 67, 70, 66, 69, 65, 68, 64, 53, 56, 52, 55, 51, 54, 50, 60, 63, 59, 62, 58, 61, 57, 46, 49, 45, 48, 44, 47, 43, 32, 35, 31, 34, 30, 33, 29, 39, 42, 38, 41, 37, 40, 36, 25, 28, 24, 27, 23, 26, 22, 11, 14, 10, 13, 9, 12, 8, 18, 21, 17, 20, 16, 19, 15, 4, 7, 3, 6, 2, 5, 1]];
cc:=[3,8,11];
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:=[[64, 70, 69, 68, 67, 66, 65, 71, 77, 76, 75, 74, 73, 72, 78, 84, 83, 82, 81, 80, 79, 43, 49, 48, 47, 46, 45, 44, 50, 56, 55, 54, 53, 52, 51, 57, 63, 62, 61, 60, 59, 58, 22, 28, 27, 26, 25, 24, 23, 29, 35, 34, 33, 32, 31, 30, 36, 42, 41, 40, 39, 38, 37, 1, 7, 6, 5, 4, 3, 2, 8, 14, 13, 12, 11, 10, 9, 15, 21, 20, 19, 18, 17, 16], [33, 30, 34, 31, 35, 32, 29, 40, 37, 41, 38, 42, 39, 36, 26, 23, 27, 24, 28, 25, 22, 12, 9, 13, 10, 14, 11, 8, 19, 16, 20, 17, 21, 18, 15, 5, 2, 6, 3, 7, 4, 1, 75, 72, 76, 73, 77, 74, 71, 82, 79, 83, 80, 84, 81, 78, 68, 65, 69, 66, 70, 67, 64, 54, 51, 55, 52, 56, 53, 50, 61, 58, 62, 59, 63, 60, 57, 47, 44, 48, 45, 49, 46, 43], [58, 63, 61, 59, 57, 62, 60, 44, 49, 47, 45, 43, 48, 46, 51, 56, 54, 52, 50, 55, 53, 79, 84, 82, 80, 78, 83, 81, 65, 70, 68, 66, 64, 69, 67, 72, 77, 75, 73, 71, 76, 74, 16, 21, 19, 17, 15, 20, 18, 2, 7, 5, 3, 1, 6, 4, 9, 14, 12, 10, 8, 13, 11, 37, 42, 40, 38, 36, 41, 39, 23, 28, 26, 24, 22, 27, 25, 30, 35, 33, 31, 29, 34, 32]];
cc:=[4,7,10];
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:=[[64, 70, 69, 68, 67, 66, 65, 71, 77, 76, 75, 74, 73, 72, 78, 84, 83, 82, 81, 80, 79, 43, 49, 48, 47, 46, 45, 44, 50, 56, 55, 54, 53, 52, 51, 57, 63, 62, 61, 60, 59, 58, 22, 28, 27, 26, 25, 24, 23, 29, 35, 34, 33, 32, 31, 30, 36, 42, 41, 40, 39, 38, 37, 1, 7, 6, 5, 4, 3, 2, 8, 14, 13, 12, 11, 10, 9, 15, 21, 20, 19, 18, 17, 16], [42, 37, 39, 41, 36, 38, 40, 28, 23, 25, 27, 22, 24, 26, 35, 30, 32, 34, 29, 31, 33, 21, 16, 18, 20, 15, 17, 19, 7, 2, 4, 6, 1, 3, 5, 14, 9, 11, 13, 8, 10, 12, 84, 79, 81, 83, 78, 80, 82, 70, 65, 67, 69, 64, 66, 68, 77, 72, 74, 76, 71, 73, 75, 63, 58, 60, 62, 57, 59, 61, 49, 44, 46, 48, 43, 45, 47, 56, 51, 53, 55, 50, 52, 54], [53, 56, 52, 55, 51, 54, 50, 60, 63, 59, 62, 58, 61, 57, 46, 49, 45, 48, 44, 47, 43, 74, 77, 73, 76, 72, 75, 71, 81, 84, 80, 83, 79, 82, 78, 67, 70, 66, 69, 65, 68, 64, 11, 14, 10, 13, 9, 12, 8, 18, 21, 17, 20, 16, 19, 15, 4, 7, 3, 6, 2, 5, 1, 32, 35, 31, 34, 30, 33, 29, 39, 42, 38, 41, 37, 40, 36, 25, 28, 24, 27, 23, 26, 22]];
cc:=[4,8,9];
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 >);
