// Magma code for the lmfdb family of higher genus curves 13.64-31.0.2-16-16
// 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:=[64,31];
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:=[0,2,16,16];
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:=[[17, 18, 19, 20, 22, 21, 24, 23, 26, 25, 28, 27, 29, 30, 31, 32, 1, 2, 3, 4, 6, 5, 8, 7, 10, 9, 12, 11, 13, 14, 15, 16, 49, 50, 51, 52, 54, 53, 56, 55, 58, 57, 60, 59, 61, 62, 63, 64, 33, 34, 35, 36, 38, 37, 40, 39, 42, 41, 44, 43, 45, 46, 47, 48], [33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 57, 58, 59, 60, 61, 62, 63, 64, 50, 49, 52, 51, 54, 53, 56, 55, 5, 6, 7, 8, 3, 4, 2, 1, 13, 14, 15, 16, 11, 12, 10, 9, 30, 29, 32, 31, 28, 27, 25, 26, 21, 22, 23, 24, 19, 20, 18, 17], [55, 56, 54, 53, 49, 50, 51, 52, 64, 63, 61, 62, 58, 57, 60, 59, 48, 47, 45, 46, 42, 41, 44, 43, 40, 39, 37, 38, 34, 33, 36, 35, 17, 18, 19, 20, 22, 21, 24, 23, 26, 25, 28, 27, 29, 30, 31, 32, 9, 10, 11, 12, 14, 13, 16, 15, 1, 2, 3, 4, 6, 5, 8, 7]];
cc:=[4,17,28];
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:=[[17, 18, 19, 20, 22, 21, 24, 23, 26, 25, 28, 27, 29, 30, 31, 32, 1, 2, 3, 4, 6, 5, 8, 7, 10, 9, 12, 11, 13, 14, 15, 16, 49, 50, 51, 52, 54, 53, 56, 55, 58, 57, 60, 59, 61, 62, 63, 64, 33, 34, 35, 36, 38, 37, 40, 39, 42, 41, 44, 43, 45, 46, 47, 48], [37, 38, 39, 40, 35, 36, 34, 33, 45, 46, 47, 48, 43, 44, 42, 41, 61, 62, 63, 64, 59, 60, 58, 57, 54, 53, 56, 55, 52, 51, 49, 50, 3, 4, 2, 1, 7, 8, 6, 5, 11, 12, 10, 9, 15, 16, 14, 13, 28, 27, 25, 26, 32, 31, 29, 30, 19, 20, 18, 17, 23, 24, 22, 21], [52, 51, 49, 50, 55, 56, 54, 53, 59, 60, 58, 57, 64, 63, 61, 62, 43, 44, 42, 41, 48, 47, 45, 46, 35, 36, 34, 33, 40, 39, 37, 38, 23, 24, 22, 21, 17, 18, 19, 20, 32, 31, 29, 30, 26, 25, 28, 27, 15, 16, 14, 13, 9, 10, 11, 12, 7, 8, 6, 5, 1, 2, 3, 4]];
cc:=[4,18,27];
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:=[[17, 18, 19, 20, 22, 21, 24, 23, 26, 25, 28, 27, 29, 30, 31, 32, 1, 2, 3, 4, 6, 5, 8, 7, 10, 9, 12, 11, 13, 14, 15, 16, 49, 50, 51, 52, 54, 53, 56, 55, 58, 57, 60, 59, 61, 62, 63, 64, 33, 34, 35, 36, 38, 37, 40, 39, 42, 41, 44, 43, 45, 46, 47, 48], [35, 36, 34, 33, 39, 40, 38, 37, 43, 44, 42, 41, 47, 48, 46, 45, 59, 60, 58, 57, 63, 64, 62, 61, 52, 51, 49, 50, 56, 55, 53, 54, 7, 8, 6, 5, 2, 1, 4, 3, 15, 16, 14, 13, 10, 9, 12, 11, 32, 31, 29, 30, 25, 26, 27, 28, 23, 24, 22, 21, 18, 17, 20, 19], [53, 54, 55, 56, 52, 51, 49, 50, 62, 61, 64, 63, 59, 60, 58, 57, 46, 45, 48, 47, 43, 44, 42, 41, 38, 37, 40, 39, 35, 36, 34, 33, 20, 19, 17, 18, 23, 24, 22, 21, 27, 28, 26, 25, 32, 31, 29, 30, 12, 11, 9, 10, 15, 16, 14, 13, 4, 3, 1, 2, 7, 8, 6, 5]];
cc:=[4,19,26];
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:=[[17, 18, 19, 20, 22, 21, 24, 23, 26, 25, 28, 27, 29, 30, 31, 32, 1, 2, 3, 4, 6, 5, 8, 7, 10, 9, 12, 11, 13, 14, 15, 16, 49, 50, 51, 52, 54, 53, 56, 55, 58, 57, 60, 59, 61, 62, 63, 64, 33, 34, 35, 36, 38, 37, 40, 39, 42, 41, 44, 43, 45, 46, 47, 48], [39, 40, 38, 37, 34, 33, 36, 35, 47, 48, 46, 45, 42, 41, 44, 43, 63, 64, 62, 61, 58, 57, 60, 59, 56, 55, 53, 54, 49, 50, 51, 52, 2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 25, 26, 27, 28, 29, 30, 31, 32, 18, 17, 20, 19, 22, 21, 24, 23], [50, 49, 52, 51, 53, 54, 55, 56, 57, 58, 59, 60, 62, 61, 64, 63, 41, 42, 43, 44, 46, 45, 48, 47, 33, 34, 35, 36, 38, 37, 40, 39, 21, 22, 23, 24, 20, 19, 17, 18, 30, 29, 32, 31, 27, 28, 26, 25, 13, 14, 15, 16, 12, 11, 9, 10, 5, 6, 7, 8, 4, 3, 1, 2]];
cc:=[4,20,25];
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 >);

// Here we add an action to data.
gen_vectors:=[[17, 18, 19, 20, 22, 21, 24, 23, 26, 25, 28, 27, 29, 30, 31, 32, 1, 2, 3, 4, 6, 5, 8, 7, 10, 9, 12, 11, 13, 14, 15, 16, 49, 50, 51, 52, 54, 53, 56, 55, 58, 57, 60, 59, 61, 62, 63, 64, 33, 34, 35, 36, 38, 37, 40, 39, 42, 41, 44, 43, 45, 46, 47, 48], [34, 33, 36, 35, 38, 37, 40, 39, 42, 41, 44, 43, 46, 45, 48, 47, 58, 57, 60, 59, 62, 61, 64, 63, 49, 50, 51, 52, 53, 54, 55, 56, 6, 5, 8, 7, 4, 3, 1, 2, 14, 13, 16, 15, 12, 11, 9, 10, 29, 30, 31, 32, 27, 28, 26, 25, 22, 21, 24, 23, 20, 19, 17, 18], [56, 55, 53, 54, 50, 49, 52, 51, 63, 64, 62, 61, 57, 58, 59, 60, 47, 48, 46, 45, 41, 42, 43, 44, 39, 40, 38, 37, 33, 34, 35, 36, 18, 17, 20, 19, 21, 22, 23, 24, 25, 26, 27, 28, 30, 29, 32, 31, 10, 9, 12, 11, 13, 14, 15, 16, 2, 1, 4, 3, 5, 6, 7, 8]];
cc:=[4,21,28];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=5;
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:=[[17, 18, 19, 20, 22, 21, 24, 23, 26, 25, 28, 27, 29, 30, 31, 32, 1, 2, 3, 4, 6, 5, 8, 7, 10, 9, 12, 11, 13, 14, 15, 16, 49, 50, 51, 52, 54, 53, 56, 55, 58, 57, 60, 59, 61, 62, 63, 64, 33, 34, 35, 36, 38, 37, 40, 39, 42, 41, 44, 43, 45, 46, 47, 48], [38, 37, 40, 39, 36, 35, 33, 34, 46, 45, 48, 47, 44, 43, 41, 42, 62, 61, 64, 63, 60, 59, 57, 58, 53, 54, 55, 56, 51, 52, 50, 49, 4, 3, 1, 2, 8, 7, 5, 6, 12, 11, 9, 10, 16, 15, 13, 14, 27, 28, 26, 25, 31, 32, 30, 29, 20, 19, 17, 18, 24, 23, 21, 22], [51, 52, 50, 49, 56, 55, 53, 54, 60, 59, 57, 58, 63, 64, 62, 61, 44, 43, 41, 42, 47, 48, 46, 45, 36, 35, 33, 34, 39, 40, 38, 37, 24, 23, 21, 22, 18, 17, 20, 19, 31, 32, 30, 29, 25, 26, 27, 28, 16, 15, 13, 14, 10, 9, 12, 11, 8, 7, 5, 6, 2, 1, 4, 3]];
cc:=[4,22,27];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=6;
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:=[[17, 18, 19, 20, 22, 21, 24, 23, 26, 25, 28, 27, 29, 30, 31, 32, 1, 2, 3, 4, 6, 5, 8, 7, 10, 9, 12, 11, 13, 14, 15, 16, 49, 50, 51, 52, 54, 53, 56, 55, 58, 57, 60, 59, 61, 62, 63, 64, 33, 34, 35, 36, 38, 37, 40, 39, 42, 41, 44, 43, 45, 46, 47, 48], [36, 35, 33, 34, 40, 39, 37, 38, 44, 43, 41, 42, 48, 47, 45, 46, 60, 59, 57, 58, 64, 63, 61, 62, 51, 52, 50, 49, 55, 56, 54, 53, 8, 7, 5, 6, 1, 2, 3, 4, 16, 15, 13, 14, 9, 10, 11, 12, 31, 32, 30, 29, 26, 25, 28, 27, 24, 23, 21, 22, 17, 18, 19, 20], [54, 53, 56, 55, 51, 52, 50, 49, 61, 62, 63, 64, 60, 59, 57, 58, 45, 46, 47, 48, 44, 43, 41, 42, 37, 38, 39, 40, 36, 35, 33, 34, 19, 20, 18, 17, 24, 23, 21, 22, 28, 27, 25, 26, 31, 32, 30, 29, 11, 12, 10, 9, 16, 15, 13, 14, 3, 4, 2, 1, 8, 7, 5, 6]];
cc:=[4,23,26];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=7;
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:=[[17, 18, 19, 20, 22, 21, 24, 23, 26, 25, 28, 27, 29, 30, 31, 32, 1, 2, 3, 4, 6, 5, 8, 7, 10, 9, 12, 11, 13, 14, 15, 16, 49, 50, 51, 52, 54, 53, 56, 55, 58, 57, 60, 59, 61, 62, 63, 64, 33, 34, 35, 36, 38, 37, 40, 39, 42, 41, 44, 43, 45, 46, 47, 48], [40, 39, 37, 38, 33, 34, 35, 36, 48, 47, 45, 46, 41, 42, 43, 44, 64, 63, 61, 62, 57, 58, 59, 60, 55, 56, 54, 53, 50, 49, 52, 51, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 26, 25, 28, 27, 30, 29, 32, 31, 17, 18, 19, 20, 21, 22, 23, 24], [49, 50, 51, 52, 54, 53, 56, 55, 58, 57, 60, 59, 61, 62, 63, 64, 42, 41, 44, 43, 45, 46, 47, 48, 34, 33, 36, 35, 37, 38, 39, 40, 22, 21, 24, 23, 19, 20, 18, 17, 29, 30, 31, 32, 28, 27, 25, 26, 14, 13, 16, 15, 11, 12, 10, 9, 6, 5, 8, 7, 3, 4, 2, 1]];
cc:=[4,24,25];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=8;
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 >);
