// Magma code for the lmfdb family of higher genus curves 8.64-53.0.2-4-32
// 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:=[64,53];
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:=[0,2,4,32];
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:=[[17, 18, 20, 19, 23, 24, 21, 22, 29, 30, 32, 31, 25, 26, 28, 27, 1, 2, 4, 3, 7, 8, 5, 6, 13, 14, 16, 15, 9, 10, 12, 11, 49, 50, 52, 51, 55, 56, 53, 54, 61, 62, 64, 63, 57, 58, 60, 59, 33, 34, 36, 35, 39, 40, 37, 38, 45, 46, 48, 47, 41, 42, 44, 43], [34, 33, 35, 36, 40, 39, 38, 37, 46, 45, 47, 48, 42, 41, 43, 44, 58, 57, 59, 60, 64, 63, 62, 61, 50, 49, 51, 52, 56, 55, 54, 53, 1, 2, 4, 3, 7, 8, 5, 6, 13, 14, 16, 15, 9, 10, 12, 11, 25, 26, 28, 27, 31, 32, 29, 30, 17, 18, 20, 19, 23, 24, 21, 22], [49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 45, 46, 47, 48, 44, 43, 41, 42, 33, 34, 35, 36, 37, 38, 39, 40, 18, 17, 20, 19, 22, 21, 24, 23, 26, 25, 28, 27, 30, 29, 32, 31, 14, 13, 16, 15, 11, 12, 10, 9, 2, 1, 4, 3, 6, 5, 8, 7]];
cc:=[3,5,12];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19, 22, 21, 24, 23, 26, 25, 28, 27, 30, 29, 32, 31, 34, 33, 36, 35, 38, 37, 40, 39, 42, 41, 44, 43, 46, 45, 48, 47, 50, 49, 52, 51, 54, 53, 56, 55, 58, 57, 60, 59, 62, 61, 64, 63];
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, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);

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

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

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

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

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

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

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