// Magma code for the lmfdb family of higher genus curves 11.16-8.0.2-2-4-4-4
// 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:=[16,8];
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:=[0,2,2,4,4,4];
genus:=11;
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:=[[5, 6, 8, 7, 1, 2, 4, 3, 13, 14, 16, 15, 9, 10, 12, 11], [5, 6, 8, 7, 1, 2, 4, 3, 13, 14, 16, 15, 9, 10, 12, 11], [3, 4, 2, 1, 7, 8, 6, 5, 11, 12, 10, 9, 15, 16, 14, 13], [9, 10, 12, 11, 15, 16, 13, 14, 2, 1, 3, 4, 8, 7, 6, 5], [11, 12, 9, 10, 14, 13, 15, 16, 4, 3, 2, 1, 5, 6, 8, 7]];
cc:=[3,3,4,5,5];
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:=[[5, 6, 8, 7, 1, 2, 4, 3, 13, 14, 16, 15, 9, 10, 12, 11], [5, 6, 8, 7, 1, 2, 4, 3, 13, 14, 16, 15, 9, 10, 12, 11], [3, 4, 2, 1, 7, 8, 6, 5, 11, 12, 10, 9, 15, 16, 14, 13], [10, 9, 11, 12, 16, 15, 14, 13, 1, 2, 4, 3, 7, 8, 5, 6], [12, 11, 10, 9, 13, 14, 16, 15, 3, 4, 1, 2, 6, 5, 7, 8]];
cc:=[3,3,4,5,5];
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 >);

// Here we add an action to data.
gen_vectors:=[[5, 6, 8, 7, 1, 2, 4, 3, 13, 14, 16, 15, 9, 10, 12, 11], [5, 6, 8, 7, 1, 2, 4, 3, 13, 14, 16, 15, 9, 10, 12, 11], [3, 4, 2, 1, 7, 8, 6, 5, 11, 12, 10, 9, 15, 16, 14, 13], [12, 11, 10, 9, 13, 14, 16, 15, 3, 4, 1, 2, 6, 5, 7, 8], [9, 10, 12, 11, 15, 16, 13, 14, 2, 1, 3, 4, 8, 7, 6, 5]];
cc:=[3,3,4,5,5];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=3;
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:=[[5, 6, 8, 7, 1, 2, 4, 3, 13, 14, 16, 15, 9, 10, 12, 11], [5, 6, 8, 7, 1, 2, 4, 3, 13, 14, 16, 15, 9, 10, 12, 11], [3, 4, 2, 1, 7, 8, 6, 5, 11, 12, 10, 9, 15, 16, 14, 13], [11, 12, 9, 10, 14, 13, 15, 16, 4, 3, 2, 1, 5, 6, 8, 7], [10, 9, 11, 12, 16, 15, 14, 13, 1, 2, 4, 3, 7, 8, 5, 6]];
cc:=[3,3,4,5,5];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=4;
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:=[[5, 6, 8, 7, 1, 2, 4, 3, 13, 14, 16, 15, 9, 10, 12, 11], [6, 5, 7, 8, 2, 1, 3, 4, 14, 13, 15, 16, 10, 9, 11, 12], [3, 4, 2, 1, 7, 8, 6, 5, 11, 12, 10, 9, 15, 16, 14, 13], [9, 10, 12, 11, 15, 16, 13, 14, 2, 1, 3, 4, 8, 7, 6, 5], [12, 11, 10, 9, 13, 14, 16, 15, 3, 4, 1, 2, 6, 5, 7, 8]];
cc:=[3,3,4,5,5];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=5;
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:=[[5, 6, 8, 7, 1, 2, 4, 3, 13, 14, 16, 15, 9, 10, 12, 11], [6, 5, 7, 8, 2, 1, 3, 4, 14, 13, 15, 16, 10, 9, 11, 12], [3, 4, 2, 1, 7, 8, 6, 5, 11, 12, 10, 9, 15, 16, 14, 13], [10, 9, 11, 12, 16, 15, 14, 13, 1, 2, 4, 3, 7, 8, 5, 6], [11, 12, 9, 10, 14, 13, 15, 16, 4, 3, 2, 1, 5, 6, 8, 7]];
cc:=[3,3,4,5,5];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=6;
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:=[[5, 6, 8, 7, 1, 2, 4, 3, 13, 14, 16, 15, 9, 10, 12, 11], [6, 5, 7, 8, 2, 1, 3, 4, 14, 13, 15, 16, 10, 9, 11, 12], [3, 4, 2, 1, 7, 8, 6, 5, 11, 12, 10, 9, 15, 16, 14, 13], [12, 11, 10, 9, 13, 14, 16, 15, 3, 4, 1, 2, 6, 5, 7, 8], [10, 9, 11, 12, 16, 15, 14, 13, 1, 2, 4, 3, 7, 8, 5, 6]];
cc:=[3,3,4,5,5];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=7;
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:=[[5, 6, 8, 7, 1, 2, 4, 3, 13, 14, 16, 15, 9, 10, 12, 11], [6, 5, 7, 8, 2, 1, 3, 4, 14, 13, 15, 16, 10, 9, 11, 12], [3, 4, 2, 1, 7, 8, 6, 5, 11, 12, 10, 9, 15, 16, 14, 13], [11, 12, 9, 10, 14, 13, 15, 16, 4, 3, 2, 1, 5, 6, 8, 7], [9, 10, 12, 11, 15, 16, 13, 14, 2, 1, 3, 4, 8, 7, 6, 5]];
cc:=[3,3,4,5,5];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=8;
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:=[[5, 6, 8, 7, 1, 2, 4, 3, 13, 14, 16, 15, 9, 10, 12, 11], [7, 8, 5, 6, 3, 4, 1, 2, 15, 16, 13, 14, 11, 12, 9, 10], [3, 4, 2, 1, 7, 8, 6, 5, 11, 12, 10, 9, 15, 16, 14, 13], [9, 10, 12, 11, 15, 16, 13, 14, 2, 1, 3, 4, 8, 7, 6, 5], [9, 10, 12, 11, 15, 16, 13, 14, 2, 1, 3, 4, 8, 7, 6, 5]];
cc:=[3,3,4,5,5];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=9;
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:=[[5, 6, 8, 7, 1, 2, 4, 3, 13, 14, 16, 15, 9, 10, 12, 11], [7, 8, 5, 6, 3, 4, 1, 2, 15, 16, 13, 14, 11, 12, 9, 10], [3, 4, 2, 1, 7, 8, 6, 5, 11, 12, 10, 9, 15, 16, 14, 13], [10, 9, 11, 12, 16, 15, 14, 13, 1, 2, 4, 3, 7, 8, 5, 6], [10, 9, 11, 12, 16, 15, 14, 13, 1, 2, 4, 3, 7, 8, 5, 6]];
cc:=[3,3,4,5,5];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=10;
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:=[[5, 6, 8, 7, 1, 2, 4, 3, 13, 14, 16, 15, 9, 10, 12, 11], [7, 8, 5, 6, 3, 4, 1, 2, 15, 16, 13, 14, 11, 12, 9, 10], [3, 4, 2, 1, 7, 8, 6, 5, 11, 12, 10, 9, 15, 16, 14, 13], [12, 11, 10, 9, 13, 14, 16, 15, 3, 4, 1, 2, 6, 5, 7, 8], [12, 11, 10, 9, 13, 14, 16, 15, 3, 4, 1, 2, 6, 5, 7, 8]];
cc:=[3,3,4,5,5];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=11;
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:=[[5, 6, 8, 7, 1, 2, 4, 3, 13, 14, 16, 15, 9, 10, 12, 11], [7, 8, 5, 6, 3, 4, 1, 2, 15, 16, 13, 14, 11, 12, 9, 10], [3, 4, 2, 1, 7, 8, 6, 5, 11, 12, 10, 9, 15, 16, 14, 13], [11, 12, 9, 10, 14, 13, 15, 16, 4, 3, 2, 1, 5, 6, 8, 7], [11, 12, 9, 10, 14, 13, 15, 16, 4, 3, 2, 1, 5, 6, 8, 7]];
cc:=[3,3,4,5,5];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=12;
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:=[[5, 6, 8, 7, 1, 2, 4, 3, 13, 14, 16, 15, 9, 10, 12, 11], [7, 8, 5, 6, 3, 4, 1, 2, 15, 16, 13, 14, 11, 12, 9, 10], [4, 3, 1, 2, 8, 7, 5, 6, 12, 11, 9, 10, 16, 15, 13, 14], [9, 10, 12, 11, 15, 16, 13, 14, 2, 1, 3, 4, 8, 7, 6, 5], [10, 9, 11, 12, 16, 15, 14, 13, 1, 2, 4, 3, 7, 8, 5, 6]];
cc:=[3,3,4,5,5];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=13;
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:=[[5, 6, 8, 7, 1, 2, 4, 3, 13, 14, 16, 15, 9, 10, 12, 11], [7, 8, 5, 6, 3, 4, 1, 2, 15, 16, 13, 14, 11, 12, 9, 10], [4, 3, 1, 2, 8, 7, 5, 6, 12, 11, 9, 10, 16, 15, 13, 14], [10, 9, 11, 12, 16, 15, 14, 13, 1, 2, 4, 3, 7, 8, 5, 6], [9, 10, 12, 11, 15, 16, 13, 14, 2, 1, 3, 4, 8, 7, 6, 5]];
cc:=[3,3,4,5,5];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=14;
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:=[[5, 6, 8, 7, 1, 2, 4, 3, 13, 14, 16, 15, 9, 10, 12, 11], [7, 8, 5, 6, 3, 4, 1, 2, 15, 16, 13, 14, 11, 12, 9, 10], [4, 3, 1, 2, 8, 7, 5, 6, 12, 11, 9, 10, 16, 15, 13, 14], [12, 11, 10, 9, 13, 14, 16, 15, 3, 4, 1, 2, 6, 5, 7, 8], [11, 12, 9, 10, 14, 13, 15, 16, 4, 3, 2, 1, 5, 6, 8, 7]];
cc:=[3,3,4,5,5];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=15;
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:=[[5, 6, 8, 7, 1, 2, 4, 3, 13, 14, 16, 15, 9, 10, 12, 11], [7, 8, 5, 6, 3, 4, 1, 2, 15, 16, 13, 14, 11, 12, 9, 10], [4, 3, 1, 2, 8, 7, 5, 6, 12, 11, 9, 10, 16, 15, 13, 14], [11, 12, 9, 10, 14, 13, 15, 16, 4, 3, 2, 1, 5, 6, 8, 7], [12, 11, 10, 9, 13, 14, 16, 15, 3, 4, 1, 2, 6, 5, 7, 8]];
cc:=[3,3,4,5,5];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=16;
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 >);
