// Magma code for the lmfdb family of higher genus curves 8.20-5.0.10-10-10
// 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:=[20,5];
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:=[0,10,10,10];
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:=[[7, 8, 9, 10, 6, 2, 3, 4, 5, 1, 17, 18, 19, 20, 16, 12, 13, 14, 15, 11], [12, 13, 14, 15, 11, 17, 18, 19, 20, 16, 2, 3, 4, 5, 1, 7, 8, 9, 10, 6], [19, 20, 16, 17, 18, 14, 15, 11, 12, 13, 9, 10, 6, 7, 8, 4, 5, 1, 2, 3]];
cc:=[9,13,18];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
full_auto:=[40,10];
full_sign:=[0,2,10,20];
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, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[7, 8, 9, 10, 6, 2, 3, 4, 5, 1, 17, 18, 19, 20, 16, 12, 13, 14, 15, 11], [14, 15, 11, 12, 13, 19, 20, 16, 17, 18, 4, 5, 1, 2, 3, 9, 10, 6, 7, 8], [17, 18, 19, 20, 16, 12, 13, 14, 15, 11, 7, 8, 9, 10, 6, 2, 3, 4, 5, 1]];
cc:=[9,14,17];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=2;
gen_vect_label:=1;
full_auto:=[40,10];
full_sign:=[0,2,10,20];
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, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[7, 8, 9, 10, 6, 2, 3, 4, 5, 1, 17, 18, 19, 20, 16, 12, 13, 14, 15, 11], [13, 14, 15, 11, 12, 18, 19, 20, 16, 17, 3, 4, 5, 1, 2, 8, 9, 10, 6, 7], [18, 19, 20, 16, 17, 13, 14, 15, 11, 12, 8, 9, 10, 6, 7, 3, 4, 5, 1, 2]];
cc:=[9,15,19];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=3;
gen_vect_label:=1;
full_auto:=[40,10];
full_sign:=[0,2,10,20];
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, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[9, 10, 6, 7, 8, 4, 5, 1, 2, 3, 19, 20, 16, 17, 18, 14, 15, 11, 12, 13], [12, 13, 14, 15, 11, 17, 18, 19, 20, 16, 2, 3, 4, 5, 1, 7, 8, 9, 10, 6], [17, 18, 19, 20, 16, 12, 13, 14, 15, 11, 7, 8, 9, 10, 6, 2, 3, 4, 5, 1]];
cc:=[10,13,17];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=4;
gen_vect_label:=1;
full_auto:=[40,10];
full_sign:=[0,2,10,20];
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, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[9, 10, 6, 7, 8, 4, 5, 1, 2, 3, 19, 20, 16, 17, 18, 14, 15, 11, 12, 13], [14, 15, 11, 12, 13, 19, 20, 16, 17, 18, 4, 5, 1, 2, 3, 9, 10, 6, 7, 8], [20, 16, 17, 18, 19, 15, 11, 12, 13, 14, 10, 6, 7, 8, 9, 5, 1, 2, 3, 4]];
cc:=[10,14,20];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=5;
gen_vect_label:=1;
full_auto:=[40,10];
full_sign:=[0,2,10,20];
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, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[9, 10, 6, 7, 8, 4, 5, 1, 2, 3, 19, 20, 16, 17, 18, 14, 15, 11, 12, 13], [15, 11, 12, 13, 14, 20, 16, 17, 18, 19, 5, 1, 2, 3, 4, 10, 6, 7, 8, 9], [19, 20, 16, 17, 18, 14, 15, 11, 12, 13, 9, 10, 6, 7, 8, 4, 5, 1, 2, 3]];
cc:=[10,16,18];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=6;
gen_vect_label:=1;
full_auto:=[40,10];
full_sign:=[0,2,10,20];
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, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[8, 9, 10, 6, 7, 3, 4, 5, 1, 2, 18, 19, 20, 16, 17, 13, 14, 15, 11, 12], [12, 13, 14, 15, 11, 17, 18, 19, 20, 16, 2, 3, 4, 5, 1, 7, 8, 9, 10, 6], [18, 19, 20, 16, 17, 13, 14, 15, 11, 12, 8, 9, 10, 6, 7, 3, 4, 5, 1, 2]];
cc:=[11,13,19];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=7;
gen_vect_label:=1;
full_auto:=[40,10];
full_sign:=[0,2,10,20];
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, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[8, 9, 10, 6, 7, 3, 4, 5, 1, 2, 18, 19, 20, 16, 17, 13, 14, 15, 11, 12], [13, 14, 15, 11, 12, 18, 19, 20, 16, 17, 3, 4, 5, 1, 2, 8, 9, 10, 6, 7], [17, 18, 19, 20, 16, 12, 13, 14, 15, 11, 7, 8, 9, 10, 6, 2, 3, 4, 5, 1]];
cc:=[11,15,17];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=8;
gen_vect_label:=1;
full_auto:=[40,10];
full_sign:=[0,2,10,20];
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, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[8, 9, 10, 6, 7, 3, 4, 5, 1, 2, 18, 19, 20, 16, 17, 13, 14, 15, 11, 12], [15, 11, 12, 13, 14, 20, 16, 17, 18, 19, 5, 1, 2, 3, 4, 10, 6, 7, 8, 9], [20, 16, 17, 18, 19, 15, 11, 12, 13, 14, 10, 6, 7, 8, 9, 5, 1, 2, 3, 4]];
cc:=[11,16,20];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=9;
gen_vect_label:=1;
full_auto:=[40,10];
full_sign:=[0,2,10,20];
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, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[10, 6, 7, 8, 9, 5, 1, 2, 3, 4, 20, 16, 17, 18, 19, 15, 11, 12, 13, 14], [14, 15, 11, 12, 13, 19, 20, 16, 17, 18, 4, 5, 1, 2, 3, 9, 10, 6, 7, 8], [19, 20, 16, 17, 18, 14, 15, 11, 12, 13, 9, 10, 6, 7, 8, 4, 5, 1, 2, 3]];
cc:=[12,14,18];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=10;
gen_vect_label:=1;
full_auto:=[40,10];
full_sign:=[0,2,10,20];
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, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[10, 6, 7, 8, 9, 5, 1, 2, 3, 4, 20, 16, 17, 18, 19, 15, 11, 12, 13, 14], [13, 14, 15, 11, 12, 18, 19, 20, 16, 17, 3, 4, 5, 1, 2, 8, 9, 10, 6, 7], [20, 16, 17, 18, 19, 15, 11, 12, 13, 14, 10, 6, 7, 8, 9, 5, 1, 2, 3, 4]];
cc:=[12,15,20];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=11;
gen_vect_label:=1;
full_auto:=[40,10];
full_sign:=[0,2,10,20];
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, full_auto:=full_auto, full_sign:=full_sign>);

// Here we add an action to data.
gen_vectors:=[[10, 6, 7, 8, 9, 5, 1, 2, 3, 4, 20, 16, 17, 18, 19, 15, 11, 12, 13, 14], [15, 11, 12, 13, 14, 20, 16, 17, 18, 19, 5, 1, 2, 3, 4, 10, 6, 7, 8, 9], [18, 19, 20, 16, 17, 13, 14, 15, 11, 12, 8, 9, 10, 6, 7, 3, 4, 5, 1, 2]];
cc:=[12,16,19];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=12;
gen_vect_label:=1;
full_auto:=[40,10];
full_sign:=[0,2,10,20];
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, full_auto:=full_auto, full_sign:=full_sign>);
