// Magma code for the lmfdb family of higher genus curves 8.36-4.0.2-2-2-9
// 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:=[36,4];
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:=[0,2,2,2,9];
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:=[[10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 2, 3, 4, 5, 6, 7, 8, 9, 28, 29, 30, 31, 32, 33, 34, 35, 36, 19, 20, 21, 22, 23, 24, 25, 26, 27], [19, 21, 20, 26, 25, 27, 23, 22, 24, 28, 30, 29, 35, 34, 36, 32, 31, 33, 1, 3, 2, 8, 7, 9, 5, 4, 6, 10, 12, 11, 17, 16, 18, 14, 13, 15], [35, 34, 36, 32, 31, 33, 29, 28, 30, 26, 25, 27, 23, 22, 24, 20, 19, 21, 17, 16, 18, 14, 13, 15, 11, 10, 12, 8, 7, 9, 5, 4, 6, 2, 1, 3], [4, 5, 6, 7, 8, 9, 3, 1, 2, 13, 14, 15, 16, 17, 18, 12, 10, 11, 22, 23, 24, 25, 26, 27, 21, 19, 20, 31, 32, 33, 34, 35, 36, 30, 28, 29]];
cc:=[2,3,4,7];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 2, 3, 4, 5, 6, 7, 8, 9, 28, 29, 30, 31, 32, 33, 34, 35, 36, 19, 20, 21, 22, 23, 24, 25, 26, 27];
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:=[[10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 2, 3, 4, 5, 6, 7, 8, 9, 28, 29, 30, 31, 32, 33, 34, 35, 36, 19, 20, 21, 22, 23, 24, 25, 26, 27], [19, 21, 20, 26, 25, 27, 23, 22, 24, 28, 30, 29, 35, 34, 36, 32, 31, 33, 1, 3, 2, 8, 7, 9, 5, 4, 6, 10, 12, 11, 17, 16, 18, 14, 13, 15], [34, 36, 35, 31, 33, 32, 28, 30, 29, 25, 27, 26, 22, 24, 23, 19, 21, 20, 16, 18, 17, 13, 15, 14, 10, 12, 11, 7, 9, 8, 4, 6, 5, 1, 3, 2], [5, 6, 4, 8, 9, 7, 1, 2, 3, 14, 15, 13, 17, 18, 16, 10, 11, 12, 23, 24, 22, 26, 27, 25, 19, 20, 21, 32, 33, 31, 35, 36, 34, 28, 29, 30]];
cc:=[2,3,4,8];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=2;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 2, 3, 4, 5, 6, 7, 8, 9, 28, 29, 30, 31, 32, 33, 34, 35, 36, 19, 20, 21, 22, 23, 24, 25, 26, 27];
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:=[[10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 2, 3, 4, 5, 6, 7, 8, 9, 28, 29, 30, 31, 32, 33, 34, 35, 36, 19, 20, 21, 22, 23, 24, 25, 26, 27], [19, 21, 20, 26, 25, 27, 23, 22, 24, 28, 30, 29, 35, 34, 36, 32, 31, 33, 1, 3, 2, 8, 7, 9, 5, 4, 6, 10, 12, 11, 17, 16, 18, 14, 13, 15], [36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [6, 4, 5, 9, 7, 8, 2, 3, 1, 15, 13, 14, 18, 16, 17, 11, 12, 10, 24, 22, 23, 27, 25, 26, 20, 21, 19, 33, 31, 32, 36, 34, 35, 29, 30, 28]];
cc:=[2,3,4,9];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=3;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![10, 11, 12, 13, 14, 15, 16, 17, 18, 1, 2, 3, 4, 5, 6, 7, 8, 9, 28, 29, 30, 31, 32, 33, 34, 35, 36, 19, 20, 21, 22, 23, 24, 25, 26, 27];
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 >);
