// Magma code for the lmfdb family of higher genus curves 3.24-5.0.2-4-12
// 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:=[24,5];
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:=[0,2,4,12];
genus:=3;
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:=[[13, 15, 14, 16, 18, 17, 19, 21, 20, 22, 24, 23, 1, 3, 2, 4, 6, 5, 7, 9, 8, 10, 12, 11], [21, 20, 19, 24, 23, 22, 18, 17, 16, 15, 14, 13, 9, 8, 7, 12, 11, 10, 6, 5, 4, 3, 2, 1], [11, 12, 10, 8, 9, 7, 2, 3, 1, 5, 6, 4, 23, 24, 22, 20, 21, 19, 14, 15, 13, 17, 18, 16]];
cc:=[3,8,12];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![4, 5, 6, 1, 2, 3, 10, 11, 12, 7, 8, 9, 16, 17, 18, 13, 14, 15, 22, 23, 24, 19, 20, 21];
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:=[[13, 15, 14, 16, 18, 17, 19, 21, 20, 22, 24, 23, 1, 3, 2, 4, 6, 5, 7, 9, 8, 10, 12, 11], [24, 23, 22, 21, 20, 19, 15, 14, 13, 18, 17, 16, 12, 11, 10, 9, 8, 7, 3, 2, 1, 6, 5, 4], [8, 9, 7, 11, 12, 10, 5, 6, 4, 2, 3, 1, 20, 21, 19, 23, 24, 22, 17, 18, 16, 14, 15, 13]];
cc:=[3,9,11];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=2;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![4, 5, 6, 1, 2, 3, 10, 11, 12, 7, 8, 9, 16, 17, 18, 13, 14, 15, 22, 23, 24, 19, 20, 21];
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:=[[16, 18, 17, 13, 15, 14, 22, 24, 23, 19, 21, 20, 4, 6, 5, 1, 3, 2, 10, 12, 11, 7, 9, 8], [21, 20, 19, 24, 23, 22, 18, 17, 16, 15, 14, 13, 9, 8, 7, 12, 11, 10, 6, 5, 4, 3, 2, 1], [8, 9, 7, 11, 12, 10, 5, 6, 4, 2, 3, 1, 20, 21, 19, 23, 24, 22, 17, 18, 16, 14, 15, 13]];
cc:=[4,8,11];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=3;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![4, 5, 6, 1, 2, 3, 10, 11, 12, 7, 8, 9, 16, 17, 18, 13, 14, 15, 22, 23, 24, 19, 20, 21];
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:=[[16, 18, 17, 13, 15, 14, 22, 24, 23, 19, 21, 20, 4, 6, 5, 1, 3, 2, 10, 12, 11, 7, 9, 8], [24, 23, 22, 21, 20, 19, 15, 14, 13, 18, 17, 16, 12, 11, 10, 9, 8, 7, 3, 2, 1, 6, 5, 4], [11, 12, 10, 8, 9, 7, 2, 3, 1, 5, 6, 4, 23, 24, 22, 20, 21, 19, 14, 15, 13, 17, 18, 16]];
cc:=[4,9,12];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=4;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![4, 5, 6, 1, 2, 3, 10, 11, 12, 7, 8, 9, 16, 17, 18, 13, 14, 15, 22, 23, 24, 19, 20, 21];
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 >);
