// Magma code for the lmfdb family of higher genus curves 8.48-25.0.2-6-24
// 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:=[48,25];
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:=[0,2,6,24];
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:=[[13, 14, 16, 15, 17, 18, 20, 19, 21, 22, 24, 23, 1, 2, 4, 3, 5, 6, 8, 7, 9, 10, 12, 11, 37, 38, 40, 39, 41, 42, 44, 43, 45, 46, 48, 47, 25, 26, 28, 27, 29, 30, 32, 31, 33, 34, 36, 35], [30, 29, 31, 32, 34, 33, 35, 36, 26, 25, 27, 28, 44, 43, 42, 41, 48, 47, 46, 45, 40, 39, 38, 37, 6, 5, 7, 8, 10, 9, 11, 12, 2, 1, 3, 4, 20, 19, 18, 17, 24, 23, 22, 21, 16, 15, 14, 13], [46, 45, 48, 47, 38, 37, 40, 39, 42, 41, 44, 43, 35, 36, 34, 33, 27, 28, 26, 25, 31, 32, 30, 29, 22, 21, 24, 23, 14, 13, 16, 15, 18, 17, 20, 19, 11, 12, 10, 9, 3, 4, 2, 1, 7, 8, 6, 5]];
cc:=[3,12,19];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=true;
cyc_auto:=S![5, 6, 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 17, 18, 19, 20, 21, 22, 23, 24, 13, 14, 15, 16, 29, 30, 31, 32, 33, 34, 35, 36, 25, 26, 27, 28, 41, 42, 43, 44, 45, 46, 47, 48, 37, 38, 39, 40];
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, cyc_auto:=cyc_auto >);

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

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

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

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

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

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

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