// Magma code for the lmfdb family of higher genus curves 14.48-18.0.4-8-12
// 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:=[48,18];
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:=[0,4,8,12];
genus:=14;
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:=[[25, 27, 26, 28, 30, 29, 34, 36, 35, 31, 33, 32, 43, 45, 44, 46, 48, 47, 37, 39, 38, 40, 42, 41, 4, 6, 5, 1, 3, 2, 7, 9, 8, 10, 12, 11, 22, 24, 23, 19, 21, 20, 16, 18, 17, 13, 15, 14], [39, 38, 37, 42, 41, 40, 45, 44, 43, 48, 47, 46, 33, 32, 31, 36, 35, 34, 30, 29, 28, 27, 26, 25, 18, 17, 16, 15, 14, 13, 24, 23, 22, 21, 20, 19, 12, 11, 10, 9, 8, 7, 3, 2, 1, 6, 5, 4], [14, 15, 13, 17, 18, 16, 23, 24, 22, 20, 21, 19, 5, 6, 4, 2, 3, 1, 8, 9, 7, 11, 12, 10, 38, 39, 37, 41, 42, 40, 47, 48, 46, 44, 45, 43, 29, 30, 28, 26, 27, 25, 32, 33, 31, 35, 36, 34]];
cc:=[6,8,11];
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:=[[25, 27, 26, 28, 30, 29, 34, 36, 35, 31, 33, 32, 43, 45, 44, 46, 48, 47, 37, 39, 38, 40, 42, 41, 4, 6, 5, 1, 3, 2, 7, 9, 8, 10, 12, 11, 22, 24, 23, 19, 21, 20, 16, 18, 17, 13, 15, 14], [38, 37, 39, 41, 40, 42, 44, 43, 45, 47, 46, 48, 32, 31, 33, 35, 34, 36, 29, 28, 30, 26, 25, 27, 17, 16, 18, 14, 13, 15, 23, 22, 24, 20, 19, 21, 11, 10, 12, 8, 7, 9, 2, 1, 3, 5, 4, 6], [15, 13, 14, 18, 16, 17, 24, 22, 23, 21, 19, 20, 6, 4, 5, 3, 1, 2, 9, 7, 8, 12, 10, 11, 39, 37, 38, 42, 40, 41, 48, 46, 47, 45, 43, 44, 30, 28, 29, 27, 25, 26, 33, 31, 32, 36, 34, 35]];
cc:=[6,8,12];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=2;
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:=[[25, 27, 26, 28, 30, 29, 34, 36, 35, 31, 33, 32, 43, 45, 44, 46, 48, 47, 37, 39, 38, 40, 42, 41, 4, 6, 5, 1, 3, 2, 7, 9, 8, 10, 12, 11, 22, 24, 23, 19, 21, 20, 16, 18, 17, 13, 15, 14], [47, 46, 48, 44, 43, 45, 38, 37, 39, 41, 40, 42, 26, 25, 27, 29, 28, 30, 32, 31, 33, 35, 34, 36, 20, 19, 21, 23, 22, 24, 17, 16, 18, 14, 13, 15, 5, 4, 6, 2, 1, 3, 11, 10, 12, 8, 7, 9], [24, 22, 23, 21, 19, 20, 18, 16, 17, 15, 13, 14, 9, 7, 8, 12, 10, 11, 3, 1, 2, 6, 4, 5, 48, 46, 47, 45, 43, 44, 42, 40, 41, 39, 37, 38, 33, 31, 32, 36, 34, 35, 27, 25, 26, 30, 28, 29]];
cc:=[6,9,11];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=3;
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:=[[25, 27, 26, 28, 30, 29, 34, 36, 35, 31, 33, 32, 43, 45, 44, 46, 48, 47, 37, 39, 38, 40, 42, 41, 4, 6, 5, 1, 3, 2, 7, 9, 8, 10, 12, 11, 22, 24, 23, 19, 21, 20, 16, 18, 17, 13, 15, 14], [48, 47, 46, 45, 44, 43, 39, 38, 37, 42, 41, 40, 27, 26, 25, 30, 29, 28, 33, 32, 31, 36, 35, 34, 21, 20, 19, 24, 23, 22, 18, 17, 16, 15, 14, 13, 6, 5, 4, 3, 2, 1, 12, 11, 10, 9, 8, 7], [23, 24, 22, 20, 21, 19, 17, 18, 16, 14, 15, 13, 8, 9, 7, 11, 12, 10, 2, 3, 1, 5, 6, 4, 47, 48, 46, 44, 45, 43, 41, 42, 40, 38, 39, 37, 32, 33, 31, 35, 36, 34, 26, 27, 25, 29, 30, 28]];
cc:=[6,9,12];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=4;
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 >);
