// Magma code for the lmfdb family of higher genus curves 14.40-3.0.8-8-10
// 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:=[40,3];
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:=[0,8,8,10];
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:=[[21, 23, 25, 22, 24, 26, 28, 30, 27, 29, 31, 33, 35, 32, 34, 36, 38, 40, 37, 39, 11, 13, 15, 12, 14, 16, 18, 20, 17, 19, 6, 8, 10, 7, 9, 1, 3, 5, 2, 4], [34, 32, 35, 33, 31, 39, 37, 40, 38, 36, 29, 27, 30, 28, 26, 24, 22, 25, 23, 21, 9, 7, 10, 8, 6, 4, 2, 5, 3, 1, 19, 17, 20, 18, 16, 14, 12, 15, 13, 11], [8, 9, 10, 6, 7, 3, 4, 5, 1, 2, 18, 19, 20, 16, 17, 13, 14, 15, 11, 12, 28, 29, 30, 26, 27, 23, 24, 25, 21, 22, 38, 39, 40, 36, 37, 33, 34, 35, 31, 32]];
cc:=[6,7,10];
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:=[[26, 28, 30, 27, 29, 21, 23, 25, 22, 24, 36, 38, 40, 37, 39, 31, 33, 35, 32, 34, 16, 18, 20, 17, 19, 11, 13, 15, 12, 14, 1, 3, 5, 2, 4, 6, 8, 10, 7, 9], [39, 37, 40, 38, 36, 34, 32, 35, 33, 31, 24, 22, 25, 23, 21, 29, 27, 30, 28, 26, 4, 2, 5, 3, 1, 9, 7, 10, 8, 6, 14, 12, 15, 13, 11, 19, 17, 20, 18, 16], [8, 9, 10, 6, 7, 3, 4, 5, 1, 2, 18, 19, 20, 16, 17, 13, 14, 15, 11, 12, 28, 29, 30, 26, 27, 23, 24, 25, 21, 22, 38, 39, 40, 36, 37, 33, 34, 35, 31, 32]];
cc:=[8,9,10];
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 >);
