// Magma code for the lmfdb family of higher genus curves 4.72-40.0.2-4-6.1
// 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:=[72,40];
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:=[0,2,4,6];
genus:=4;
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:=[[19, 22, 25, 20, 23, 26, 21, 24, 27, 28, 31, 34, 29, 32, 35, 30, 33, 36, 1, 4, 7, 2, 5, 8, 3, 6, 9, 10, 13, 16, 11, 14, 17, 12, 15, 18, 55, 58, 61, 56, 59, 62, 57, 60, 63, 64, 67, 70, 65, 68, 71, 66, 69, 72, 37, 40, 43, 38, 41, 44, 39, 42, 45, 46, 49, 52, 47, 50, 53, 48, 51, 54], [60, 63, 57, 59, 62, 56, 58, 61, 55, 69, 72, 66, 68, 71, 65, 67, 70, 64, 51, 54, 48, 50, 53, 47, 49, 52, 46, 42, 45, 39, 41, 44, 38, 40, 43, 37, 24, 27, 21, 23, 26, 20, 22, 25, 19, 33, 36, 30, 32, 35, 29, 31, 34, 28, 15, 18, 12, 14, 17, 11, 13, 16, 10, 6, 9, 3, 5, 8, 2, 4, 7, 1], [54, 53, 52, 48, 47, 46, 51, 50, 49, 45, 44, 43, 39, 38, 37, 42, 41, 40, 63, 62, 61, 57, 56, 55, 60, 59, 58, 72, 71, 70, 66, 65, 64, 69, 68, 67, 18, 17, 16, 12, 11, 10, 15, 14, 13, 9, 8, 7, 3, 2, 1, 6, 5, 4, 27, 26, 25, 21, 20, 19, 24, 23, 22, 36, 35, 34, 30, 29, 28, 33, 32, 31]];
cc:=[2,7,9];
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:=false;
is_cyclic_trigonal:=true;
cyc_auto:=S![2, 3, 1, 5, 6, 4, 8, 9, 7, 11, 12, 10, 14, 15, 13, 17, 18, 16, 20, 21, 19, 23, 24, 22, 26, 27, 25, 29, 30, 28, 32, 33, 31, 35, 36, 34, 38, 39, 37, 41, 42, 40, 44, 45, 43, 47, 48, 46, 50, 51, 49, 53, 54, 52, 56, 57, 55, 59, 60, 58, 62, 63, 61, 65, 66, 64, 68, 69, 67, 71, 72, 70];
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 >);
