// Magma code for the lmfdb family of higher genus curves 4.72-42.0.2-3-12.2
// 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:=[72,42];
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:=[0,2,3,12];
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:=[[37, 39, 38, 40, 45, 47, 46, 48, 41, 43, 42, 44, 49, 51, 50, 52, 57, 59, 58, 60, 53, 55, 54, 56, 61, 63, 62, 64, 69, 71, 70, 72, 65, 67, 66, 68, 1, 3, 2, 4, 9, 11, 10, 12, 5, 7, 6, 8, 13, 15, 14, 16, 21, 23, 22, 24, 17, 19, 18, 20, 25, 27, 26, 28, 33, 35, 34, 36, 29, 31, 30, 32], [36, 34, 33, 35, 28, 26, 25, 27, 32, 30, 29, 31, 12, 10, 9, 11, 4, 2, 1, 3, 8, 6, 5, 7, 24, 22, 21, 23, 16, 14, 13, 15, 20, 18, 17, 19, 72, 70, 69, 71, 64, 62, 61, 63, 68, 66, 65, 67, 48, 46, 45, 47, 40, 38, 37, 39, 44, 42, 41, 43, 60, 58, 57, 59, 52, 50, 49, 51, 56, 54, 53, 55], [58, 59, 60, 57, 54, 55, 56, 53, 50, 51, 52, 49, 70, 71, 72, 69, 66, 67, 68, 65, 62, 63, 64, 61, 46, 47, 48, 45, 42, 43, 44, 41, 38, 39, 40, 37, 22, 23, 24, 21, 18, 19, 20, 17, 14, 15, 16, 13, 34, 35, 36, 33, 30, 31, 32, 29, 26, 27, 28, 25, 10, 11, 12, 9, 6, 7, 8, 5, 2, 3, 4, 1]];
cc:=[3,8,14];
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:=false;
is_cyclic_trigonal:=true;
cyc_auto:=S![13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48];
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 >);
