// Magma code for the lmfdb family of higher genus curves 6.60-5.0.2-2-2-3.1
// 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:=[60,5];
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:=[0,2,2,2,3];
genus:=6;
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:=[[14, 10, 53, 6, 12, 4, 15, 38, 11, 2, 9, 5, 23, 1, 7, 39, 60, 48, 56, 37, 34, 30, 13, 26, 32, 24, 35, 58, 31, 22, 29, 25, 43, 21, 27, 59, 20, 8, 16, 57, 54, 50, 33, 46, 52, 44, 55, 18, 51, 42, 49, 45, 3, 41, 47, 19, 40, 28, 36, 17], [51, 25, 24, 43, 42, 36, 55, 54, 18, 17, 21, 40, 39, 28, 27, 46, 10, 9, 53, 52, 11, 45, 44, 3, 2, 56, 15, 14, 38, 37, 41, 60, 59, 48, 47, 6, 30, 29, 13, 12, 31, 5, 4, 23, 22, 16, 35, 34, 58, 57, 1, 20, 19, 8, 7, 26, 50, 49, 33, 32], [39, 43, 22, 46, 55, 24, 18, 52, 56, 40, 54, 28, 37, 31, 25, 29, 53, 7, 41, 50, 59, 3, 42, 6, 15, 44, 38, 12, 16, 60, 14, 48, 57, 51, 45, 49, 13, 27, 1, 10, 19, 23, 2, 26, 35, 4, 58, 32, 36, 20, 34, 8, 17, 11, 5, 9, 33, 47, 21, 30], [23, 6, 52, 39, 15, 53, 11, 37, 24, 5, 38, 1, 22, 54, 10, 8, 56, 47, 29, 40, 43, 26, 12, 59, 35, 13, 31, 57, 44, 25, 58, 21, 42, 14, 30, 28, 16, 7, 49, 60, 3, 46, 32, 19, 55, 33, 51, 17, 4, 45, 18, 41, 2, 34, 50, 48, 36, 27, 9, 20]];
cc:=[2,2,2,3];
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, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);
