// Magma code for the lmfdb family of higher genus curves 4.60-5.0.2-5-5.1
// 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:=[0,2,5,5];
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:=[[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], [2, 54, 1, 55, 3, 7, 39, 6, 40, 8, 12, 24, 11, 25, 13, 17, 49, 16, 50, 18, 22, 14, 21, 15, 23, 27, 59, 26, 60, 28, 32, 44, 31, 45, 33, 37, 9, 36, 10, 38, 42, 34, 41, 35, 43, 47, 19, 46, 20, 48, 52, 4, 51, 5, 53, 57, 29, 56, 30, 58], [53, 14, 12, 45, 41, 38, 4, 2, 20, 16, 23, 9, 7, 30, 26, 48, 39, 37, 55, 51, 13, 34, 32, 5, 1, 58, 24, 22, 40, 36, 43, 29, 27, 50, 46, 8, 59, 57, 15, 11, 33, 54, 52, 25, 21, 18, 44, 42, 60, 56, 3, 49, 47, 10, 6, 28, 19, 17, 35, 31]];
cc:=[2,4,5];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
full_auto:=[120,34];
full_sign:=[0,2,4,5];
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, full_auto:=full_auto, full_sign:=full_sign>);
