// Magma code for the lmfdb family of higher genus curves 5.60-5.0.3-3-5.2
// 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:=[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:=[0,3,3,5];
genus:=5;
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:=[[4, 21, 13, 42, 45, 9, 51, 3, 17, 20, 14, 36, 8, 27, 30, 19, 6, 38, 52, 55, 24, 41, 33, 2, 5, 29, 11, 23, 37, 40, 34, 56, 28, 47, 50, 39, 26, 58, 12, 15, 44, 1, 53, 22, 25, 49, 31, 43, 57, 60, 54, 16, 48, 7, 10, 59, 46, 18, 32, 35], [31, 40, 17, 24, 28, 46, 25, 27, 54, 43, 56, 55, 42, 39, 18, 1, 30, 32, 9, 13, 51, 60, 37, 44, 48, 6, 45, 47, 14, 3, 16, 15, 2, 59, 38, 21, 50, 52, 29, 33, 11, 20, 57, 4, 8, 26, 5, 7, 34, 23, 36, 35, 22, 19, 58, 41, 10, 12, 49, 53], [52, 23, 15, 41, 34, 37, 53, 5, 16, 49, 22, 38, 10, 26, 59, 47, 8, 40, 51, 4, 12, 43, 35, 1, 54, 57, 13, 25, 36, 9, 42, 58, 30, 46, 19, 7, 28, 60, 11, 24, 32, 3, 55, 21, 14, 17, 33, 45, 56, 29, 2, 18, 50, 6, 39, 27, 48, 20, 31, 44]];
cc:=[3,3,5];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=2;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
full_auto:=[120,35];
full_sign:=[0,2,3,10];
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>);
