// Magma code for the lmfdb family of higher genus curves 13.52-1.0.4-4-26.12
// 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:=[52,1];
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:=[0,4,4,26];
genus:=13;
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:=[[40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15], [42, 41, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 29, 28, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 3, 2, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 16, 15, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17], [25, 26, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 12, 13, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 51, 52, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 38, 39, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37]];
cc:=[4,4,16];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=12;
gen_vect_label:=1;
full_auto:=[104,5];
full_sign:=[0,2,4,52];
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>);
