// Magma code for the lmfdb family of higher genus curves 4.36-11.0.3-3-6.4
// 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:=[36,11];
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:=[0,3,3,6];
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:=[[25, 27, 28, 26, 29, 31, 32, 30, 33, 35, 36, 34, 1, 3, 4, 2, 5, 7, 8, 6, 9, 11, 12, 10, 13, 15, 16, 14, 17, 19, 20, 18, 21, 23, 24, 22], [23, 22, 24, 21, 15, 14, 16, 13, 19, 18, 20, 17, 35, 34, 36, 33, 27, 26, 28, 25, 31, 30, 32, 29, 11, 10, 12, 9, 3, 2, 4, 1, 7, 6, 8, 5], [7, 8, 5, 6, 11, 12, 9, 10, 3, 4, 1, 2, 19, 20, 17, 18, 23, 24, 21, 22, 15, 16, 13, 14, 31, 32, 29, 30, 35, 36, 33, 34, 27, 28, 25, 26]];
cc:=[6,9,11];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=4;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
full_auto:=[72,42];
full_sign:=[0,2,3,12];
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>);
