// Magma code for the lmfdb family of higher genus curves 10.72-39.0.2-8-8
// 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:=[72,39];
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:=[0,2,8,8];
genus:=10;
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:=[[10, 12, 11, 16, 18, 17, 13, 15, 14, 1, 3, 2, 7, 9, 8, 4, 6, 5, 28, 30, 29, 34, 36, 35, 31, 33, 32, 19, 21, 20, 25, 27, 26, 22, 24, 23, 46, 48, 47, 52, 54, 53, 49, 51, 50, 37, 39, 38, 43, 45, 44, 40, 42, 41, 64, 66, 65, 70, 72, 71, 67, 69, 68, 55, 57, 56, 61, 63, 62, 58, 60, 59], [45, 38, 40, 43, 39, 41, 44, 37, 42, 54, 47, 49, 52, 48, 50, 53, 46, 51, 63, 56, 58, 61, 57, 59, 62, 55, 60, 72, 65, 67, 70, 66, 68, 71, 64, 69, 27, 20, 22, 25, 21, 23, 26, 19, 24, 36, 29, 31, 34, 30, 32, 35, 28, 33, 18, 11, 13, 16, 12, 14, 17, 10, 15, 9, 2, 4, 7, 3, 5, 8, 1, 6], [60, 57, 63, 56, 62, 59, 61, 58, 55, 69, 66, 72, 65, 71, 68, 70, 67, 64, 51, 48, 54, 47, 53, 50, 52, 49, 46, 42, 39, 45, 38, 44, 41, 43, 40, 37, 15, 12, 18, 11, 17, 14, 16, 13, 10, 6, 3, 9, 2, 8, 5, 7, 4, 1, 33, 30, 36, 29, 35, 32, 34, 31, 28, 24, 21, 27, 20, 26, 23, 25, 22, 19]];
cc:=[2,6,7];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
full_auto:=[432,734];
full_sign:=[0,2,3,8];
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>);

// Here we add an action to data.
gen_vectors:=[[10, 12, 11, 16, 18, 17, 13, 15, 14, 1, 3, 2, 7, 9, 8, 4, 6, 5, 28, 30, 29, 34, 36, 35, 31, 33, 32, 19, 21, 20, 25, 27, 26, 22, 24, 23, 46, 48, 47, 52, 54, 53, 49, 51, 50, 37, 39, 38, 43, 45, 44, 40, 42, 41, 64, 66, 65, 70, 72, 71, 67, 69, 68, 55, 57, 56, 61, 63, 62, 58, 60, 59], [49, 47, 54, 51, 46, 53, 50, 48, 52, 40, 38, 45, 42, 37, 44, 41, 39, 43, 67, 65, 72, 69, 64, 71, 68, 66, 70, 58, 56, 63, 60, 55, 62, 59, 57, 61, 31, 29, 36, 33, 28, 35, 32, 30, 34, 22, 20, 27, 24, 19, 26, 23, 21, 25, 4, 2, 9, 6, 1, 8, 5, 3, 7, 13, 11, 18, 15, 10, 17, 14, 12, 16], [72, 66, 69, 64, 67, 70, 68, 71, 65, 63, 57, 60, 55, 58, 61, 59, 62, 56, 45, 39, 42, 37, 40, 43, 41, 44, 38, 54, 48, 51, 46, 49, 52, 50, 53, 47, 9, 3, 6, 1, 4, 7, 5, 8, 2, 18, 12, 15, 10, 13, 16, 14, 17, 11, 27, 21, 24, 19, 22, 25, 23, 26, 20, 36, 30, 33, 28, 31, 34, 32, 35, 29]];
cc:=[2,8,9];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=2;
gen_vect_label:=1;
full_auto:=[432,734];
full_sign:=[0,2,3,8];
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>);
