// Magma code for the lmfdb family of higher genus curves 13.96-68.0.3-4-6.1
// 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:=[96,68];
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:=[0,3,4,6];
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:=[[17, 20, 18, 19, 30, 31, 29, 32, 21, 24, 22, 23, 28, 25, 27, 26, 33, 36, 34, 35, 46, 47, 45, 48, 37, 40, 38, 39, 44, 41, 43, 42, 1, 4, 2, 3, 14, 15, 13, 16, 5, 8, 6, 7, 12, 9, 11, 10, 65, 68, 66, 67, 78, 79, 77, 80, 69, 72, 70, 71, 76, 73, 75, 74, 81, 84, 82, 83, 94, 95, 93, 96, 85, 88, 86, 87, 92, 89, 91, 90, 49, 52, 50, 51, 62, 63, 61, 64, 53, 56, 54, 55, 60, 57, 59, 58], [53, 54, 55, 56, 51, 52, 49, 50, 61, 62, 63, 64, 59, 60, 57, 58, 69, 70, 71, 72, 67, 68, 65, 66, 77, 78, 79, 80, 75, 76, 73, 74, 85, 86, 87, 88, 83, 84, 81, 82, 93, 94, 95, 96, 91, 92, 89, 90, 5, 6, 7, 8, 3, 4, 1, 2, 13, 14, 15, 16, 11, 12, 9, 10, 21, 22, 23, 24, 19, 20, 17, 18, 29, 30, 31, 32, 27, 28, 25, 26, 37, 38, 39, 40, 35, 36, 33, 34, 45, 46, 47, 48, 43, 44, 41, 42], [92, 90, 89, 91, 81, 83, 84, 82, 86, 88, 87, 85, 94, 96, 95, 93, 60, 58, 57, 59, 49, 51, 52, 50, 54, 56, 55, 53, 62, 64, 63, 61, 76, 74, 73, 75, 65, 67, 68, 66, 70, 72, 71, 69, 78, 80, 79, 77, 44, 42, 41, 43, 33, 35, 36, 34, 38, 40, 39, 37, 46, 48, 47, 45, 12, 10, 9, 11, 1, 3, 4, 2, 6, 8, 7, 5, 14, 16, 15, 13, 28, 26, 25, 27, 17, 19, 20, 18, 22, 24, 23, 21, 30, 32, 31, 29]];
cc:=[5,11,16];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
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, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);
