// Magma code for the lmfdb family of higher genus curves 5.96-3.0.3-3-4.2
// 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:=[96,3];
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:=[0,3,3,4];
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:=[[33, 34, 40, 39, 36, 35, 37, 38, 59, 60, 62, 61, 58, 57, 63, 64, 41, 42, 48, 47, 44, 43, 45, 46, 56, 55, 49, 50, 53, 54, 52, 51, 65, 66, 72, 71, 68, 67, 69, 70, 91, 92, 94, 93, 90, 89, 95, 96, 73, 74, 80, 79, 76, 75, 77, 78, 88, 87, 81, 82, 85, 86, 84, 83, 1, 2, 8, 7, 4, 3, 5, 6, 27, 28, 30, 29, 26, 25, 31, 32, 9, 10, 16, 15, 12, 11, 13, 14, 24, 23, 17, 18, 21, 22, 20, 19], [92, 91, 95, 96, 94, 93, 89, 90, 78, 77, 73, 74, 76, 75, 79, 80, 67, 68, 72, 71, 69, 70, 66, 65, 84, 83, 87, 88, 86, 85, 81, 82, 28, 27, 31, 32, 30, 29, 25, 26, 14, 13, 9, 10, 12, 11, 15, 16, 3, 4, 8, 7, 5, 6, 2, 1, 20, 19, 23, 24, 22, 21, 17, 18, 60, 59, 63, 64, 62, 61, 57, 58, 46, 45, 41, 42, 44, 43, 47, 48, 35, 36, 40, 39, 37, 38, 34, 33, 52, 51, 55, 56, 54, 53, 49, 50], [25, 26, 27, 28, 29, 30, 31, 32, 22, 21, 24, 23, 18, 17, 20, 19, 15, 16, 13, 14, 11, 12, 9, 10, 4, 3, 2, 1, 8, 7, 6, 5, 57, 58, 59, 60, 61, 62, 63, 64, 54, 53, 56, 55, 50, 49, 52, 51, 47, 48, 45, 46, 43, 44, 41, 42, 36, 35, 34, 33, 40, 39, 38, 37, 89, 90, 91, 92, 93, 94, 95, 96, 86, 85, 88, 87, 82, 81, 84, 83, 79, 80, 77, 78, 75, 76, 73, 74, 68, 67, 66, 65, 72, 71, 70, 69]];
cc:=[5,6,8];
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:=[192,181];
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>);
