// Magma code for the lmfdb family of higher genus curves 8.24-1.0.6-8-8
// 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:=[24,1];
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:=[0,6,8,8];
genus:=8;
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:=[[5, 6, 4, 2, 3, 1, 11, 12, 10, 8, 9, 7, 17, 18, 16, 14, 15, 13, 23, 24, 22, 20, 21, 19], [13, 15, 14, 16, 18, 17, 19, 21, 20, 22, 24, 23, 7, 9, 8, 10, 12, 11, 4, 6, 5, 1, 3, 2], [21, 20, 19, 24, 23, 22, 18, 17, 16, 15, 14, 13, 6, 5, 4, 3, 2, 1, 12, 11, 10, 9, 8, 7]];
cc:=[6,7,8];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
full_auto:=[48,17];
full_sign:=[0,2,8,12];
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>);

// Here we add an action to data.
gen_vectors:=[[5, 6, 4, 2, 3, 1, 11, 12, 10, 8, 9, 7, 17, 18, 16, 14, 15, 13, 23, 24, 22, 20, 21, 19], [16, 18, 17, 13, 15, 14, 22, 24, 23, 19, 21, 20, 10, 12, 11, 7, 9, 8, 1, 3, 2, 4, 6, 5], [24, 23, 22, 21, 20, 19, 15, 14, 13, 18, 17, 16, 3, 2, 1, 6, 5, 4, 9, 8, 7, 12, 11, 10]];
cc:=[6,9,10];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=2;
gen_vect_label:=1;
full_auto:=[48,17];
full_sign:=[0,2,8,12];
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>);
