// Magma code for the lmfdb family of higher genus curves 8.42-2.0.3-6-6.2
// 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:=[42,2];
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:=[0,3,6,6];
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:=[[15, 19, 16, 20, 17, 21, 18, 1, 5, 2, 6, 3, 7, 4, 8, 12, 9, 13, 10, 14, 11, 36, 40, 37, 41, 38, 42, 39, 22, 26, 23, 27, 24, 28, 25, 29, 33, 30, 34, 31, 35, 32], [40, 37, 41, 38, 42, 39, 36, 26, 23, 27, 24, 28, 25, 22, 33, 30, 34, 31, 35, 32, 29, 19, 16, 20, 17, 21, 18, 15, 5, 2, 6, 3, 7, 4, 1, 12, 9, 13, 10, 14, 11, 8], [41, 38, 42, 39, 36, 40, 37, 27, 24, 28, 25, 22, 26, 23, 34, 31, 35, 32, 29, 33, 30, 20, 17, 21, 18, 15, 19, 16, 6, 3, 7, 4, 1, 5, 2, 13, 10, 14, 11, 8, 12, 9]];
cc:=[4,6,6];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=2;
gen_vect_label:=1;
full_auto:=[84,7];
full_sign:=[0,2,6,6];
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:=[[15, 19, 16, 20, 17, 21, 18, 1, 5, 2, 6, 3, 7, 4, 8, 12, 9, 13, 10, 14, 11, 36, 40, 37, 41, 38, 42, 39, 22, 26, 23, 27, 24, 28, 25, 29, 33, 30, 34, 31, 35, 32], [41, 38, 42, 39, 36, 40, 37, 27, 24, 28, 25, 22, 26, 23, 34, 31, 35, 32, 29, 33, 30, 20, 17, 21, 18, 15, 19, 16, 6, 3, 7, 4, 1, 5, 2, 13, 10, 14, 11, 8, 12, 9], [37, 41, 38, 42, 39, 36, 40, 23, 27, 24, 28, 25, 22, 26, 30, 34, 31, 35, 32, 29, 33, 16, 20, 17, 21, 18, 15, 19, 2, 6, 3, 7, 4, 1, 5, 9, 13, 10, 14, 11, 8, 12]];
cc:=[4,6,6];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=2;
gen_vect_label:=2;
full_auto:=[84,7];
full_sign:=[0,2,6,6];
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>);
