// Magma code for the lmfdb family of higher genus curves 14.78-1.0.3-6-6.2
// 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:=[78,1];
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:=[0,3,6,6];
genus:=14;
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:=[[27, 36, 32, 28, 37, 33, 29, 38, 34, 30, 39, 35, 31, 1, 10, 6, 2, 11, 7, 3, 12, 8, 4, 13, 9, 5, 14, 23, 19, 15, 24, 20, 16, 25, 21, 17, 26, 22, 18, 66, 75, 71, 67, 76, 72, 68, 77, 73, 69, 78, 74, 70, 40, 49, 45, 41, 50, 46, 42, 51, 47, 43, 52, 48, 44, 53, 62, 58, 54, 63, 59, 55, 64, 60, 56, 65, 61, 57], [76, 67, 71, 75, 66, 70, 74, 78, 69, 73, 77, 68, 72, 50, 41, 45, 49, 40, 44, 48, 52, 43, 47, 51, 42, 46, 63, 54, 58, 62, 53, 57, 61, 65, 56, 60, 64, 55, 59, 37, 28, 32, 36, 27, 31, 35, 39, 30, 34, 38, 29, 33, 11, 2, 6, 10, 1, 5, 9, 13, 4, 8, 12, 3, 7, 24, 15, 19, 23, 14, 18, 22, 26, 17, 21, 25, 16, 20], [78, 69, 73, 77, 68, 72, 76, 67, 71, 75, 66, 70, 74, 52, 43, 47, 51, 42, 46, 50, 41, 45, 49, 40, 44, 48, 65, 56, 60, 64, 55, 59, 63, 54, 58, 62, 53, 57, 61, 39, 30, 34, 38, 29, 33, 37, 28, 32, 36, 27, 31, 35, 13, 4, 8, 12, 3, 7, 11, 2, 6, 10, 1, 5, 9, 26, 17, 21, 25, 16, 20, 24, 15, 19, 23, 14, 18, 22]];
cc:=[4,6,6];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=2;
gen_vect_label:=1;
full_auto:=[156,8];
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:=[[27, 36, 32, 28, 37, 33, 29, 38, 34, 30, 39, 35, 31, 1, 10, 6, 2, 11, 7, 3, 12, 8, 4, 13, 9, 5, 14, 23, 19, 15, 24, 20, 16, 25, 21, 17, 26, 22, 18, 66, 75, 71, 67, 76, 72, 68, 77, 73, 69, 78, 74, 70, 40, 49, 45, 41, 50, 46, 42, 51, 47, 43, 52, 48, 44, 53, 62, 58, 54, 63, 59, 55, 64, 60, 56, 65, 61, 57], [73, 77, 68, 72, 76, 67, 71, 75, 66, 70, 74, 78, 69, 47, 51, 42, 46, 50, 41, 45, 49, 40, 44, 48, 52, 43, 60, 64, 55, 59, 63, 54, 58, 62, 53, 57, 61, 65, 56, 34, 38, 29, 33, 37, 28, 32, 36, 27, 31, 35, 39, 30, 8, 12, 3, 7, 11, 2, 6, 10, 1, 5, 9, 13, 4, 21, 25, 16, 20, 24, 15, 19, 23, 14, 18, 22, 26, 17], [77, 68, 72, 76, 67, 71, 75, 66, 70, 74, 78, 69, 73, 51, 42, 46, 50, 41, 45, 49, 40, 44, 48, 52, 43, 47, 64, 55, 59, 63, 54, 58, 62, 53, 57, 61, 65, 56, 60, 38, 29, 33, 37, 28, 32, 36, 27, 31, 35, 39, 30, 34, 12, 3, 7, 11, 2, 6, 10, 1, 5, 9, 13, 4, 8, 25, 16, 20, 24, 15, 19, 23, 14, 18, 22, 26, 17, 21]];
cc:=[4,6,6];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=2;
gen_vect_label:=2;
full_auto:=[156,8];
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>);
