// Magma code for the lmfdb family of higher genus curves 14.78-1.0.3-6-6.1
// 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:=[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:=[[14, 17, 20, 23, 26, 16, 19, 22, 25, 15, 18, 21, 24, 27, 30, 33, 36, 39, 29, 32, 35, 38, 28, 31, 34, 37, 1, 4, 7, 10, 13, 3, 6, 9, 12, 2, 5, 8, 11, 53, 56, 59, 62, 65, 55, 58, 61, 64, 54, 57, 60, 63, 66, 69, 72, 75, 78, 68, 71, 74, 77, 67, 70, 73, 76, 40, 43, 46, 49, 52, 42, 45, 48, 51, 41, 44, 47, 50], [57, 54, 64, 61, 58, 55, 65, 62, 59, 56, 53, 63, 60, 70, 67, 77, 74, 71, 68, 78, 75, 72, 69, 66, 76, 73, 44, 41, 51, 48, 45, 42, 52, 49, 46, 43, 40, 50, 47, 18, 15, 25, 22, 19, 16, 26, 23, 20, 17, 14, 24, 21, 31, 28, 38, 35, 32, 29, 39, 36, 33, 30, 27, 37, 34, 5, 2, 12, 9, 6, 3, 13, 10, 7, 4, 1, 11, 8], [65, 62, 59, 56, 53, 63, 60, 57, 54, 64, 61, 58, 55, 78, 75, 72, 69, 66, 76, 73, 70, 67, 77, 74, 71, 68, 52, 49, 46, 43, 40, 50, 47, 44, 41, 51, 48, 45, 42, 26, 23, 20, 17, 14, 24, 21, 18, 15, 25, 22, 19, 16, 39, 36, 33, 30, 27, 37, 34, 31, 28, 38, 35, 32, 29, 13, 10, 7, 4, 1, 11, 8, 5, 2, 12, 9, 6, 3]];
cc:=[3,5,5];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
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:=[[14, 17, 20, 23, 26, 16, 19, 22, 25, 15, 18, 21, 24, 27, 30, 33, 36, 39, 29, 32, 35, 38, 28, 31, 34, 37, 1, 4, 7, 10, 13, 3, 6, 9, 12, 2, 5, 8, 11, 53, 56, 59, 62, 65, 55, 58, 61, 64, 54, 57, 60, 63, 66, 69, 72, 75, 78, 68, 71, 74, 77, 67, 70, 73, 76, 40, 43, 46, 49, 52, 42, 45, 48, 51, 41, 44, 47, 50], [61, 58, 55, 65, 62, 59, 56, 53, 63, 60, 57, 54, 64, 74, 71, 68, 78, 75, 72, 69, 66, 76, 73, 70, 67, 77, 48, 45, 42, 52, 49, 46, 43, 40, 50, 47, 44, 41, 51, 22, 19, 16, 26, 23, 20, 17, 14, 24, 21, 18, 15, 25, 35, 32, 29, 39, 36, 33, 30, 27, 37, 34, 31, 28, 38, 9, 6, 3, 13, 10, 7, 4, 1, 11, 8, 5, 2, 12], [64, 61, 58, 55, 65, 62, 59, 56, 53, 63, 60, 57, 54, 77, 74, 71, 68, 78, 75, 72, 69, 66, 76, 73, 70, 67, 51, 48, 45, 42, 52, 49, 46, 43, 40, 50, 47, 44, 41, 25, 22, 19, 16, 26, 23, 20, 17, 14, 24, 21, 18, 15, 38, 35, 32, 29, 39, 36, 33, 30, 27, 37, 34, 31, 28, 12, 9, 6, 3, 13, 10, 7, 4, 1, 11, 8, 5, 2]];
cc:=[3,5,5];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
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>);
