// Magma code for the lmfdb family of higher genus curves 15.84-1.0.3-4-12.1
// 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:=[84,1];
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:=[0,3,4,12];
genus:=15;
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, 22, 26, 23, 27, 24, 28, 25, 29, 33, 30, 34, 31, 35, 32, 36, 40, 37, 41, 38, 42, 39, 1, 5, 2, 6, 3, 7, 4, 8, 12, 9, 13, 10, 14, 11, 57, 61, 58, 62, 59, 63, 60, 64, 68, 65, 69, 66, 70, 67, 71, 75, 72, 76, 73, 77, 74, 78, 82, 79, 83, 80, 84, 81, 43, 47, 44, 48, 45, 49, 46, 50, 54, 51, 55, 52, 56, 53], [45, 44, 43, 49, 48, 47, 46, 52, 51, 50, 56, 55, 54, 53, 59, 58, 57, 63, 62, 61, 60, 66, 65, 64, 70, 69, 68, 67, 73, 72, 71, 77, 76, 75, 74, 80, 79, 78, 84, 83, 82, 81, 10, 9, 8, 14, 13, 12, 11, 3, 2, 1, 7, 6, 5, 4, 24, 23, 22, 28, 27, 26, 25, 17, 16, 15, 21, 20, 19, 18, 38, 37, 36, 42, 41, 40, 39, 31, 30, 29, 35, 34, 33, 32], [82, 80, 78, 83, 81, 79, 84, 75, 73, 71, 76, 74, 72, 77, 54, 52, 50, 55, 53, 51, 56, 47, 45, 43, 48, 46, 44, 49, 68, 66, 64, 69, 67, 65, 70, 61, 59, 57, 62, 60, 58, 63, 33, 31, 29, 34, 32, 30, 35, 40, 38, 36, 41, 39, 37, 42, 5, 3, 1, 6, 4, 2, 7, 12, 10, 8, 13, 11, 9, 14, 19, 17, 15, 20, 18, 16, 21, 26, 24, 22, 27, 25, 23, 28]];
cc:=[3,5,13];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
full_auto:=[336,134];
full_sign:=[0,2,3,12];
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>);
