// Magma code for the lmfdb family of higher genus curves 13.144-184.0.3-3-6.1
// 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:=[144,184];
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:=[0,3,3,6];
genus:=13;
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:=[[65, 67, 68, 66, 73, 75, 76, 74, 77, 79, 80, 78, 69, 71, 72, 70, 81, 83, 84, 82, 89, 91, 92, 90, 93, 95, 96, 94, 85, 87, 88, 86, 49, 51, 52, 50, 57, 59, 60, 58, 61, 63, 64, 62, 53, 55, 56, 54, 113, 115, 116, 114, 121, 123, 124, 122, 125, 127, 128, 126, 117, 119, 120, 118, 129, 131, 132, 130, 137, 139, 140, 138, 141, 143, 144, 142, 133, 135, 136, 134, 97, 99, 100, 98, 105, 107, 108, 106, 109, 111, 112, 110, 101, 103, 104, 102, 17, 19, 20, 18, 25, 27, 28, 26, 29, 31, 32, 30, 21, 23, 24, 22, 33, 35, 36, 34, 41, 43, 44, 42, 45, 47, 48, 46, 37, 39, 40, 38, 1, 3, 4, 2, 9, 11, 12, 10, 13, 15, 16, 14, 5, 7, 8, 6], [92, 90, 89, 91, 88, 86, 85, 87, 96, 94, 93, 95, 84, 82, 81, 83, 60, 58, 57, 59, 56, 54, 53, 55, 64, 62, 61, 63, 52, 50, 49, 51, 76, 74, 73, 75, 72, 70, 69, 71, 80, 78, 77, 79, 68, 66, 65, 67, 140, 138, 137, 139, 136, 134, 133, 135, 144, 142, 141, 143, 132, 130, 129, 131, 108, 106, 105, 107, 104, 102, 101, 103, 112, 110, 109, 111, 100, 98, 97, 99, 124, 122, 121, 123, 120, 118, 117, 119, 128, 126, 125, 127, 116, 114, 113, 115, 44, 42, 41, 43, 40, 38, 37, 39, 48, 46, 45, 47, 36, 34, 33, 35, 12, 10, 9, 11, 8, 6, 5, 7, 16, 14, 13, 15, 4, 2, 1, 3, 28, 26, 25, 27, 24, 22, 21, 23, 32, 30, 29, 31, 20, 18, 17, 19], [58, 60, 59, 57, 62, 64, 63, 61, 50, 52, 51, 49, 54, 56, 55, 53, 74, 76, 75, 73, 78, 80, 79, 77, 66, 68, 67, 65, 70, 72, 71, 69, 90, 92, 91, 89, 94, 96, 95, 93, 82, 84, 83, 81, 86, 88, 87, 85, 106, 108, 107, 105, 110, 112, 111, 109, 98, 100, 99, 97, 102, 104, 103, 101, 122, 124, 123, 121, 126, 128, 127, 125, 114, 116, 115, 113, 118, 120, 119, 117, 138, 140, 139, 137, 142, 144, 143, 141, 130, 132, 131, 129, 134, 136, 135, 133, 10, 12, 11, 9, 14, 16, 15, 13, 2, 4, 3, 1, 6, 8, 7, 5, 26, 28, 27, 25, 30, 32, 31, 29, 18, 20, 19, 17, 22, 24, 23, 21, 42, 44, 43, 41, 46, 48, 47, 45, 34, 36, 35, 33, 38, 40, 39, 37]];
cc:=[9,11,15];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
full_auto:=[288,1024];
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>);
