// Magma code for the lmfdb family of higher genus curves 13.180-19.0.3-3-5.1
// 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:=[180,19];
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:=[0,3,3,5];
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:=[[6, 180, 12, 29, 153, 11, 105, 2, 99, 118, 1, 35, 7, 114, 43, 96, 50, 177, 144, 88, 26, 140, 32, 49, 173, 31, 65, 22, 119, 78, 21, 55, 27, 74, 3, 116, 10, 137, 164, 108, 46, 160, 52, 9, 133, 51, 85, 42, 79, 98, 41, 15, 47, 94, 23, 76, 30, 157, 124, 68, 66, 60, 72, 89, 33, 71, 165, 62, 159, 178, 61, 95, 67, 174, 103, 156, 110, 57, 24, 148, 86, 20, 92, 109, 53, 91, 125, 82, 179, 138, 81, 115, 87, 134, 63, 176, 70, 17, 44, 168, 106, 40, 112, 69, 13, 111, 145, 102, 139, 158, 101, 75, 107, 154, 83, 136, 90, 37, 4, 128, 126, 120, 132, 149, 93, 131, 45, 122, 39, 58, 121, 155, 127, 54, 163, 36, 170, 117, 84, 28, 146, 80, 152, 169, 113, 151, 5, 142, 59, 18, 141, 175, 147, 14, 123, 56, 130, 77, 104, 48, 166, 100, 172, 129, 73, 171, 25, 162, 19, 38, 161, 135, 167, 34, 143, 16, 150, 97, 64, 8], [129, 117, 131, 123, 15, 134, 42, 121, 128, 5, 124, 152, 126, 133, 10, 39, 167, 116, 138, 180, 149, 77, 151, 143, 35, 154, 2, 141, 148, 25, 144, 172, 146, 153, 30, 59, 127, 76, 158, 140, 169, 97, 171, 163, 55, 174, 22, 161, 168, 45, 164, 132, 166, 173, 50, 19, 147, 96, 178, 160, 9, 177, 11, 3, 75, 14, 102, 1, 8, 65, 4, 32, 6, 13, 70, 99, 47, 176, 18, 60, 29, 137, 31, 23, 95, 34, 62, 21, 28, 85, 24, 52, 26, 33, 90, 119, 7, 136, 38, 20, 49, 157, 51, 43, 115, 54, 82, 41, 48, 105, 44, 12, 46, 53, 110, 79, 27, 156, 58, 40, 69, 57, 71, 63, 135, 74, 162, 61, 68, 125, 64, 92, 66, 73, 130, 159, 107, 56, 78, 120, 89, 17, 91, 83, 155, 94, 122, 81, 88, 145, 84, 112, 86, 93, 150, 179, 67, 16, 98, 80, 109, 37, 111, 103, 175, 114, 142, 101, 108, 165, 104, 72, 106, 113, 170, 139, 87, 36, 118, 100], [60, 33, 179, 66, 37, 165, 178, 104, 71, 52, 95, 103, 34, 61, 147, 110, 148, 49, 156, 162, 20, 53, 139, 86, 57, 125, 138, 64, 91, 12, 115, 63, 54, 81, 167, 70, 168, 9, 176, 122, 40, 13, 159, 106, 17, 145, 158, 84, 111, 32, 75, 83, 14, 101, 127, 90, 128, 29, 136, 142, 120, 93, 59, 126, 97, 45, 58, 164, 131, 112, 155, 163, 94, 121, 27, 170, 28, 109, 36, 42, 80, 113, 19, 146, 117, 5, 18, 124, 151, 72, 175, 123, 114, 141, 47, 130, 48, 69, 56, 2, 100, 73, 39, 166, 77, 25, 38, 144, 171, 92, 135, 143, 74, 161, 7, 150, 8, 89, 16, 22, 180, 153, 119, 6, 157, 105, 118, 44, 11, 172, 35, 43, 154, 1, 87, 50, 88, 169, 96, 102, 140, 173, 79, 26, 177, 65, 78, 4, 31, 132, 55, 3, 174, 21, 107, 10, 108, 129, 116, 62, 160, 133, 99, 46, 137, 85, 98, 24, 51, 152, 15, 23, 134, 41, 67, 30, 68, 149, 76, 82]];
cc:=[5,6,8];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
full_auto:=[360,121];
full_sign:=[0,2,3,10];
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>);
