// Magma code for the lmfdb family of higher genus curves 10.162-14.0.2-3-18.6
// 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:=[162,14];
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:=[0,2,3,18];
genus:=10;
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:=[[82, 83, 84, 89, 90, 88, 87, 85, 86, 100, 101, 102, 107, 108, 106, 105, 103, 104, 91, 92, 93, 98, 99, 97, 96, 94, 95, 109, 110, 111, 116, 117, 115, 114, 112, 113, 127, 128, 129, 134, 135, 133, 132, 130, 131, 118, 119, 120, 125, 126, 124, 123, 121, 122, 136, 137, 138, 143, 144, 142, 141, 139, 140, 154, 155, 156, 161, 162, 160, 159, 157, 158, 145, 146, 147, 152, 153, 151, 150, 148, 149, 1, 2, 3, 8, 9, 7, 6, 4, 5, 19, 20, 21, 26, 27, 25, 24, 22, 23, 10, 11, 12, 17, 18, 16, 15, 13, 14, 28, 29, 30, 35, 36, 34, 33, 31, 32, 46, 47, 48, 53, 54, 52, 51, 49, 50, 37, 38, 39, 44, 45, 43, 42, 40, 41, 55, 56, 57, 62, 63, 61, 60, 58, 59, 73, 74, 75, 80, 81, 79, 78, 76, 77, 64, 65, 66, 71, 72, 70, 69, 67, 68], [77, 78, 76, 79, 80, 81, 75, 73, 74, 57, 55, 56, 59, 60, 58, 61, 62, 63, 72, 70, 71, 65, 66, 64, 67, 68, 69, 24, 22, 23, 26, 27, 25, 19, 20, 21, 1, 2, 3, 6, 4, 5, 8, 9, 7, 16, 17, 18, 12, 10, 11, 14, 15, 13, 51, 49, 50, 53, 54, 52, 46, 47, 48, 28, 29, 30, 33, 31, 32, 35, 36, 34, 43, 44, 45, 39, 37, 38, 41, 42, 40, 158, 159, 157, 160, 161, 162, 156, 154, 155, 138, 136, 137, 140, 141, 139, 142, 143, 144, 153, 151, 152, 146, 147, 145, 148, 149, 150, 105, 103, 104, 107, 108, 106, 100, 101, 102, 82, 83, 84, 87, 85, 86, 89, 90, 88, 97, 98, 99, 93, 91, 92, 95, 96, 94, 132, 130, 131, 134, 135, 133, 127, 128, 129, 109, 110, 111, 114, 112, 113, 116, 117, 115, 124, 125, 126, 120, 118, 119, 122, 123, 121], [127, 128, 129, 135, 133, 134, 131, 132, 130, 126, 124, 125, 122, 123, 121, 118, 119, 120, 114, 112, 113, 110, 111, 109, 115, 116, 117, 154, 155, 156, 162, 160, 161, 158, 159, 157, 153, 151, 152, 149, 150, 148, 145, 146, 147, 141, 139, 140, 137, 138, 136, 142, 143, 144, 101, 102, 100, 106, 107, 108, 105, 103, 104, 97, 98, 99, 96, 94, 95, 92, 93, 91, 85, 86, 87, 84, 82, 83, 89, 90, 88, 46, 47, 48, 54, 52, 53, 50, 51, 49, 45, 43, 44, 41, 42, 40, 37, 38, 39, 33, 31, 32, 29, 30, 28, 34, 35, 36, 73, 74, 75, 81, 79, 80, 77, 78, 76, 72, 70, 71, 68, 69, 67, 64, 65, 66, 60, 58, 59, 56, 57, 55, 61, 62, 63, 20, 21, 19, 25, 26, 27, 24, 22, 23, 16, 17, 18, 15, 13, 14, 11, 12, 10, 4, 5, 6, 3, 1, 2, 8, 9, 7]];
cc:=[2,8,21];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=6;
gen_vect_label:=1;
is_hyperelliptic:=false;
is_cyclic_trigonal:=false;
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, is_hyperelliptic:=is_hyperelliptic,is_cyclic_trigonal:=is_cyclic_trigonal >);
