// Magma code for the lmfdb family of higher genus curves 10.144-182.0.2-4-8.1
// 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:=[144,182];
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:=[0,2,4,8];
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:=[[37, 39, 38, 42, 41, 40, 44, 43, 45, 46, 48, 47, 51, 50, 49, 53, 52, 54, 64, 66, 65, 69, 68, 67, 71, 70, 72, 55, 57, 56, 60, 59, 58, 62, 61, 63, 1, 3, 2, 6, 5, 4, 8, 7, 9, 10, 12, 11, 15, 14, 13, 17, 16, 18, 28, 30, 29, 33, 32, 31, 35, 34, 36, 19, 21, 20, 24, 23, 22, 26, 25, 27, 109, 111, 110, 114, 113, 112, 116, 115, 117, 118, 120, 119, 123, 122, 121, 125, 124, 126, 136, 138, 137, 141, 140, 139, 143, 142, 144, 127, 129, 128, 132, 131, 130, 134, 133, 135, 73, 75, 74, 78, 77, 76, 80, 79, 81, 82, 84, 83, 87, 86, 85, 89, 88, 90, 100, 102, 101, 105, 104, 103, 107, 106, 108, 91, 93, 92, 96, 95, 94, 98, 97, 99], [119, 125, 122, 120, 126, 123, 118, 124, 121, 110, 116, 113, 111, 117, 114, 109, 115, 112, 128, 134, 131, 129, 135, 132, 127, 133, 130, 137, 143, 140, 138, 144, 141, 136, 142, 139, 101, 107, 104, 102, 108, 105, 100, 106, 103, 92, 98, 95, 93, 99, 96, 91, 97, 94, 83, 89, 86, 84, 90, 87, 82, 88, 85, 74, 80, 77, 75, 81, 78, 73, 79, 76, 56, 62, 59, 57, 63, 60, 55, 61, 58, 65, 71, 68, 66, 72, 69, 64, 70, 67, 38, 44, 41, 39, 45, 42, 37, 43, 40, 47, 53, 50, 48, 54, 51, 46, 52, 49, 2, 8, 5, 3, 9, 6, 1, 7, 4, 11, 17, 14, 12, 18, 15, 10, 16, 13, 29, 35, 32, 30, 36, 33, 28, 34, 31, 20, 26, 23, 21, 27, 24, 19, 25, 22], [80, 73, 78, 81, 74, 76, 79, 75, 77, 89, 82, 87, 90, 83, 85, 88, 84, 86, 98, 91, 96, 99, 92, 94, 97, 93, 95, 107, 100, 105, 108, 101, 103, 106, 102, 104, 143, 136, 141, 144, 137, 139, 142, 138, 140, 134, 127, 132, 135, 128, 130, 133, 129, 131, 116, 109, 114, 117, 110, 112, 115, 111, 113, 125, 118, 123, 126, 119, 121, 124, 120, 122, 26, 19, 24, 27, 20, 22, 25, 21, 23, 35, 28, 33, 36, 29, 31, 34, 30, 32, 17, 10, 15, 18, 11, 13, 16, 12, 14, 8, 1, 6, 9, 2, 4, 7, 3, 5, 53, 46, 51, 54, 47, 49, 52, 48, 50, 44, 37, 42, 45, 38, 40, 43, 39, 41, 71, 64, 69, 72, 65, 67, 70, 66, 68, 62, 55, 60, 63, 56, 58, 61, 57, 59]];
cc:=[3,6,8];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
full_auto:=[432,734];
full_sign:=[0,2,3,8];
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>);
