// Magma code for the lmfdb family of higher genus curves 15.144-109.0.2-4-18.1
// 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:=[144,109];
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:=[0,2,4,18];
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:=[[73, 75, 74, 76, 81, 83, 82, 84, 77, 79, 78, 80, 101, 103, 102, 104, 97, 99, 98, 100, 105, 107, 106, 108, 89, 91, 90, 92, 85, 87, 86, 88, 93, 95, 94, 96, 109, 111, 110, 112, 117, 119, 118, 120, 113, 115, 114, 116, 137, 139, 138, 140, 133, 135, 134, 136, 141, 143, 142, 144, 125, 127, 126, 128, 121, 123, 122, 124, 129, 131, 130, 132, 1, 3, 2, 4, 9, 11, 10, 12, 5, 7, 6, 8, 29, 31, 30, 32, 25, 27, 26, 28, 33, 35, 34, 36, 17, 19, 18, 20, 13, 15, 14, 16, 21, 23, 22, 24, 37, 39, 38, 40, 45, 47, 46, 48, 41, 43, 42, 44, 65, 67, 66, 68, 61, 63, 62, 64, 69, 71, 70, 72, 53, 55, 54, 56, 49, 51, 50, 52, 57, 59, 58, 60], [140, 137, 138, 139, 136, 133, 134, 135, 144, 141, 142, 143, 128, 125, 126, 127, 124, 121, 122, 123, 132, 129, 130, 131, 116, 113, 114, 115, 112, 109, 110, 111, 120, 117, 118, 119, 104, 101, 102, 103, 100, 97, 98, 99, 108, 105, 106, 107, 92, 89, 90, 91, 88, 85, 86, 87, 96, 93, 94, 95, 80, 77, 78, 79, 76, 73, 74, 75, 84, 81, 82, 83, 68, 65, 66, 67, 64, 61, 62, 63, 72, 69, 70, 71, 56, 53, 54, 55, 52, 49, 50, 51, 60, 57, 58, 59, 44, 41, 42, 43, 40, 37, 38, 39, 48, 45, 46, 47, 32, 29, 30, 31, 28, 25, 26, 27, 36, 33, 34, 35, 20, 17, 18, 19, 16, 13, 14, 15, 24, 21, 22, 23, 8, 5, 6, 7, 4, 1, 2, 3, 12, 9, 10, 11], [51, 50, 52, 49, 55, 54, 56, 53, 59, 58, 60, 57, 63, 62, 64, 61, 67, 66, 68, 65, 71, 70, 72, 69, 47, 46, 48, 45, 39, 38, 40, 37, 43, 42, 44, 41, 15, 14, 16, 13, 19, 18, 20, 17, 23, 22, 24, 21, 27, 26, 28, 25, 31, 30, 32, 29, 35, 34, 36, 33, 11, 10, 12, 9, 3, 2, 4, 1, 7, 6, 8, 5, 123, 122, 124, 121, 127, 126, 128, 125, 131, 130, 132, 129, 135, 134, 136, 133, 139, 138, 140, 137, 143, 142, 144, 141, 119, 118, 120, 117, 111, 110, 112, 109, 115, 114, 116, 113, 87, 86, 88, 85, 91, 90, 92, 89, 95, 94, 96, 93, 99, 98, 100, 97, 103, 102, 104, 101, 107, 106, 108, 105, 83, 82, 84, 81, 75, 74, 76, 73, 79, 78, 80, 77]];
cc:=[5,9,16];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
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 >);
