// Magma code for the lmfdb family of higher genus curves 7.144-127.0.2-3-12.2
// 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:=[144,127];
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:=[0,2,3,12];
genus:=7;
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:=[[79, 80, 83, 84, 81, 82, 74, 73, 78, 77, 76, 75, 91, 92, 95, 96, 93, 94, 86, 85, 90, 89, 88, 87, 103, 104, 107, 108, 105, 106, 98, 97, 102, 101, 100, 99, 115, 116, 119, 120, 117, 118, 110, 109, 114, 113, 112, 111, 127, 128, 131, 132, 129, 130, 122, 121, 126, 125, 124, 123, 139, 140, 143, 144, 141, 142, 134, 133, 138, 137, 136, 135, 8, 7, 12, 11, 10, 9, 1, 2, 5, 6, 3, 4, 20, 19, 24, 23, 22, 21, 13, 14, 17, 18, 15, 16, 32, 31, 36, 35, 34, 33, 25, 26, 29, 30, 27, 28, 44, 43, 48, 47, 46, 45, 37, 38, 41, 42, 39, 40, 56, 55, 60, 59, 58, 57, 49, 50, 53, 54, 51, 52, 68, 67, 72, 71, 70, 69, 61, 62, 65, 66, 63, 64], [34, 33, 36, 35, 32, 31, 46, 45, 48, 47, 44, 43, 39, 40, 41, 42, 37, 38, 27, 28, 29, 30, 25, 26, 58, 57, 60, 59, 56, 55, 70, 69, 72, 71, 68, 67, 63, 64, 65, 66, 61, 62, 51, 52, 53, 54, 49, 50, 10, 9, 12, 11, 8, 7, 22, 21, 24, 23, 20, 19, 15, 16, 17, 18, 13, 14, 3, 4, 5, 6, 1, 2, 106, 105, 108, 107, 104, 103, 118, 117, 120, 119, 116, 115, 111, 112, 113, 114, 109, 110, 99, 100, 101, 102, 97, 98, 130, 129, 132, 131, 128, 127, 142, 141, 144, 143, 140, 139, 135, 136, 137, 138, 133, 134, 123, 124, 125, 126, 121, 122, 82, 81, 84, 83, 80, 79, 94, 93, 96, 95, 92, 91, 87, 88, 89, 90, 85, 86, 75, 76, 77, 78, 73, 74], [136, 135, 134, 133, 138, 137, 130, 129, 128, 127, 132, 131, 141, 142, 139, 140, 143, 144, 123, 124, 121, 122, 125, 126, 88, 87, 86, 85, 90, 89, 82, 81, 80, 79, 84, 83, 93, 94, 91, 92, 95, 96, 75, 76, 73, 74, 77, 78, 112, 111, 110, 109, 114, 113, 106, 105, 104, 103, 108, 107, 117, 118, 115, 116, 119, 120, 99, 100, 97, 98, 101, 102, 63, 64, 61, 62, 65, 66, 57, 58, 55, 56, 59, 60, 70, 69, 68, 67, 72, 71, 52, 51, 50, 49, 54, 53, 15, 16, 13, 14, 17, 18, 9, 10, 7, 8, 11, 12, 22, 21, 20, 19, 24, 23, 4, 3, 2, 1, 6, 5, 39, 40, 37, 38, 41, 42, 33, 34, 31, 32, 35, 36, 46, 45, 44, 43, 48, 47, 28, 27, 26, 25, 30, 29]];
cc:=[3,7,21];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=2;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 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 >);
