// Magma code for the lmfdb family of higher genus curves 13.120-35.0.2-5-10.1
// 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:=[120,35];
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:=[0,2,5,10];
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, 5, 14, 38, 2, 1, 10, 29, 108, 7, 16, 15, 99, 3, 12, 11, 20, 104, 53, 17, 26, 25, 34, 58, 22, 21, 30, 49, 8, 27, 36, 35, 119, 23, 32, 31, 40, 4, 73, 37, 46, 45, 54, 78, 42, 41, 50, 69, 28, 47, 56, 55, 19, 43, 52, 51, 60, 24, 93, 57, 66, 65, 74, 98, 62, 61, 70, 89, 48, 67, 76, 75, 39, 63, 72, 71, 80, 44, 113, 77, 86, 85, 94, 118, 82, 81, 90, 109, 68, 87, 96, 95, 59, 83, 92, 91, 100, 64, 13, 97, 106, 105, 114, 18, 102, 101, 110, 9, 88, 107, 116, 115, 79, 103, 112, 111, 120, 84, 33, 117], [2, 4, 1, 50, 78, 7, 9, 6, 100, 83, 12, 14, 11, 115, 33, 17, 19, 16, 65, 48, 22, 24, 21, 70, 98, 27, 29, 26, 120, 103, 32, 34, 31, 15, 53, 37, 39, 36, 85, 68, 42, 44, 41, 90, 118, 47, 49, 46, 20, 3, 52, 54, 51, 35, 73, 57, 59, 56, 105, 88, 62, 64, 61, 110, 18, 67, 69, 66, 40, 23, 72, 74, 71, 55, 93, 77, 79, 76, 5, 108, 82, 84, 81, 10, 38, 87, 89, 86, 60, 43, 92, 94, 91, 75, 113, 97, 99, 96, 25, 8, 102, 104, 101, 30, 58, 107, 109, 106, 80, 63, 112, 114, 111, 95, 13, 117, 119, 116, 45, 28], [14, 6, 47, 5, 113, 29, 1, 97, 10, 118, 99, 16, 112, 15, 23, 104, 11, 62, 20, 28, 34, 26, 67, 25, 13, 49, 21, 117, 30, 18, 119, 36, 12, 35, 43, 4, 31, 82, 40, 48, 54, 46, 87, 45, 33, 69, 41, 17, 50, 38, 19, 56, 32, 55, 63, 24, 51, 102, 60, 68, 74, 66, 107, 65, 53, 89, 61, 37, 70, 58, 39, 76, 52, 75, 83, 44, 71, 2, 80, 88, 94, 86, 7, 85, 73, 109, 81, 57, 90, 78, 59, 96, 72, 95, 103, 64, 91, 22, 100, 108, 114, 106, 27, 105, 93, 9, 101, 77, 110, 98, 79, 116, 92, 115, 3, 84, 111, 42, 120, 8]];
cc:=[3,6,9];
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>);
