// Magma code for the lmfdb family of higher genus curves 5.120-35.0.2-3-10.1
// 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:=[0,2,3,10];
genus:=5;
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], [107, 74, 98, 66, 20, 37, 89, 48, 61, 25, 52, 39, 63, 76, 95, 2, 44, 113, 71, 110, 7, 94, 118, 86, 40, 57, 109, 68, 81, 45, 72, 59, 83, 96, 115, 22, 64, 13, 91, 10, 27, 114, 18, 106, 60, 77, 9, 88, 101, 65, 92, 79, 103, 116, 15, 42, 84, 33, 111, 30, 47, 14, 38, 6, 80, 97, 29, 108, 1, 85, 112, 99, 3, 16, 35, 62, 104, 53, 11, 50, 67, 34, 58, 26, 100, 117, 49, 8, 21, 105, 12, 119, 23, 36, 55, 82, 4, 73, 31, 70, 87, 54, 78, 46, 120, 17, 69, 28, 41, 5, 32, 19, 43, 56, 75, 102, 24, 93, 51, 90], [48, 11, 39, 100, 107, 98, 26, 109, 50, 37, 113, 96, 4, 65, 52, 63, 101, 54, 115, 2, 68, 31, 59, 120, 7, 118, 46, 9, 70, 57, 13, 116, 24, 85, 72, 83, 1, 74, 15, 22, 88, 51, 79, 20, 27, 18, 66, 29, 90, 77, 33, 16, 44, 105, 92, 103, 21, 94, 35, 42, 108, 71, 99, 40, 47, 38, 86, 49, 110, 97, 53, 36, 64, 5, 112, 3, 41, 114, 55, 62, 8, 91, 119, 60, 67, 58, 106, 69, 10, 117, 73, 56, 84, 25, 12, 23, 61, 14, 75, 82, 28, 111, 19, 80, 87, 78, 6, 89, 30, 17, 93, 76, 104, 45, 32, 43, 81, 34, 95, 102]];
cc:=[3,5,9];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60];
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, hyp_involution:=hyp_involution,is_cyclic_trigonal:=is_cyclic_trigonal >);
