// Magma code for the lmfdb family of higher genus curves 5.120-35.0.2-3-10.2
// 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:=[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], [72, 68, 106, 19, 35, 87, 63, 36, 24, 105, 37, 78, 51, 94, 10, 42, 73, 1, 109, 60, 92, 88, 6, 39, 55, 107, 83, 56, 44, 5, 57, 98, 71, 114, 30, 62, 93, 21, 9, 80, 112, 108, 26, 59, 75, 7, 103, 76, 64, 25, 77, 118, 91, 14, 50, 82, 113, 41, 29, 100, 12, 8, 46, 79, 95, 27, 3, 96, 84, 45, 97, 18, 111, 34, 70, 102, 13, 61, 49, 120, 32, 28, 66, 99, 115, 47, 23, 116, 104, 65, 117, 38, 11, 54, 90, 2, 33, 81, 69, 20, 52, 48, 86, 119, 15, 67, 43, 16, 4, 85, 17, 58, 31, 74, 110, 22, 53, 101, 89, 40], [104, 91, 70, 88, 27, 34, 41, 65, 73, 12, 59, 66, 80, 43, 102, 9, 116, 75, 38, 97, 4, 111, 90, 108, 47, 54, 61, 85, 93, 32, 79, 86, 100, 63, 2, 29, 16, 95, 58, 117, 24, 11, 110, 8, 67, 74, 81, 105, 113, 52, 99, 106, 120, 83, 22, 49, 36, 115, 78, 17, 44, 31, 10, 28, 87, 94, 101, 5, 13, 72, 119, 6, 20, 103, 42, 69, 56, 15, 98, 37, 64, 51, 30, 48, 107, 114, 1, 25, 33, 92, 19, 26, 40, 3, 62, 89, 76, 35, 118, 57, 84, 71, 50, 68, 7, 14, 21, 45, 53, 112, 39, 46, 60, 23, 82, 109, 96, 55, 18, 77]];
cc:=[3,5,10];
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:=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 >);
