// Magma code for the lmfdb family of higher genus curves 14.120-5.0.3-4-5.2
// 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:=[120,5];
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:=[0,3,4,5];
genus:=14;
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:=[[3, 7, 5, 33, 1, 13, 8, 2, 106, 4, 17, 19, 14, 6, 21, 23, 18, 11, 20, 12, 22, 15, 24, 16, 27, 31, 29, 57, 25, 37, 32, 26, 10, 28, 41, 43, 38, 30, 45, 47, 42, 35, 44, 36, 46, 39, 48, 40, 51, 55, 53, 81, 49, 61, 56, 50, 34, 52, 65, 67, 62, 54, 69, 71, 66, 59, 68, 60, 70, 63, 72, 64, 75, 79, 77, 105, 73, 85, 80, 74, 58, 76, 89, 91, 86, 78, 93, 95, 90, 83, 92, 84, 94, 87, 96, 88, 99, 103, 101, 9, 97, 109, 104, 98, 82, 100, 113, 115, 110, 102, 117, 119, 114, 107, 116, 108, 118, 111, 120, 112], [98, 30, 20, 25, 10, 100, 24, 5, 118, 14, 115, 113, 18, 8, 47, 45, 35, 3, 36, 13, 111, 7, 112, 33, 2, 54, 44, 49, 34, 4, 48, 29, 22, 38, 19, 17, 42, 32, 71, 69, 59, 27, 60, 37, 15, 31, 16, 57, 26, 78, 68, 73, 58, 28, 72, 53, 46, 62, 43, 41, 66, 56, 95, 93, 83, 51, 84, 61, 39, 55, 40, 81, 50, 102, 92, 97, 82, 52, 96, 77, 70, 86, 67, 65, 90, 80, 119, 117, 107, 75, 108, 85, 63, 79, 64, 105, 74, 6, 116, 1, 106, 76, 120, 101, 94, 110, 91, 89, 114, 104, 23, 21, 11, 99, 12, 109, 87, 103, 88, 9], [106, 29, 17, 38, 7, 104, 21, 13, 119, 3, 107, 108, 19, 33, 39, 40, 44, 6, 42, 1, 120, 4, 118, 2, 10, 53, 41, 62, 31, 8, 45, 37, 23, 27, 11, 12, 43, 57, 63, 64, 68, 30, 66, 25, 24, 28, 22, 26, 34, 77, 65, 86, 55, 32, 69, 61, 47, 51, 35, 36, 67, 81, 87, 88, 92, 54, 90, 49, 48, 52, 46, 50, 58, 101, 89, 110, 79, 56, 93, 85, 71, 75, 59, 60, 91, 105, 111, 112, 116, 78, 114, 73, 72, 76, 70, 74, 82, 5, 113, 14, 103, 80, 117, 109, 95, 99, 83, 84, 115, 9, 15, 16, 20, 102, 18, 97, 96, 100, 94, 98]];
cc:=[3,4,6];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=2;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![6, 4, 13, 2, 14, 1, 33, 10, 103, 8, 12, 11, 3, 5, 16, 15, 19, 20, 17, 18, 23, 24, 21, 22, 30, 28, 37, 26, 38, 25, 57, 34, 7, 32, 36, 35, 27, 29, 40, 39, 43, 44, 41, 42, 47, 48, 45, 46, 54, 52, 61, 50, 62, 49, 81, 58, 31, 56, 60, 59, 51, 53, 64, 63, 67, 68, 65, 66, 71, 72, 69, 70, 78, 76, 85, 74, 86, 73, 105, 82, 55, 80, 84, 83, 75, 77, 88, 87, 91, 92, 89, 90, 95, 96, 93, 94, 102, 100, 109, 98, 110, 97, 9, 106, 79, 104, 108, 107, 99, 101, 112, 111, 115, 116, 113, 114, 119, 120, 117, 118];
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 >);
