// Magma code for the lmfdb family of higher genus curves 14.112-5.0.2-4-56.5
// 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:=[112,5];
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:=[0,2,4,56];
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:=[[57, 63, 62, 61, 60, 59, 58, 64, 70, 69, 68, 67, 66, 65, 78, 84, 83, 82, 81, 80, 79, 71, 77, 76, 75, 74, 73, 72, 99, 105, 104, 103, 102, 101, 100, 106, 112, 111, 110, 109, 108, 107, 85, 91, 90, 89, 88, 87, 86, 92, 98, 97, 96, 95, 94, 93, 1, 7, 6, 5, 4, 3, 2, 8, 14, 13, 12, 11, 10, 9, 22, 28, 27, 26, 25, 24, 23, 15, 21, 20, 19, 18, 17, 16, 43, 49, 48, 47, 46, 45, 44, 50, 56, 55, 54, 53, 52, 51, 29, 35, 34, 33, 32, 31, 30, 36, 42, 41, 40, 39, 38, 37], [95, 94, 93, 92, 98, 97, 96, 88, 87, 86, 85, 91, 90, 89, 102, 101, 100, 99, 105, 104, 103, 109, 108, 107, 106, 112, 111, 110, 60, 59, 58, 57, 63, 62, 61, 67, 66, 65, 64, 70, 69, 68, 81, 80, 79, 78, 84, 83, 82, 74, 73, 72, 71, 77, 76, 75, 39, 38, 37, 36, 42, 41, 40, 32, 31, 30, 29, 35, 34, 33, 46, 45, 44, 43, 49, 48, 47, 53, 52, 51, 50, 56, 55, 54, 4, 3, 2, 1, 7, 6, 5, 11, 10, 9, 8, 14, 13, 12, 25, 24, 23, 22, 28, 27, 26, 18, 17, 16, 15, 21, 20, 19], [47, 48, 49, 43, 44, 45, 46, 54, 55, 56, 50, 51, 52, 53, 40, 41, 42, 36, 37, 38, 39, 33, 34, 35, 29, 30, 31, 32, 12, 13, 14, 8, 9, 10, 11, 5, 6, 7, 1, 2, 3, 4, 26, 27, 28, 22, 23, 24, 25, 19, 20, 21, 15, 16, 17, 18, 103, 104, 105, 99, 100, 101, 102, 110, 111, 112, 106, 107, 108, 109, 96, 97, 98, 92, 93, 94, 95, 89, 90, 91, 85, 86, 87, 88, 68, 69, 70, 64, 65, 66, 67, 61, 62, 63, 57, 58, 59, 60, 82, 83, 84, 78, 79, 80, 81, 75, 76, 77, 71, 72, 73, 74]];
cc:=[3,5,24];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=5;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![8, 9, 10, 11, 12, 13, 14, 1, 2, 3, 4, 5, 6, 7, 22, 23, 24, 25, 26, 27, 28, 15, 16, 17, 18, 19, 20, 21, 36, 37, 38, 39, 40, 41, 42, 29, 30, 31, 32, 33, 34, 35, 50, 51, 52, 53, 54, 55, 56, 43, 44, 45, 46, 47, 48, 49, 64, 65, 66, 67, 68, 69, 70, 57, 58, 59, 60, 61, 62, 63, 78, 79, 80, 81, 82, 83, 84, 71, 72, 73, 74, 75, 76, 77, 92, 93, 94, 95, 96, 97, 98, 85, 86, 87, 88, 89, 90, 91, 106, 107, 108, 109, 110, 111, 112, 99, 100, 101, 102, 103, 104, 105];
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 >);
