// Magma code for the lmfdb family of higher genus curves 9.128-75.0.2-4-8.2
// 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:=[128,75];
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:=[0,2,4,8];
genus:=9;
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:=[[33, 34, 35, 36, 37, 38, 39, 40, 47, 48, 45, 46, 43, 44, 41, 42, 51, 52, 49, 50, 55, 56, 53, 54, 61, 62, 63, 64, 57, 58, 59, 60, 1, 2, 3, 4, 5, 6, 7, 8, 15, 16, 13, 14, 11, 12, 9, 10, 19, 20, 17, 18, 23, 24, 21, 22, 29, 30, 31, 32, 25, 26, 27, 28, 97, 98, 99, 100, 101, 102, 103, 104, 111, 112, 109, 110, 107, 108, 105, 106, 115, 116, 113, 114, 119, 120, 117, 118, 125, 126, 127, 128, 121, 122, 123, 124, 65, 66, 67, 68, 69, 70, 71, 72, 79, 80, 77, 78, 75, 76, 73, 74, 83, 84, 81, 82, 87, 88, 85, 86, 93, 94, 95, 96, 89, 90, 91, 92], [65, 66, 67, 68, 70, 69, 72, 71, 73, 74, 75, 76, 78, 77, 80, 79, 85, 86, 87, 88, 82, 81, 84, 83, 93, 94, 95, 96, 90, 89, 92, 91, 113, 114, 115, 116, 118, 117, 120, 119, 121, 122, 123, 124, 126, 125, 128, 127, 103, 104, 101, 102, 100, 99, 98, 97, 111, 112, 109, 110, 108, 107, 106, 105, 9, 10, 11, 12, 14, 13, 16, 15, 1, 2, 3, 4, 6, 5, 8, 7, 30, 29, 32, 31, 25, 26, 27, 28, 22, 21, 24, 23, 17, 18, 19, 20, 64, 63, 62, 61, 59, 60, 57, 58, 56, 55, 54, 53, 51, 52, 49, 50, 41, 42, 43, 44, 46, 45, 48, 47, 33, 34, 35, 36, 38, 37, 40, 39], [111, 112, 109, 110, 108, 107, 106, 105, 97, 98, 99, 100, 102, 101, 104, 103, 121, 122, 123, 124, 126, 125, 128, 127, 119, 120, 117, 118, 116, 115, 114, 113, 93, 94, 95, 96, 90, 89, 92, 91, 83, 84, 81, 82, 88, 87, 86, 85, 73, 74, 75, 76, 78, 77, 80, 79, 71, 72, 69, 70, 68, 67, 66, 65, 33, 34, 35, 36, 38, 37, 40, 39, 47, 48, 45, 46, 44, 43, 42, 41, 56, 55, 54, 53, 51, 52, 49, 50, 58, 57, 60, 59, 61, 62, 63, 64, 22, 21, 24, 23, 17, 18, 19, 20, 28, 27, 26, 25, 31, 32, 29, 30, 1, 2, 3, 4, 6, 5, 8, 7, 15, 16, 13, 14, 12, 11, 10, 9]];
cc:=[9,16,23];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=2;
gen_vect_label:=1;
is_hyperelliptic:=false;
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,is_cyclic_trigonal:=is_cyclic_trigonal >);
