// Magma code for the lmfdb family of higher genus curves 3.32-9.0.2-4-8.8
// The results are stored in a list of records called 'data'
RecFormat:=recformat;
data:=[];
// Create group as a permutation group, and generate data which is the same for all entries.
gp_id:=[32,9];
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;
signature:=[0,2,4,8];
genus:=3;
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:=[[11, 12, 9, 10, 16, 15, 14, 13, 3, 4, 1, 2, 8, 7, 6, 5, 27, 28, 25, 26, 32, 31, 30, 29, 19, 20, 17, 18, 24, 23, 22, 21], [19, 20, 17, 18, 24, 23, 22, 21, 31, 32, 29, 30, 27, 28, 25, 26, 1, 2, 3, 4, 6, 5, 8, 7, 13, 14, 15, 16, 9, 10, 11, 12], [27, 28, 25, 26, 31, 32, 29, 30, 24, 23, 22, 21, 19, 20, 17, 18, 9, 10, 11, 12, 13, 14, 15, 16, 6, 5, 8, 7, 1, 2, 3, 4]];
cc:=[6,10,14];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=8;
gen_vect_label:=1;
is_hyperelliptic:=true;
hyp_involution:=S![3, 4, 1, 2, 7, 8, 5, 6, 11, 12, 9, 10, 15, 16, 13, 14, 19, 20, 17, 18, 23, 24, 21, 22, 27, 28, 25, 26, 31, 32, 29, 30];
is_cyclic_trigonal:=false;
Append(~data, rec);