// Magma code for the lmfdb family of higher genus curves 4.40-8.0.2-4-10.3
// 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:=[40,8];
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:=[0,2,4,10];
genus:=4;
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:=[[21, 25, 24, 23, 22, 26, 30, 29, 28, 27, 36, 40, 39, 38, 37, 31, 35, 34, 33, 32, 1, 5, 4, 3, 2, 6, 10, 9, 8, 7, 16, 20, 19, 18, 17, 11, 15, 14, 13, 12], [34, 33, 32, 31, 35, 39, 38, 37, 36, 40, 29, 28, 27, 26, 30, 24, 23, 22, 21, 25, 14, 13, 12, 11, 15, 19, 18, 17, 16, 20, 9, 8, 7, 6, 10, 4, 3, 2, 1, 5], [13, 14, 15, 11, 12, 18, 19, 20, 16, 17, 3, 4, 5, 1, 2, 8, 9, 10, 6, 7, 33, 34, 35, 31, 32, 38, 39, 40, 36, 37, 23, 24, 25, 21, 22, 28, 29, 30, 26, 27]];
cc:=[4,5,12];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=3;
gen_vect_label:=1;
braid_class:=1;
topological_class:=[1, 1];
is_hyperelliptic:=true;
hyp_involution:=S![6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 16, 17, 18, 19, 20, 11, 12, 13, 14, 15, 26, 27, 28, 29, 30, 21, 22, 23, 24, 25, 36, 37, 38, 39, 40, 31, 32, 33, 34, 35];
is_cyclic_trigonal:=false;
Append(~data, rec);