// Magma code for the lmfdb family of higher genus curves 15.40-2.0.4-40-40.1
// 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:=[40,2];
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:=[0,4,40,40];
genus:=15;
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, 4, 2, 1, 7, 8, 6, 5, 11, 12, 10, 9, 15, 16, 14, 13, 19, 20, 18, 17, 23, 24, 22, 21, 27, 28, 26, 25, 31, 32, 30, 29, 35, 36, 34, 33, 39, 40, 38, 37], [25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 21, 22, 23, 24, 7, 8, 6, 5, 11, 12, 10, 9, 15, 16, 14, 13, 19, 20, 18, 17, 3, 4, 2, 1], [38, 37, 40, 39, 22, 21, 24, 23, 26, 25, 28, 27, 30, 29, 32, 31, 34, 33, 36, 35, 20, 19, 17, 18, 4, 3, 1, 2, 8, 7, 5, 6, 12, 11, 9, 10, 16, 15, 13, 14]];
cc:=[3,25,36];
gen_vectors_as_perm:=[S!perm : perm in gen_vectors];
passport_label:=1;
gen_vect_label:=1;
full_auto:=[80,5];
full_sign:=[0,2,8,40];
Append(~data, rec);