// Magma code for the lmfdb family of higher genus curves 10.40-6.0.2-2-2-20.4 // 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:=[40,6]; 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:=[0,2,2,2,20]; genus:=10; 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:=[[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], [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], [32, 31, 35, 34, 33, 37, 36, 40, 39, 38, 22, 21, 25, 24, 23, 27, 26, 30, 29, 28, 12, 11, 15, 14, 13, 17, 16, 20, 19, 18, 2, 1, 5, 4, 3, 7, 6, 10, 9, 8], [15, 11, 12, 13, 14, 20, 16, 17, 18, 19, 10, 6, 7, 8, 9, 5, 1, 2, 3, 4, 35, 31, 32, 33, 34, 40, 36, 37, 38, 39, 30, 26, 27, 28, 29, 25, 21, 22, 23, 24]]; cc:=[2,3,4,13]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=4; gen_vect_label:=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);