// Magma code for the lmfdb family of higher genus curves 12.48-7.0.2-2-2-24.3 // 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:=[48,7]; 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:=[0,2,2,2,24]; genus:=12; 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:=[[4, 5, 6, 1, 2, 3, 10, 11, 12, 7, 8, 9, 16, 17, 18, 13, 14, 15, 22, 23, 24, 19, 20, 21, 28, 29, 30, 25, 26, 27, 34, 35, 36, 31, 32, 33, 40, 41, 42, 37, 38, 39, 46, 47, 48, 43, 44, 45], [25, 27, 26, 28, 30, 29, 34, 36, 35, 31, 33, 32, 43, 45, 44, 46, 48, 47, 37, 39, 38, 40, 42, 41, 1, 3, 2, 4, 6, 5, 10, 12, 11, 7, 9, 8, 19, 21, 20, 22, 24, 23, 13, 15, 14, 16, 18, 17], [42, 41, 40, 39, 38, 37, 45, 44, 43, 48, 47, 46, 30, 29, 28, 27, 26, 25, 33, 32, 31, 36, 35, 34, 18, 17, 16, 15, 14, 13, 21, 20, 19, 24, 23, 22, 6, 5, 4, 3, 2, 1, 9, 8, 7, 12, 11, 10], [20, 21, 19, 23, 24, 22, 17, 18, 16, 14, 15, 13, 2, 3, 1, 5, 6, 4, 8, 9, 7, 11, 12, 10, 44, 45, 43, 47, 48, 46, 41, 42, 40, 38, 39, 37, 26, 27, 25, 29, 30, 28, 32, 33, 31, 35, 36, 34]]; cc:=[2,3,4,14]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=3; gen_vect_label:=1; is_hyperelliptic:=true; hyp_involution:=S![4, 5, 6, 1, 2, 3, 10, 11, 12, 7, 8, 9, 16, 17, 18, 13, 14, 15, 22, 23, 24, 19, 20, 21, 28, 29, 30, 25, 26, 27, 34, 35, 36, 31, 32, 33, 40, 41, 42, 37, 38, 39, 46, 47, 48, 43, 44, 45]; is_cyclic_trigonal:=false; Append(~data, rec);