// Magma code for the lmfdb family of higher genus curves 12.104-8.0.2-4-26.3 // 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:=[104,8]; 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:=[0,2,4,26]; 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:=[[53, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 66, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 92, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 79, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 1, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 14, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 40, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 27, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28], [87, 86, 85, 84, 83, 82, 81, 80, 79, 91, 90, 89, 88, 100, 99, 98, 97, 96, 95, 94, 93, 92, 104, 103, 102, 101, 74, 73, 72, 71, 70, 69, 68, 67, 66, 78, 77, 76, 75, 61, 60, 59, 58, 57, 56, 55, 54, 53, 65, 64, 63, 62, 35, 34, 33, 32, 31, 30, 29, 28, 27, 39, 38, 37, 36, 48, 47, 46, 45, 44, 43, 42, 41, 40, 52, 51, 50, 49, 22, 21, 20, 19, 18, 17, 16, 15, 14, 26, 25, 24, 23, 9, 8, 7, 6, 5, 4, 3, 2, 1, 13, 12, 11, 10], [32, 33, 34, 35, 36, 37, 38, 39, 27, 28, 29, 30, 31, 45, 46, 47, 48, 49, 50, 51, 52, 40, 41, 42, 43, 44, 6, 7, 8, 9, 10, 11, 12, 13, 1, 2, 3, 4, 5, 19, 20, 21, 22, 23, 24, 25, 26, 14, 15, 16, 17, 18, 84, 85, 86, 87, 88, 89, 90, 91, 79, 80, 81, 82, 83, 97, 98, 99, 100, 101, 102, 103, 104, 92, 93, 94, 95, 96, 58, 59, 60, 61, 62, 63, 64, 65, 53, 54, 55, 56, 57, 71, 72, 73, 74, 75, 76, 77, 78, 66, 67, 68, 69, 70]]; cc:=[4,5,20]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=3; gen_vect_label:=1; is_hyperelliptic:=true; hyp_involution:=S![14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91]; is_cyclic_trigonal:=false; Append(~data, rec);