// Magma code for the lmfdb family of higher genus curves 14.120-30.0.2-4-30.1 // 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:=[120,30]; 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:=[0,2,4,30]; genus:=14; 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:=[[61, 65, 64, 63, 62, 71, 75, 74, 73, 72, 66, 70, 69, 68, 67, 76, 80, 79, 78, 77, 86, 90, 89, 88, 87, 81, 85, 84, 83, 82, 106, 110, 109, 108, 107, 116, 120, 119, 118, 117, 111, 115, 114, 113, 112, 91, 95, 94, 93, 92, 101, 105, 104, 103, 102, 96, 100, 99, 98, 97, 1, 5, 4, 3, 2, 11, 15, 14, 13, 12, 6, 10, 9, 8, 7, 16, 20, 19, 18, 17, 26, 30, 29, 28, 27, 21, 25, 24, 23, 22, 46, 50, 49, 48, 47, 56, 60, 59, 58, 57, 51, 55, 54, 53, 52, 31, 35, 34, 33, 32, 41, 45, 44, 43, 42, 36, 40, 39, 38, 37], [105, 104, 103, 102, 101, 100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 120, 119, 118, 117, 116, 115, 114, 113, 112, 111, 110, 109, 108, 107, 106, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [37, 38, 39, 40, 36, 42, 43, 44, 45, 41, 32, 33, 34, 35, 31, 52, 53, 54, 55, 51, 57, 58, 59, 60, 56, 47, 48, 49, 50, 46, 7, 8, 9, 10, 6, 12, 13, 14, 15, 11, 2, 3, 4, 5, 1, 22, 23, 24, 25, 21, 27, 28, 29, 30, 26, 17, 18, 19, 20, 16, 97, 98, 99, 100, 96, 102, 103, 104, 105, 101, 92, 93, 94, 95, 91, 112, 113, 114, 115, 111, 117, 118, 119, 120, 116, 107, 108, 109, 110, 106, 67, 68, 69, 70, 66, 72, 73, 74, 75, 71, 62, 63, 64, 65, 61, 82, 83, 84, 85, 81, 87, 88, 89, 90, 86, 77, 78, 79, 80, 76]]; cc:=[4,6,26]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=1; gen_vect_label:=1; is_hyperelliptic:=true; hyp_involution:=S![16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105]; is_cyclic_trigonal:=false; Append(~data, rec);