// Magma code for the lmfdb family of higher genus curves 4.120-34.0.2-4-5.1 // 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:=[120,34]; 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:=[0,2,4,5]; genus:=4; 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, 19, 23, 87, 65, 1, 44, 13, 92, 70, 31, 49, 8, 97, 20, 36, 54, 78, 2, 15, 26, 39, 3, 107, 45, 21, 64, 33, 112, 50, 11, 69, 28, 117, 40, 16, 74, 58, 22, 35, 46, 59, 103, 7, 25, 41, 84, 53, 12, 30, 111, 89, 48, 17, 60, 116, 94, 38, 42, 55, 66, 79, 83, 27, 5, 61, 104, 73, 32, 10, 91, 109, 68, 37, 80, 96, 114, 18, 62, 75, 86, 99, 63, 47, 105, 81, 4, 93, 52, 110, 71, 9, 88, 57, 100, 76, 14, 118, 82, 95, 106, 119, 43, 67, 85, 101, 24, 113, 72, 90, 51, 29, 108, 77, 120, 56, 34, 98, 102, 115], [7, 20, 21, 89, 63, 2, 45, 11, 94, 68, 32, 50, 6, 99, 18, 37, 55, 76, 4, 13, 27, 40, 1, 109, 43, 22, 65, 31, 114, 48, 12, 70, 26, 119, 38, 17, 75, 56, 24, 33, 47, 60, 101, 9, 23, 42, 85, 51, 14, 28, 112, 90, 46, 19, 58, 117, 95, 36, 44, 53, 67, 80, 81, 29, 3, 62, 105, 71, 34, 8, 92, 110, 66, 39, 78, 97, 115, 16, 64, 73, 87, 100, 61, 49, 103, 82, 5, 91, 54, 108, 72, 10, 86, 59, 98, 77, 15, 116, 84, 93, 107, 120, 41, 69, 83, 102, 25, 111, 74, 88, 52, 30, 106, 79, 118, 57, 35, 96, 104, 113], [3, 1, 5, 2, 4, 8, 6, 10, 7, 9, 13, 11, 15, 12, 14, 18, 16, 20, 17, 19, 23, 21, 25, 22, 24, 28, 26, 30, 27, 29, 33, 31, 35, 32, 34, 38, 36, 40, 37, 39, 43, 41, 45, 42, 44, 48, 46, 50, 47, 49, 53, 51, 55, 52, 54, 58, 56, 60, 57, 59, 63, 61, 65, 62, 64, 68, 66, 70, 67, 69, 73, 71, 75, 72, 74, 78, 76, 80, 77, 79, 83, 81, 85, 82, 84, 88, 86, 90, 87, 89, 93, 91, 95, 92, 94, 98, 96, 100, 97, 99, 103, 101, 105, 102, 104, 108, 106, 110, 107, 109, 113, 111, 115, 112, 114, 118, 116, 120, 117, 119]]; cc:=[2,5,6]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=1; gen_vect_label:=1; braid_class:=1; topological_class:=[1, 1]; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Append(~data, rec);