// Magma code for the lmfdb family of higher genus curves 14.40-2.0.5-8-40 // 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:=[40,2]; 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:=[0,5,8,40]; 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:=[[5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 21, 22, 23, 24], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 3, 4, 2, 1, 7, 8, 6, 5, 11, 12, 10, 9, 15, 16, 14, 13, 19, 20, 18, 17], [40, 39, 37, 38, 24, 23, 21, 22, 28, 27, 25, 26, 32, 31, 29, 30, 36, 35, 33, 34, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]]; cc:=[5,9,40]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=1; gen_vect_label:=1; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 21, 22, 23, 24], [23, 24, 22, 21, 27, 28, 26, 25, 31, 32, 30, 29, 35, 36, 34, 33, 39, 40, 38, 37, 2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19], [38, 37, 40, 39, 22, 21, 24, 23, 26, 25, 28, 27, 30, 29, 32, 31, 34, 33, 36, 35, 20, 19, 17, 18, 4, 3, 1, 2, 8, 7, 5, 6, 12, 11, 9, 10, 16, 15, 13, 14]]; cc:=[5,10,36]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=2; gen_vect_label:=1; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 21, 22, 23, 24], [22, 21, 24, 23, 26, 25, 28, 27, 30, 29, 32, 31, 34, 33, 36, 35, 38, 37, 40, 39, 4, 3, 1, 2, 8, 7, 5, 6, 12, 11, 9, 10, 16, 15, 13, 14, 20, 19, 17, 18], [39, 40, 38, 37, 23, 24, 22, 21, 27, 28, 26, 25, 31, 32, 30, 29, 35, 36, 34, 33, 18, 17, 20, 19, 2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15]]; cc:=[5,11,32]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=3; gen_vect_label:=1; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 21, 22, 23, 24], [24, 23, 21, 22, 28, 27, 25, 26, 32, 31, 29, 30, 36, 35, 33, 34, 40, 39, 37, 38, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [37, 38, 39, 40, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 19, 20, 18, 17, 3, 4, 2, 1, 7, 8, 6, 5, 11, 12, 10, 9, 15, 16, 14, 13]]; cc:=[5,12,28]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=4; gen_vect_label:=1; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 21, 22, 23, 24, 25, 26, 27, 28], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 3, 4, 2, 1, 7, 8, 6, 5, 11, 12, 10, 9, 15, 16, 14, 13, 19, 20, 18, 17], [36, 35, 33, 34, 40, 39, 37, 38, 24, 23, 21, 22, 28, 27, 25, 26, 32, 31, 29, 30, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]]; cc:=[6,9,34]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=5; gen_vect_label:=1; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 21, 22, 23, 24, 25, 26, 27, 28], [23, 24, 22, 21, 27, 28, 26, 25, 31, 32, 30, 29, 35, 36, 34, 33, 39, 40, 38, 37, 2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19], [34, 33, 36, 35, 38, 37, 40, 39, 22, 21, 24, 23, 26, 25, 28, 27, 30, 29, 32, 31, 16, 15, 13, 14, 20, 19, 17, 18, 4, 3, 1, 2, 8, 7, 5, 6, 12, 11, 9, 10]]; cc:=[6,10,30]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=6; gen_vect_label:=1; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 21, 22, 23, 24, 25, 26, 27, 28], [22, 21, 24, 23, 26, 25, 28, 27, 30, 29, 32, 31, 34, 33, 36, 35, 38, 37, 40, 39, 4, 3, 1, 2, 8, 7, 5, 6, 12, 11, 9, 10, 16, 15, 13, 14, 20, 19, 17, 18], [35, 36, 34, 33, 39, 40, 38, 37, 23, 24, 22, 21, 27, 28, 26, 25, 31, 32, 30, 29, 14, 13, 16, 15, 18, 17, 20, 19, 2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11]]; cc:=[6,11,26]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=7; gen_vect_label:=1; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 21, 22, 23, 24, 25, 26, 27, 28], [24, 23, 21, 22, 28, 27, 25, 26, 32, 31, 29, 30, 36, 35, 33, 34, 40, 39, 37, 38, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [33, 34, 35, 36, 37, 38, 39, 40, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 15, 16, 14, 13, 19, 20, 18, 17, 3, 4, 2, 1, 7, 8, 6, 5, 11, 12, 10, 9]]; cc:=[6,12,38]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=8; gen_vect_label:=1; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 33, 34, 35, 36, 37, 38, 39, 40, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 3, 4, 2, 1, 7, 8, 6, 5, 11, 12, 10, 9, 15, 16, 14, 13, 19, 20, 18, 17], [32, 31, 29, 30, 36, 35, 33, 34, 40, 39, 37, 38, 24, 23, 21, 22, 28, 27, 25, 26, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8]]; cc:=[7,9,27]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=9; gen_vect_label:=1; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 33, 34, 35, 36, 37, 38, 39, 40, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32], [23, 24, 22, 21, 27, 28, 26, 25, 31, 32, 30, 29, 35, 36, 34, 33, 39, 40, 38, 37, 2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19], [30, 29, 32, 31, 34, 33, 36, 35, 38, 37, 40, 39, 22, 21, 24, 23, 26, 25, 28, 27, 12, 11, 9, 10, 16, 15, 13, 14, 20, 19, 17, 18, 4, 3, 1, 2, 8, 7, 5, 6]]; cc:=[7,10,39]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=10; gen_vect_label:=1; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 33, 34, 35, 36, 37, 38, 39, 40, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32], [22, 21, 24, 23, 26, 25, 28, 27, 30, 29, 32, 31, 34, 33, 36, 35, 38, 37, 40, 39, 4, 3, 1, 2, 8, 7, 5, 6, 12, 11, 9, 10, 16, 15, 13, 14, 20, 19, 17, 18], [31, 32, 30, 29, 35, 36, 34, 33, 39, 40, 38, 37, 23, 24, 22, 21, 27, 28, 26, 25, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19, 2, 1, 4, 3, 6, 5, 8, 7]]; cc:=[7,11,35]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=11; gen_vect_label:=1; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 33, 34, 35, 36, 37, 38, 39, 40, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32], [24, 23, 21, 22, 28, 27, 25, 26, 32, 31, 29, 30, 36, 35, 33, 34, 40, 39, 37, 38, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 21, 22, 23, 24, 25, 26, 27, 28, 11, 12, 10, 9, 15, 16, 14, 13, 19, 20, 18, 17, 3, 4, 2, 1, 7, 8, 6, 5]]; cc:=[7,12,31]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=12; gen_vect_label:=1; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 37, 38, 39, 40, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 3, 4, 2, 1, 7, 8, 6, 5, 11, 12, 10, 9, 15, 16, 14, 13, 19, 20, 18, 17], [28, 27, 25, 26, 32, 31, 29, 30, 36, 35, 33, 34, 40, 39, 37, 38, 24, 23, 21, 22, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 1, 2, 3, 4]]; cc:=[8,9,37]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=13; gen_vect_label:=1; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 37, 38, 39, 40, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36], [23, 24, 22, 21, 27, 28, 26, 25, 31, 32, 30, 29, 35, 36, 34, 33, 39, 40, 38, 37, 2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19], [26, 25, 28, 27, 30, 29, 32, 31, 34, 33, 36, 35, 38, 37, 40, 39, 22, 21, 24, 23, 8, 7, 5, 6, 12, 11, 9, 10, 16, 15, 13, 14, 20, 19, 17, 18, 4, 3, 1, 2]]; cc:=[8,10,33]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=14; gen_vect_label:=1; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 37, 38, 39, 40, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36], [22, 21, 24, 23, 26, 25, 28, 27, 30, 29, 32, 31, 34, 33, 36, 35, 38, 37, 40, 39, 4, 3, 1, 2, 8, 7, 5, 6, 12, 11, 9, 10, 16, 15, 13, 14, 20, 19, 17, 18], [27, 28, 26, 25, 31, 32, 30, 29, 35, 36, 34, 33, 39, 40, 38, 37, 23, 24, 22, 21, 6, 5, 8, 7, 10, 9, 12, 11, 14, 13, 16, 15, 18, 17, 20, 19, 2, 1, 4, 3]]; cc:=[8,11,29]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=15; gen_vect_label:=1; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[17, 18, 19, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 37, 38, 39, 40, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36], [24, 23, 21, 22, 28, 27, 25, 26, 32, 31, 29, 30, 36, 35, 33, 34, 40, 39, 37, 38, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 21, 22, 23, 24, 7, 8, 6, 5, 11, 12, 10, 9, 15, 16, 14, 13, 19, 20, 18, 17, 3, 4, 2, 1]]; cc:=[8,12,25]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=16; gen_vect_label:=1; is_hyperelliptic:=false; is_cyclic_trigonal:=false; Append(~data, rec);