// Magma code for the lmfdb family of higher genus curves 8.34-2.0.2-17-34 // 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:=[34,2]; 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:=[0,2,17,34]; genus:=8; 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:=[[18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 1, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 18], [34, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 17, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16]]; cc:=[2,3,34]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=1; gen_vect_label:=1; is_hyperelliptic:=true; hyp_involution:=S![18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 1, 2, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 18, 19], [33, 34, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 16, 17, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]]; cc:=[2,4,26]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=2; gen_vect_label:=1; is_hyperelliptic:=true; hyp_involution:=S![18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 1, 2, 3, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 18, 19, 20], [32, 33, 34, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 15, 16, 17, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]]; cc:=[2,5,33]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=3; gen_vect_label:=1; is_hyperelliptic:=true; hyp_involution:=S![18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 1, 2, 3, 4, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 18, 19, 20, 21], [31, 32, 33, 34, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 14, 15, 16, 17, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]]; cc:=[2,6,25]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=4; gen_vect_label:=1; is_hyperelliptic:=true; hyp_involution:=S![18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 1, 2, 3, 4, 5, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 18, 19, 20, 21, 22], [30, 31, 32, 33, 34, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 13, 14, 15, 16, 17, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]]; cc:=[2,7,32]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=5; gen_vect_label:=1; is_hyperelliptic:=true; hyp_involution:=S![18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 1, 2, 3, 4, 5, 6, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 18, 19, 20, 21, 22, 23], [29, 30, 31, 32, 33, 34, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 12, 13, 14, 15, 16, 17, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11]]; cc:=[2,8,24]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=6; gen_vect_label:=1; is_hyperelliptic:=true; hyp_involution:=S![18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 1, 2, 3, 4, 5, 6, 7, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 18, 19, 20, 21, 22, 23, 24], [28, 29, 30, 31, 32, 33, 34, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 11, 12, 13, 14, 15, 16, 17, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]]; cc:=[2,9,31]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=7; gen_vect_label:=1; is_hyperelliptic:=true; hyp_involution:=S![18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [9, 10, 11, 12, 13, 14, 15, 16, 17, 1, 2, 3, 4, 5, 6, 7, 8, 26, 27, 28, 29, 30, 31, 32, 33, 34, 18, 19, 20, 21, 22, 23, 24, 25], [27, 28, 29, 30, 31, 32, 33, 34, 18, 19, 20, 21, 22, 23, 24, 25, 26, 10, 11, 12, 13, 14, 15, 16, 17, 1, 2, 3, 4, 5, 6, 7, 8, 9]]; cc:=[2,10,23]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=8; gen_vect_label:=1; is_hyperelliptic:=true; hyp_involution:=S![18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [10, 11, 12, 13, 14, 15, 16, 17, 1, 2, 3, 4, 5, 6, 7, 8, 9, 27, 28, 29, 30, 31, 32, 33, 34, 18, 19, 20, 21, 22, 23, 24, 25, 26], [26, 27, 28, 29, 30, 31, 32, 33, 34, 18, 19, 20, 21, 22, 23, 24, 25, 9, 10, 11, 12, 13, 14, 15, 16, 17, 1, 2, 3, 4, 5, 6, 7, 8]]; cc:=[2,11,30]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=9; gen_vect_label:=1; is_hyperelliptic:=true; hyp_involution:=S![18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [11, 12, 13, 14, 15, 16, 17, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 28, 29, 30, 31, 32, 33, 34, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27], [25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 18, 19, 20, 21, 22, 23, 24, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 1, 2, 3, 4, 5, 6, 7]]; cc:=[2,12,22]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=10; gen_vect_label:=1; is_hyperelliptic:=true; hyp_involution:=S![18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [12, 13, 14, 15, 16, 17, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 29, 30, 31, 32, 33, 34, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28], [24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 18, 19, 20, 21, 22, 23, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 1, 2, 3, 4, 5, 6]]; cc:=[2,13,29]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=11; gen_vect_label:=1; is_hyperelliptic:=true; hyp_involution:=S![18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [13, 14, 15, 16, 17, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 30, 31, 32, 33, 34, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29], [23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 18, 19, 20, 21, 22, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 1, 2, 3, 4, 5]]; cc:=[2,14,21]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=12; gen_vect_label:=1; is_hyperelliptic:=true; hyp_involution:=S![18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [14, 15, 16, 17, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 31, 32, 33, 34, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30], [22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 18, 19, 20, 21, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 1, 2, 3, 4]]; cc:=[2,15,28]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=13; gen_vect_label:=1; is_hyperelliptic:=true; hyp_involution:=S![18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [15, 16, 17, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 32, 33, 34, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 18, 19, 20, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 1, 2, 3]]; cc:=[2,16,20]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=14; gen_vect_label:=1; is_hyperelliptic:=true; hyp_involution:=S![18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [16, 17, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 33, 34, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32], [20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 18, 19, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 1, 2]]; cc:=[2,17,27]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=15; gen_vect_label:=1; is_hyperelliptic:=true; hyp_involution:=S![18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]; is_cyclic_trigonal:=false; Append(~data, rec); // Here we add an action to data. gen_vectors:=[[18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [17, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 34, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33], [19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 18, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 1]]; cc:=[2,18,19]; gen_vectors_as_perm:=[S!perm : perm in gen_vectors]; passport_label:=16; gen_vect_label:=1; is_hyperelliptic:=true; hyp_involution:=S![18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]; is_cyclic_trigonal:=false; Append(~data, rec);