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Label Polynomial Discriminant Galois group Class group Regulator
18.6.352...173.1 $x^{18} - 5 x^{17} - 5 x^{16} + 50 x^{15} - 19 x^{14} - 161 x^{13} + 161 x^{12} + 169 x^{11} - 271 x^{10} - 54 x^{9} + 120 x^{8} + 191 x^{7} - 70 x^{6} - 84 x^{5} + 67 x^{4} - 104 x^{3} + 71 x^{2} - 17 x + 1$ $7^{16}\cdot 13^{9}$ $C_6^2.C_6$ (as 18T92) trivial $68288.0528189$
18.6.352...173.2 $x^{18} + x^{16} - 19 x^{14} - 77 x^{12} - 63 x^{11} - 133 x^{10} - 259 x^{9} + 28 x^{8} + 28 x^{7} + 525 x^{6} + 623 x^{5} + 655 x^{4} + 805 x^{3} - 136 x^{2} - 7 x + 1$ $7^{16}\cdot 13^{9}$ $C_6^2.C_6$ (as 18T92) trivial $52315.3010244$
18.6.107...169.1 $x^{18} - 9 x^{17} + 42 x^{16} - 132 x^{15} + 296 x^{14} - 476 x^{13} + 518 x^{12} - 274 x^{11} - 201 x^{10} + 609 x^{9} - 652 x^{8} + 334 x^{7} + 42 x^{6} - 210 x^{5} + 164 x^{4} - 62 x^{3} + 7 x^{2} + 3 x - 1$ $7^{16}\cdot 13^{9}\cdot 43\cdot 71$ $C_2\wr C_9.C_3$ (as 18T586) $[2]$ $1819314.2171$
18.8.710...224.1 $x^{18} - 6 x^{16} - 12 x^{14} + 98 x^{12} + 35 x^{10} - 434 x^{8} - 168 x^{6} + 508 x^{4} + 270 x^{2} + 1$ $-\,2^{18}\cdot 7^{16}\cdot 13^{8}$ $C_2\wr C_9.C_3$ (as 18T586) trivial $10734408.4303$
18.12.710...224.1 $x^{18} - 5 x^{16} - 20 x^{14} + 84 x^{12} + 126 x^{10} - 350 x^{8} - 252 x^{6} + 190 x^{4} - 26 x^{2} + 1$ $-\,2^{18}\cdot 7^{16}\cdot 13^{8}$ $C_2^6:C_9:C_6$ (as 18T429) trivial $35891617.2365$
18.16.710...224.1 $x^{18} - 20 x^{16} + 156 x^{14} - 602 x^{12} + 1204 x^{10} - 1197 x^{8} + 504 x^{6} - 24 x^{4} - 24 x^{2} + 1$ $-\,2^{18}\cdot 7^{16}\cdot 13^{8}$ $C_2\wr C_9.C_3$ (as 18T586) trivial $81911787.8703$
18.4.710...224.1 $x^{18} + 11 x^{16} + 18 x^{14} - 126 x^{12} - 476 x^{10} - 357 x^{8} + 546 x^{6} + 898 x^{4} + 337 x^{2} + 1$ $-\,2^{18}\cdot 7^{16}\cdot 13^{8}$ $C_2^6:C_9:C_6$ (as 18T429) trivial $5689835.16326$
18.8.710...224.2 $x^{18} - 10 x^{16} + 4 x^{14} + 105 x^{12} - 98 x^{10} - 189 x^{8} - 7 x^{6} + 51 x^{4} + 15 x^{2} + 1$ $-\,2^{18}\cdot 7^{16}\cdot 13^{8}$ $C_2\wr C_9.C_3$ (as 18T586) trivial $13793556.6829$
18.4.710...224.2 $x^{18} + 9 x^{16} + 15 x^{14} - 56 x^{12} - 175 x^{10} - 84 x^{8} + 98 x^{6} + 78 x^{4} + 16 x^{2} + 1$ $-\,2^{18}\cdot 7^{16}\cdot 13^{8}$ $C_2^6:C_9:C_6$ (as 18T429) trivial $5620711.4386$
18.12.710...224.2 $x^{18} - 12 x^{16} + 36 x^{14} + 35 x^{12} - 217 x^{10} + 28 x^{8} + 280 x^{6} - 13 x^{4} - 12 x^{2} + 1$ $-\,2^{18}\cdot 7^{16}\cdot 13^{8}$ $C_2^6:C_9:C_6$ (as 18T429) trivial $39631655.7608$
18.16.710...224.2 $x^{18} - 17 x^{16} + 109 x^{14} - 329 x^{12} + 462 x^{10} - 217 x^{8} - 84 x^{6} + 93 x^{4} - 20 x^{2} + 1$ $-\,2^{18}\cdot 7^{16}\cdot 13^{8}$ $C_2\wr C_9.C_3$ (as 18T586) trivial $71840848.746$
18.8.710...224.3 $x^{18} - 5 x^{16} - 20 x^{14} + 63 x^{12} + 203 x^{10} - 91 x^{8} - 637 x^{6} - 559 x^{4} - 145 x^{2} + 1$ $-\,2^{18}\cdot 7^{16}\cdot 13^{8}$ $C_2\wr C_9.C_3$ (as 18T586) trivial $15150286.6758$
18.12.710...224.3 $x^{18} - 13 x^{16} + 37 x^{14} + 70 x^{12} - 273 x^{10} - 63 x^{8} + 455 x^{6} - 66 x^{4} - 10 x^{2} + 1$ $-\,2^{18}\cdot 7^{16}\cdot 13^{8}$ $C_2\wr C_9.C_3$ (as 18T586) trivial $25929729.0328$
18.4.710...224.3 $x^{18} + 11 x^{16} + 11 x^{14} - 175 x^{12} - 637 x^{10} - 826 x^{8} - 413 x^{6} - 40 x^{4} + 8 x^{2} + 1$ $-\,2^{18}\cdot 7^{16}\cdot 13^{8}$ $C_2\wr C_9.C_3$ (as 18T586) trivial $4875998.52619$
18.12.710...224.4 $x^{18} - 5 x^{16} - 34 x^{14} + 238 x^{12} - 343 x^{10} - 77 x^{8} + 469 x^{6} - 300 x^{4} + 51 x^{2} + 1$ $-\,2^{18}\cdot 7^{16}\cdot 13^{8}$ $C_2\wr C_9.C_3$ (as 18T586) trivial $25417863.7751$
18.4.710...224.4 $x^{18} + 16 x^{16} + 92 x^{14} + 210 x^{12} + 63 x^{10} - 364 x^{8} - 245 x^{6} + 155 x^{4} + 58 x^{2} + 1$ $-\,2^{18}\cdot 7^{16}\cdot 13^{8}$ $C_2\wr C_9.C_3$ (as 18T586) trivial $5373559.17224$
18.8.710...224.4 $x^{18} + 8 x^{16} - 5 x^{14} - 98 x^{12} - 42 x^{10} + 280 x^{8} + 168 x^{6} - 59 x^{4} - 31 x^{2} + 1$ $-\,2^{18}\cdot 7^{16}\cdot 13^{8}$ $C_2\wr C_9.C_3$ (as 18T586) trivial $11719884.4343$
18.12.710...224.5 $x^{18} - 3 x^{16} - 38 x^{14} + 105 x^{12} + 413 x^{10} - 938 x^{8} - 952 x^{6} + 352 x^{4} - 34 x^{2} + 1$ $-\,2^{18}\cdot 7^{16}\cdot 13^{8}$ $C_2\wr C_9.C_3$ (as 18T586) trivial $35260778.93402842$
18.8.710...224.5 $x^{18} - 5 x^{16} - 27 x^{14} + 70 x^{12} + 266 x^{10} + 56 x^{8} - 112 x^{6} - 41 x^{4} + 2 x^{2} + 1$ $-\,2^{18}\cdot 7^{16}\cdot 13^{8}$ $C_2\wr C_9.C_3$ (as 18T586) trivial $11212452.649150472$
18.12.710...224.6 $x^{18} + x^{16} - 33 x^{14} - 56 x^{12} + 189 x^{10} + 175 x^{8} - 420 x^{6} + 179 x^{4} - 24 x^{2} + 1$ $-\,2^{18}\cdot 7^{16}\cdot 13^{8}$ $C_2\wr C_9.C_3$ (as 18T586) trivial $36290154.7544971$
18.12.710...224.7 $x^{18} - 10 x^{16} - 17 x^{14} + 294 x^{12} - 819 x^{10} + 910 x^{8} - 343 x^{6} - 61 x^{4} + 43 x^{2} + 1$ $-\,2^{18}\cdot 7^{16}\cdot 13^{8}$ $C_2\wr C_9.C_3$ (as 18T586) trivial $34336984.17967955$
18.10.923...912.1 $x^{18} - 56 x^{14} + 91 x^{12} + 805 x^{10} - 2254 x^{8} - 539 x^{6} + 5096 x^{4} - 2548 x^{2} - 637$ $2^{18}\cdot 7^{16}\cdot 13^{9}$ $C_2\wr C_9.C_3$ (as 18T586) trivial $81344316.5986$
18.14.923...912.1 $x^{18} - 12 x^{16} + 43 x^{14} - 7 x^{12} - 252 x^{10} + 490 x^{8} - 301 x^{6} - 13 x^{4} + 65 x^{2} - 13$ $2^{18}\cdot 7^{16}\cdot 13^{9}$ $C_2\wr C_9.C_3$ (as 18T586) trivial $183811394.33$
18.6.923...912.1 $x^{18} - 6 x^{16} - 89 x^{14} + 63 x^{12} + 2492 x^{10} + 8197 x^{8} + 10619 x^{6} + 5408 x^{4} + 585 x^{2} - 13$ $2^{18}\cdot 7^{16}\cdot 13^{9}$ $C_2\wr C_9.C_3$ (as 18T586) trivial $28904863.5505$
18.18.923...912.1 $x^{18} - 26 x^{16} + 274 x^{14} - 1498 x^{12} + 4522 x^{10} - 7469 x^{8} + 6433 x^{6} - 2652 x^{4} + 429 x^{2} - 13$ $2^{18}\cdot 7^{16}\cdot 13^{9}$ $C_6^2.C_6$ (as 18T92) trivial $394895778.547$
18.14.923...912.2 $x^{18} - 24 x^{16} + 214 x^{14} - 882 x^{12} + 1645 x^{10} - 952 x^{8} - 539 x^{6} + 611 x^{4} - 104 x^{2} - 13$ $2^{18}\cdot 7^{16}\cdot 13^{9}$ $C_2\wr C_9.C_3$ (as 18T586) trivial $208183206.332$
18.18.923...912.2 $x^{18} - 27 x^{16} + 289 x^{14} - 1645 x^{12} + 5523 x^{10} - 11298 x^{8} + 13839 x^{6} - 9334 x^{4} + 2678 x^{2} - 13$ $2^{18}\cdot 7^{16}\cdot 13^{9}$ $C_6^2.C_6$ (as 18T92) trivial $494241653.327$
18.10.923...912.2 $x^{18} + 8 x^{16} - 26 x^{14} - 70 x^{12} + 154 x^{10} + 133 x^{8} - 266 x^{6} - 52 x^{4} + 130 x^{2} - 13$ $2^{18}\cdot 7^{16}\cdot 13^{9}$ $C_2\wr C_9.C_3$ (as 18T586) trivial $82774405.8808$
18.6.923...912.2 $x^{18} + x^{16} - 82 x^{14} - 525 x^{12} - 1267 x^{10} - 1211 x^{8} - 175 x^{6} + 221 x^{4} + 39 x^{2} - 13$ $2^{18}\cdot 7^{16}\cdot 13^{9}$ $C_2\wr C_9.C_3$ (as 18T586) trivial $31748662.565636445$
18.10.923...912.3 $x^{18} - 10 x^{16} - 3 x^{14} + 252 x^{12} - 301 x^{10} - 1862 x^{8} + 2247 x^{6} + 2977 x^{4} - 377 x^{2} - 13$ $2^{18}\cdot 7^{16}\cdot 13^{9}$ $C_2\wr C_9.C_3$ (as 18T586) trivial $68629466.23531401$
18.0.246...664.1 $x^{18} + 30 x^{16} + 330 x^{14} + 1729 x^{12} + 4557 x^{10} + 5880 x^{8} + 3689 x^{6} + 1002 x^{4} + 72 x^{2} + 1$ $-\,2^{18}\cdot 3^{24}\cdot 7^{16}$ $C_2^6:C_9:C_6$ (as 18T429) $[2, 84]$ $228539.22783$
18.12.246...664.1 $x^{18} - 3 x^{16} - 87 x^{14} + 210 x^{12} + 1722 x^{10} - 3654 x^{8} + 1715 x^{6} - 159 x^{4} - 27 x^{2} + 1$ $-\,2^{18}\cdot 3^{24}\cdot 7^{16}$ $C_2\wr C_9.C_3$ (as 18T586) trivial $773041958.205$
18.12.246...664.2 $x^{18} - 3 x^{16} - 108 x^{14} + 833 x^{12} - 1953 x^{10} + 1050 x^{8} + 651 x^{6} - 264 x^{4} + 15 x^{2} + 1$ $-\,2^{18}\cdot 3^{24}\cdot 7^{16}$ $C_2\wr C_9.C_3$ (as 18T586) trivial $689940919.02$
18.12.246...664.3 $x^{18} - 6 x^{16} - 96 x^{14} + 651 x^{12} - 966 x^{10} - 525 x^{8} + 1085 x^{6} + 459 x^{4} - 45 x^{2} + 1$ $-\,2^{18}\cdot 3^{24}\cdot 7^{16}$ $C_2\wr C_9.C_3$ (as 18T586) trivial $629457564.359531$
18.18.664...928.1 $x^{18} - 33 x^{16} + 414 x^{14} - 2583 x^{12} + 8757 x^{10} - 16254 x^{8} + 15435 x^{6} - 6264 x^{4} + 891 x^{2} - 27$ $2^{18}\cdot 3^{27}\cdot 7^{16}$ $C_2^6:C_9:C_6$ (as 18T429) trivial $14650519009.4$
18.18.869...008.1 $x^{18} - 82 x^{16} + 2563 x^{14} - 38815 x^{12} + 306005 x^{10} - 1286299 x^{8} + 2798880 x^{6} - 2856321 x^{4} + 1114724 x^{2} - 122317$ $2^{18}\cdot 7^{16}\cdot 13^{9}\cdot 97^{2}$ $C_2\wr C_9.C_3$ (as 18T586) trivial $41810018985.0$
18.18.869...008.2 $x^{18} - 66 x^{16} + 1747 x^{14} - 23660 x^{12} + 173859 x^{10} - 685517 x^{8} + 1396052 x^{6} - 1433185 x^{4} + 689767 x^{2} - 122317$ $2^{18}\cdot 7^{16}\cdot 13^{9}\cdot 97^{2}$ $C_2\wr C_9.C_3$ (as 18T586) trivial $44941476547.0$
18.10.339...000.1 $x^{18} - 2478 x^{16} - 112 x^{15} + 2459709 x^{14} + 453600 x^{13} - 1292979282 x^{12} - 507210228 x^{11} + 404036823414 x^{10} + 253906327164 x^{9} - 79844792664420 x^{8} - 62576227131768 x^{7} + 10287960929585969 x^{6} + 8082633399186780 x^{5} - 865964297572230780 x^{4} - 610067841691379792 x^{3} + 45961921416610779552 x^{2} + 20390395790890075776 x - 1196238029621636356544$ $2^{12}\cdot 3^{24}\cdot 5^{9}\cdot 7^{16}\cdot 167^{4}\cdot 1553^{4}$ $C_3^6:C_2^3:A_4$ (as 18T745) not computed
18.6.149...237.1 $x^{18} - 5 x^{17} - 167092 x^{16} - 6293108 x^{15} + 15147117318 x^{14} + 1239771250977 x^{13} - 964894717697022 x^{12} - 79024118783915444 x^{11} + 40905695726290329643 x^{10} + 1752262724262342673750 x^{9} - 1006634066616846254757866 x^{8} + 18321039766632181867356660 x^{7} + 8098863706831968529908410745 x^{6} - 740994041132933517703084589593 x^{5} + 110478192347390225209685351504156 x^{4} - 13562072589845197116991211424188309 x^{3} + 971794879679832603306037394765956329 x^{2} - 60687786693039134944942253816609702386 x + 2007723962703142442575911905590863883969$ $7^{16}\cdot 13^{7}\cdot 853^{4}\cdot 34087690279^{4}$ $C_3^4.(C_6\times A_4)$ (as 18T489) not computed
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