Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)
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| Label | Polynomial | Discriminant | Galois group | Class group |
|---|---|---|---|---|
| 18.0.680...571.1 | $x^{18} - 7 x^{17} + 31 x^{16} - 98 x^{15} + 331 x^{14} - 957 x^{13} + 2693 x^{12} - 6227 x^{11} + 15226 x^{10} - 30674 x^{9} + 66392 x^{8} - 111391 x^{7} + 216508 x^{6} - 293668 x^{5} + 517517 x^{4} - 511304 x^{3} + 833369 x^{2} - 453934 x + 713641$ | $-\,11^{9}\cdot 19^{16}$ | $C_{18}$ (as 18T1) | $[2, 542]$ |
| 18.0.735...592.1 | $x^{18} + 38 x^{16} + 608 x^{14} + 5320 x^{12} + 27664 x^{10} + 86944 x^{8} + 160512 x^{6} + 160512 x^{4} + 72960 x^{2} + 9728$ | $-\,2^{27}\cdot 19^{17}$ | $C_{18}$ (as 18T1) | $[1026]$ |
| 18.0.232...771.2 | $x^{18} - 9 x^{17} + 45 x^{16} - 156 x^{15} + 504 x^{14} - 1512 x^{13} + 4272 x^{12} - 10422 x^{11} + 24552 x^{10} - 51962 x^{9} + 108099 x^{8} - 193914 x^{7} + 351249 x^{6} - 518733 x^{5} + 814050 x^{4} - 933768 x^{3} + 1272483 x^{2} - 860841 x + 992091$ | $-\,3^{44}\cdot 11^{9}$ | $C_{18}$ (as 18T1) | $[1791]$ |
| 18.0.383...792.1 | $x^{18} - 2 x^{17} + 36 x^{16} - 124 x^{15} + 667 x^{14} - 2334 x^{13} + 8164 x^{12} - 20338 x^{11} + 54321 x^{10} - 96972 x^{9} + 150518 x^{8} - 244982 x^{7} + 834376 x^{6} - 2158328 x^{5} + 4885022 x^{4} - 8338866 x^{3} + 13279313 x^{2} - 14690014 x + 10525279$ | $-\,2^{18}\cdot 19^{16}\cdot 37^{3}$ | $C_2^2:C_{18}$ (as 18T26) | $[2, 2, 570]$ |
| 18.0.383...792.2 | $x^{18} + 46 x^{16} + 875 x^{14} + 8918 x^{12} + 52728 x^{10} + 183435 x^{8} + 367668 x^{6} + 408591 x^{4} + 229992 x^{2} + 50653$ | $-\,2^{18}\cdot 19^{16}\cdot 37^{3}$ | $C_2^6:C_{18}$ (as 18T264) | $[2, 2, 468]$ |
| 18.0.383...792.3 | $x^{18} + 48 x^{16} + 853 x^{14} + 7782 x^{12} + 41204 x^{10} + 132931 x^{8} + 262797 x^{6} + 307840 x^{4} + 194398 x^{2} + 50653$ | $-\,2^{18}\cdot 19^{16}\cdot 37^{3}$ | $C_2^6:C_{18}$ (as 18T264) | $[2, 2, 608]$ |
| 18.0.516...624.1 | $x^{18} + 36 x^{16} + 525 x^{14} + 4014 x^{12} + 17550 x^{10} + 45426 x^{8} + 69728 x^{6} + 61395 x^{4} + 28116 x^{2} + 5041$ | $-\,2^{18}\cdot 3^{24}\cdot 7^{12}\cdot 71^{2}$ | $C_2^3:A_4^2$ (as 18T263) | $[2, 2, 2, 160]$ |
| 18.0.553...104.1 | $x^{18} + 48 x^{16} + 867 x^{14} + 8006 x^{12} + 42207 x^{10} + 132831 x^{8} + 251956 x^{6} + 280899 x^{4} + 168873 x^{2} + 42121$ | $-\,2^{18}\cdot 3^{24}\cdot 73^{3}\cdot 577^{3}$ | $S_4^3.C_6$ (as 18T767) | $[2, 1252]$ |
| 18.0.705...031.1 | $x^{18} - 3 x^{17} + 45 x^{16} - 70 x^{15} + 768 x^{14} - 195 x^{13} + 7003 x^{12} + 6999 x^{11} + 44889 x^{10} + 82138 x^{9} + 231111 x^{8} + 417480 x^{7} + 847530 x^{6} + 1108374 x^{5} + 1683297 x^{4} + 1332753 x^{3} + 931392 x^{2} - 168924 x + 112589$ | $-\,3^{24}\cdot 7^{12}\cdot 71^{5}$ | $C_2\times A_4^2$ (as 18T109) | $[2, 2, 2, 170]$ |
| 18.0.752...000.1 | $x^{18} - 3 x^{17} - 9 x^{16} + 46 x^{15} + 39 x^{14} - 449 x^{13} + 87 x^{12} + 3323 x^{11} - 5496 x^{10} - 10508 x^{9} + 47263 x^{8} - 31209 x^{7} - 119189 x^{6} + 233575 x^{5} - 20211 x^{4} - 344955 x^{3} + 416495 x^{2} - 217450 x + 52025$ | $-\,2^{12}\cdot 5^{9}\cdot 7^{9}\cdot 13^{12}$ | $S_3 \times C_3$ (as 18T3) | $[2, 14, 42]$ |
| 18.0.921...571.4 | $x^{18} - 9 x^{17} + 33 x^{16} - 52 x^{15} + 84 x^{14} - 540 x^{13} + 3178 x^{12} - 11892 x^{11} + 36576 x^{10} - 94398 x^{9} + 242916 x^{8} - 534324 x^{7} + 1183880 x^{6} - 2079090 x^{5} + 3606933 x^{4} - 4490689 x^{3} + 5618562 x^{2} - 3981963 x + 3180563$ | $-\,3^{24}\cdot 7^{12}\cdot 11^{9}$ | $C_6 \times C_3$ (as 18T2) | $[36, 36]$ |
| 18.0.949...704.1 | $x^{18} + 42 x^{16} + 693 x^{14} + 5880 x^{12} + 28224 x^{10} + 79380 x^{8} + 130536 x^{6} + 120393 x^{4} + 55566 x^{2} + 9261$ | $-\,2^{18}\cdot 3^{27}\cdot 7^{15}$ | $C_6 \times C_3$ (as 18T2) | $[2, 2, 2, 182]$ |
| 18.0.110...375.2 | $x^{18} - 7 x^{17} + 40 x^{16} - 154 x^{15} + 627 x^{14} - 1979 x^{13} + 6508 x^{12} - 16865 x^{11} + 47380 x^{10} - 103535 x^{9} + 254065 x^{8} - 459765 x^{7} + 999805 x^{6} - 1439914 x^{5} + 2800752 x^{4} - 2907231 x^{3} + 5123532 x^{2} - 2913750 x + 4775041$ | $-\,3^{9}\cdot 5^{9}\cdot 19^{16}$ | $C_{18}$ (as 18T1) | $[3258]$ |
| 18.0.120...096.1 | $x^{18} + 48 x^{16} + 873 x^{14} + 8175 x^{12} + 43777 x^{10} + 137970 x^{8} + 250326 x^{6} + 242159 x^{4} + 106935 x^{2} + 16361$ | $-\,2^{30}\cdot 37^{6}\cdot 16361^{3}$ | $S_4^3.D_6$ (as 18T837) | $[4, 560]$ |
| 18.0.139...231.1 | $x^{18} - 3 x^{17} + 13 x^{16} - 14 x^{15} + 49 x^{14} - 22 x^{13} - 184 x^{12} - 344 x^{11} + 2538 x^{10} - 15190 x^{9} + 54562 x^{8} - 33440 x^{7} + 69570 x^{6} - 112288 x^{5} + 224883 x^{4} - 115871 x^{3} + 162369 x^{2} - 11584 x + 215851$ | $-\,3^{9}\cdot 7^{12}\cdot 13^{15}$ | $C_6 \times C_3$ (as 18T2) | $[2, 2, 2, 2, 76]$ |
| 18.0.141...736.4 | $x^{18} - 6 x^{17} + 39 x^{16} - 146 x^{15} + 609 x^{14} - 1806 x^{13} + 5568 x^{12} - 12930 x^{11} + 30840 x^{10} - 58068 x^{9} + 121791 x^{8} - 196452 x^{7} + 321467 x^{6} - 380358 x^{5} + 651183 x^{4} - 775582 x^{3} + 1625814 x^{2} - 1190916 x + 1075033$ | $-\,2^{27}\cdot 3^{27}\cdot 7^{12}$ | $C_6 \times C_3$ (as 18T2) | $[2, 18, 54]$ |
| 18.0.165...256.1 | $x^{18} + 57 x^{16} + 1314 x^{14} + 15789 x^{12} + 106527 x^{10} + 406209 x^{8} + 836429 x^{6} + 820710 x^{4} + 272034 x^{2} + 16129$ | $-\,2^{18}\cdot 3^{24}\cdot 7^{12}\cdot 127^{2}$ | $C_2^3:A_4^2$ (as 18T263) | $[2, 2, 2, 252]$ |
| 18.0.176...392.1 | $x^{18} + 61 x^{16} + 1420 x^{14} + 16587 x^{12} + 107327 x^{10} + 402576 x^{8} + 882073 x^{6} + 1091004 x^{4} + 689157 x^{2} + 169457$ | $-\,2^{18}\cdot 7^{12}\cdot 169457^{3}$ | $S_4^3.C_6$ (as 18T765) | $[2, 2176]$ |
| 18.0.269...000.1 | $x^{18} + 24 x^{16} + 243 x^{14} + 1359 x^{12} + 4617 x^{10} + 9864 x^{8} + 13230 x^{6} + 10719 x^{4} + 4743 x^{2} + 867$ | $-\,2^{30}\cdot 3^{33}\cdot 5^{6}\cdot 17^{2}$ | $C_2^4:(A_4\times D_6)$ (as 18T366) | $[2, 2, 340]$ |
| 18.0.282...528.1 | $x^{18} + 57 x^{16} + 1368 x^{14} + 17955 x^{12} + 140049 x^{10} + 660231 x^{8} + 1828332 x^{6} + 2742498 x^{4} + 1869885 x^{2} + 373977$ | $-\,2^{18}\cdot 3^{9}\cdot 19^{17}$ | $C_{18}$ (as 18T1) | $[2, 2786]$ |
| 18.0.313...839.1 | $x^{18} + 54 x^{16} + 1215 x^{14} + 14742 x^{12} + 104247 x^{10} - 1810 x^{9} + 433026 x^{8} - 48870 x^{7} + 1010394 x^{6} - 439830 x^{5} + 1180980 x^{4} - 1466100 x^{3} + 531441 x^{2} - 1319490 x + 3335149$ | $-\,3^{45}\cdot 13^{9}$ | $C_{18}$ (as 18T1) | $[2524]$ |
| 18.0.316...879.3 | $x^{18} - 15 x^{16} - 6 x^{15} + 162 x^{14} + 192 x^{13} - 1032 x^{12} - 3222 x^{11} + 2442 x^{10} + 28042 x^{9} + 34182 x^{8} - 85296 x^{7} - 251841 x^{6} - 140562 x^{5} + 260853 x^{4} + 730068 x^{3} + 946224 x^{2} + 563136 x + 123904$ | $-\,3^{31}\cdot 13^{15}$ | $S_3 \times C_6$ (as 18T6) | $[3, 468]$ |
| 18.0.384...464.1 | $x^{18} - 3 x^{17} - 20 x^{16} + 106 x^{15} - 41 x^{14} - 887 x^{13} + 3829 x^{12} - 10697 x^{11} + 24681 x^{10} - 49615 x^{9} + 89621 x^{8} - 136105 x^{7} + 189892 x^{6} - 209572 x^{5} + 227493 x^{4} - 178187 x^{3} + 150282 x^{2} - 71876 x + 51944$ | $-\,2^{12}\cdot 37^{6}\cdot 101^{6}\cdot 151^{3}$ | $D_6\times S_4$ (as 18T111) | $[1134]$ |
| 18.0.429...352.1 | $x^{18} + 36 x^{16} + 484 x^{14} + 3305 x^{12} + 12769 x^{10} + 28966 x^{8} + 38380 x^{6} + 28335 x^{4} + 10332 x^{2} + 1323$ | $-\,2^{18}\cdot 3^{9}\cdot 7^{6}\cdot 643^{6}$ | $A_4^3:D_6$ (as 18T632) | $[2, 2, 2, 240]$ |
| 18.0.432...768.1 | $x^{18} - 6 x^{17} + 21 x^{16} - 66 x^{15} + 297 x^{14} - 742 x^{13} + 1346 x^{12} - 4058 x^{11} + 9676 x^{10} - 2428 x^{9} + 22175 x^{8} - 86316 x^{7} - 133405 x^{6} - 23318 x^{5} + 742493 x^{4} + 1890250 x^{3} + 3195846 x^{2} + 1805644 x + 966337$ | $-\,2^{27}\cdot 7^{12}\cdot 13^{12}$ | $C_6 \times C_3$ (as 18T2) | $[4, 268]$ |
| 18.0.519...191.1 | $x^{18} - 3 x^{17} + 8 x^{16} + 12 x^{15} + 181 x^{14} - 201 x^{13} + 554 x^{12} + 4448 x^{11} + 1722 x^{10} - 19194 x^{9} + 21415 x^{8} + 61786 x^{7} - 43679 x^{6} - 81955 x^{5} + 216263 x^{4} + 55577 x^{3} - 55738 x^{2} - 11032 x + 352312$ | $-\,3^{9}\cdot 13^{15}\cdot 61^{6}$ | $S_3 \times C_6$ (as 18T6) | $[2, 2, 2, 140]$ |
| 18.0.544...631.1 | $x^{18} - 3 x^{17} - 11 x^{16} + 48 x^{15} + 79 x^{14} - 462 x^{13} + 125 x^{12} + 1926 x^{11} - 955 x^{10} - 7360 x^{9} + 17789 x^{8} - 11474 x^{7} + 16059 x^{6} - 53184 x^{5} + 183762 x^{4} - 280185 x^{3} + 373368 x^{2} - 294300 x + 284488$ | $-\,7^{12}\cdot 239^{3}\cdot 257^{6}$ | $A_4\times D_6$ (as 18T60) | $[1028]$ |
| 18.0.581...247.1 | $x^{18} - x^{17} + 58 x^{16} - 58 x^{15} + 1426 x^{14} - 1426 x^{13} + 19381 x^{12} - 19381 x^{11} + 159430 x^{10} - 159430 x^{9} + 819661 x^{8} - 819661 x^{7} + 2647993 x^{6} - 2647993 x^{5} + 5390491 x^{4} - 5390491 x^{3} + 7260376 x^{2} - 7260376 x + 7634353$ | $-\,13^{9}\cdot 19^{17}$ | $C_{18}$ (as 18T1) | $[9774]$ |
| 18.0.609...424.2 | $x^{18} + 48 x^{16} + 828 x^{14} + 6972 x^{12} + 31500 x^{10} + 77112 x^{8} + 96516 x^{6} + 52272 x^{4} + 8208 x^{2} + 216$ | $-\,2^{33}\cdot 3^{21}\cdot 7^{14}$ | $S_3 \times C_6$ (as 18T6) | $[3, 3, 126]$ |
| 18.0.891...000.1 | $x^{18} + 38 x^{16} + 609 x^{14} + 5357 x^{12} + 28133 x^{10} + 89540 x^{8} + 166180 x^{6} + 159887 x^{4} + 57967 x^{2} + 2401$ | $-\,2^{30}\cdot 5^{6}\cdot 7^{4}\cdot 19^{12}$ | $A_4^2:C_2^2$ (as 18T175) | $[2, 1120]$ |
| 18.0.119...048.1 | $x^{18} + 37 x^{16} + 518 x^{14} + 3515 x^{12} + 12284 x^{10} + 22200 x^{8} + 20683 x^{6} + 9287 x^{4} + 1591 x^{2} + 37$ | $-\,2^{18}\cdot 37^{17}$ | $C_{18}$ (as 18T1) | $[1526]$ |
| 18.0.142...143.1 | $x^{18} - 28 x^{16} - 35 x^{15} + 399 x^{14} + 861 x^{13} - 2733 x^{12} - 10241 x^{11} + 6986 x^{10} + 68229 x^{9} + 60851 x^{8} - 195468 x^{7} - 422265 x^{6} + 150430 x^{5} + 1760248 x^{4} + 3109309 x^{3} + 3147438 x^{2} + 2033283 x + 894823$ | $-\,7^{12}\cdot 19^{12}\cdot 167^{3}$ | $C_6\times A_4$ (as 18T25) | $[1659]$ |
| 18.0.147...000.1 | $x^{18} - 2 x^{17} + 30 x^{16} - 50 x^{15} + 552 x^{14} - 814 x^{13} + 6983 x^{12} - 8936 x^{11} + 65641 x^{10} - 72082 x^{9} + 465597 x^{8} - 424984 x^{7} + 2471666 x^{6} - 1778572 x^{5} + 9429355 x^{4} - 4814010 x^{3} + 23461605 x^{2} - 6474360 x + 29134601$ | $-\,2^{18}\cdot 5^{9}\cdot 19^{16}$ | $C_{18}$ (as 18T1) | $[8582]$ |
| 18.0.179...424.4 | $x^{18} + 24 x^{16} - 6 x^{15} + 387 x^{14} + 6 x^{13} + 3941 x^{12} - 36 x^{11} + 28167 x^{10} + 5912 x^{9} + 163782 x^{8} + 50502 x^{7} + 623048 x^{6} + 233514 x^{5} + 2503317 x^{4} + 2370846 x^{3} + 8823831 x^{2} + 5384334 x + 8256151$ | $-\,2^{27}\cdot 3^{24}\cdot 7^{15}$ | $C_6 \times C_3$ (as 18T2) | $[2, 18, 252]$ |
| 18.0.185...608.1 | $x^{18} - 6 x^{17} + 42 x^{16} - 162 x^{15} + 666 x^{14} - 1946 x^{13} + 5146 x^{12} - 10402 x^{11} + 17101 x^{10} - 23298 x^{9} + 62720 x^{8} - 128674 x^{7} + 171273 x^{6} - 132222 x^{5} + 221722 x^{4} - 340356 x^{3} + 777688 x^{2} - 587872 x + 444536$ | $-\,2^{18}\cdot 7^{12}\cdot 13^{15}$ | $C_6 \times C_3$ (as 18T2) | $[2, 2, 2, 18, 18]$ |
| 18.0.188...504.1 | $x^{18} - 3 x^{17} - 11 x^{16} + 42 x^{15} + 94 x^{14} - 371 x^{13} - 124 x^{12} + 1413 x^{11} + 903 x^{10} - 5469 x^{9} + 9062 x^{8} - 5182 x^{7} + 25901 x^{6} - 43606 x^{5} + 124818 x^{4} - 136344 x^{3} + 216724 x^{2} - 113160 x + 268808$ | $-\,2^{12}\cdot 7^{12}\cdot 79^{6}\cdot 239^{3}$ | $A_4\times D_6$ (as 18T60) | $[2, 750]$ |
| 18.0.206...199.1 | $x^{18} - 3 x^{17} - 11 x^{16} + 36 x^{15} + 109 x^{14} - 280 x^{13} - 343 x^{12} + 840 x^{11} + 2253 x^{10} - 2652 x^{9} + 3677 x^{8} - 4472 x^{7} + 28097 x^{6} - 19796 x^{5} + 88116 x^{4} - 42357 x^{3} + 170128 x^{2} + 30576 x + 260288$ | $-\,3^{6}\cdot 7^{12}\cdot 107^{6}\cdot 239^{3}$ | $A_4\times D_6$ (as 18T60) | $[1472]$ |
| 18.0.216...875.3 | $x^{18} - 3 x^{17} + x^{16} - x^{15} + 124 x^{14} + 20 x^{13} - 15 x^{12} - 355 x^{11} + 4994 x^{10} + 14123 x^{9} + 44804 x^{8} + 14520 x^{7} + 74956 x^{6} - 52128 x^{5} + 378444 x^{4} + 597223 x^{3} + 2217367 x^{2} + 2753785 x + 3521939$ | $-\,5^{9}\cdot 7^{15}\cdot 13^{12}$ | $C_6 \times C_3$ (as 18T2) | $[6, 6, 78]$ |
| 18.0.216...928.3 | $x^{18} + 36 x^{16} - 60 x^{15} + 468 x^{14} - 1440 x^{13} + 6276 x^{12} - 11160 x^{11} + 48168 x^{10} - 58400 x^{9} + 171936 x^{8} - 208800 x^{7} + 440208 x^{6} - 303840 x^{5} + 590976 x^{4} + 188640 x^{3} + 451008 x^{2} + 1259712$ | $-\,2^{12}\cdot 3^{24}\cdot 83^{9}$ | $S_3 \times C_3$ (as 18T3) | $[2, 2, 2, 126]$ |
| 18.0.250...144.1 | $x^{18} + 56 x^{16} + 1174 x^{14} + 11479 x^{12} + 53662 x^{10} + 118116 x^{8} + 128427 x^{6} + 68376 x^{4} + 16428 x^{2} + 1369$ | $-\,2^{26}\cdot 37^{8}\cdot 101^{6}$ | $C_2^7:S_3^2$ (as 18T461) | $[2, 2, 326]$ |
| 18.0.265...127.2 | $x^{18} - 3 x^{17} - 24 x^{16} + 80 x^{15} + 264 x^{14} - 996 x^{13} - 208 x^{12} + 3414 x^{11} - 1398 x^{10} - 4424 x^{9} + 45528 x^{8} - 108612 x^{7} + 306560 x^{6} - 431268 x^{5} + 994161 x^{4} - 776387 x^{3} + 1606332 x^{2} - 619836 x + 1068904$ | $-\,3^{24}\cdot 7^{9}\cdot 13^{12}$ | $C_6 \times C_3$ (as 18T2) | $[4, 532]$ |
| 18.0.284...824.1 | $x^{18} - 7 x^{17} + 60 x^{15} + 97 x^{14} - 405 x^{13} - 125 x^{12} + 549 x^{11} + 883 x^{10} - 2153 x^{9} + 8299 x^{8} + 11149 x^{7} + 22162 x^{6} + 11574 x^{5} + 59219 x^{4} + 22797 x^{3} + 82674 x^{2} - 31620 x + 103528$ | $-\,2^{12}\cdot 3^{6}\cdot 37^{6}\cdot 47^{6}\cdot 151^{3}$ | $D_6\times S_4$ (as 18T111) | $[1620]$ |
| 18.0.317...299.2 | $x^{18} - 9 x^{17} + 63 x^{16} - 300 x^{15} + 1368 x^{14} - 5040 x^{13} + 18192 x^{12} - 54630 x^{11} + 164196 x^{10} - 411866 x^{9} + 1056267 x^{8} - 2200338 x^{7} + 4844985 x^{6} - 8116569 x^{5} + 15278400 x^{4} - 19032684 x^{3} + 30278943 x^{2} - 21799593 x + 28658393$ | $-\,3^{44}\cdot 19^{9}$ | $C_{18}$ (as 18T1) | $[2, 3746]$ |
| 18.0.320...399.1 | $x^{18} - 15 x^{16} - 3 x^{15} + 141 x^{14} + 96 x^{13} - 491 x^{12} - 705 x^{11} + 1944 x^{10} + 2782 x^{9} + 5673 x^{8} + 5436 x^{7} + 21931 x^{6} + 16989 x^{5} + 67347 x^{4} + 59093 x^{3} + 112566 x^{2} + 67080 x + 165887$ | $-\,3^{24}\cdot 199^{3}\cdot 229^{6}$ | $A_4\times D_6$ (as 18T60) | $[2, 526]$ |
| 18.0.346...375.1 | $x^{18} - 6 x^{17} + 9 x^{16} + 10 x^{15} + 48 x^{14} - 84 x^{13} - 486 x^{12} + 372 x^{11} + 3765 x^{10} + 6720 x^{9} + 26967 x^{8} - 27264 x^{7} + 6863 x^{6} - 52260 x^{5} + 123351 x^{4} + 147158 x^{3} + 602835 x^{2} + 711594 x + 1307431$ | $-\,3^{27}\cdot 5^{9}\cdot 13^{12}$ | $C_6 \times C_3$ (as 18T2) | $[2, 14, 98]$ |
| 18.0.374...000.1 | $x^{18} + 45 x^{16} + 708 x^{14} + 5093 x^{12} + 18705 x^{10} + 36303 x^{8} + 37039 x^{6} + 19110 x^{4} + 4500 x^{2} + 375$ | $-\,2^{18}\cdot 3^{27}\cdot 5^{3}\cdot 107^{6}$ | $A_4^2:C_2^2$ (as 18T175) | $[2, 2, 2, 182]$ |
| 18.0.374...000.2 | $x^{18} + 27 x^{16} + 300 x^{14} + 1790 x^{12} + 6291 x^{10} + 13431 x^{8} + 17229 x^{6} + 12465 x^{4} + 4275 x^{2} + 375$ | $-\,2^{18}\cdot 3^{27}\cdot 5^{3}\cdot 107^{6}$ | $C_2^4:(C_6\times S_4)$ (as 18T367) | $[2, 2, 2, 308]$ |
| 18.0.418...759.1 | $x^{18} - 3 x^{17} - 23 x^{16} + 100 x^{15} + 223 x^{14} - 1582 x^{13} + 171 x^{12} + 12526 x^{11} - 16859 x^{10} - 53738 x^{9} + 170699 x^{8} - 35072 x^{7} - 476903 x^{6} + 521104 x^{5} + 1242660 x^{4} - 4311235 x^{3} + 6237456 x^{2} - 5065556 x + 2301032$ | $-\,7^{12}\cdot 19^{12}\cdot 239^{3}$ | $C_6\times A_4$ (as 18T25) | $[2, 674]$ |
| 18.0.426...968.6 | $x^{18} + 48 x^{16} + 960 x^{14} + 10380 x^{12} + 65808 x^{10} + 247680 x^{8} + 531252 x^{6} + 576072 x^{4} + 226800 x^{2} + 1512$ | $-\,2^{33}\cdot 3^{21}\cdot 7^{15}$ | $S_3 \times C_6$ (as 18T6) | $[2, 1638]$ |
| 18.0.497...287.1 | $x^{18} - 7 x^{17} + 6 x^{16} + 62 x^{15} - 87 x^{14} - 453 x^{13} + 1582 x^{12} - 2109 x^{11} + 4032 x^{10} - 13245 x^{9} + 41381 x^{8} - 73223 x^{7} + 125132 x^{6} - 153409 x^{5} + 331388 x^{4} - 449504 x^{3} + 758771 x^{2} - 538288 x + 477047$ | $-\,7^{9}\cdot 37^{16}$ | $C_{18}$ (as 18T1) | $[9, 171]$ |