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 |
|---|---|---|---|---|
| 18.0.149...808.1 | $x^{18} + 75 x^{16} + 2178 x^{14} + 32829 x^{12} + 283689 x^{10} + 1444041 x^{8} + 4240305 x^{6} + 6661035 x^{4} + 4752513 x^{2} + 1137267$ | $-\,2^{18}\cdot 3^{27}\cdot 73^{3}\cdot 577^{3}$ | $S_4^3.C_6$ (as 18T767) | $[2, 4, 1548]$ |
| 18.0.350...571.1 | $x^{18} + 72 x^{16} + 2160 x^{14} + 34944 x^{12} + 329472 x^{10} - 4693 x^{9} + 1824768 x^{8} - 168948 x^{7} + 5677056 x^{6} - 2027376 x^{5} + 8847360 x^{4} - 9010560 x^{3} + 5308416 x^{2} - 10812672 x + 22810681$ | $-\,3^{45}\cdot 17^{9}$ | $C_{18}$ (as 18T1) | $[2, 2, 2774]$ |
| 18.0.504...000.2 | $x^{18} + 27 x^{16} + 495 x^{14} + 6219 x^{12} + 59292 x^{10} - 2 x^{9} + 430038 x^{8} + 378 x^{7} + 2361801 x^{6} - 8244 x^{5} + 9427185 x^{4} + 39510 x^{3} + 24883956 x^{2} - 34668 x + 33385281$ | $-\,2^{18}\cdot 3^{44}\cdot 5^{9}$ | $C_{18}$ (as 18T1) | $[24966]$ |
| 18.0.519...303.1 | $x^{18} - 7 x^{17} + 58 x^{16} - 266 x^{15} + 1435 x^{14} - 5199 x^{13} + 21866 x^{12} - 64937 x^{11} + 227650 x^{10} - 559943 x^{9} + 1686287 x^{8} - 3386581 x^{7} + 8904619 x^{6} - 13996282 x^{5} + 32437184 x^{4} - 36161351 x^{3} + 74452082 x^{2} - 44882086 x + 83092129$ | $-\,19^{16}\cdot 23^{9}$ | $C_{18}$ (as 18T1) | $[13149]$ |
| 18.0.649...683.1 | $x^{18} - x^{17} + 77 x^{16} - 77 x^{15} + 2509 x^{14} - 2509 x^{13} + 45069 x^{12} - 45069 x^{11} + 487693 x^{10} - 487693 x^{9} + 3269901 x^{8} - 3269901 x^{7} + 13542669 x^{6} - 13542669 x^{5} + 34088205 x^{4} - 34088205 x^{3} + 52765965 x^{2} - 52765965 x + 57746701$ | $-\,17^{9}\cdot 19^{17}$ | $C_{18}$ (as 18T1) | $[38836]$ |
| 18.0.762...544.1 | $x^{18} - 2 x^{17} + 39 x^{16} - 66 x^{15} + 860 x^{14} - 1276 x^{13} + 12807 x^{12} - 16470 x^{11} + 138889 x^{10} - 152462 x^{9} + 1120553 x^{8} - 1017454 x^{7} + 6677144 x^{6} - 4749676 x^{5} + 28239050 x^{4} - 14144668 x^{3} + 76910381 x^{2} - 20623090 x + 103115431$ | $-\,2^{27}\cdot 3^{9}\cdot 19^{16}$ | $C_{18}$ (as 18T1) | $[18506]$ |
| 18.0.869...008.1 | $x^{18} + 66 x^{16} + 1747 x^{14} + 23660 x^{12} + 173859 x^{10} + 685517 x^{8} + 1396052 x^{6} + 1433185 x^{4} + 689767 x^{2} + 122317$ | $-\,2^{18}\cdot 7^{16}\cdot 13^{9}\cdot 97^{2}$ | $C_2\wr C_9.C_3$ (as 18T586) | $[2, 4, 1584]$ |
| 18.0.111...351.1 | $x^{18} - 6 x^{17} + 57 x^{16} - 212 x^{15} + 1206 x^{14} - 2976 x^{13} + 12940 x^{12} - 17568 x^{11} + 83169 x^{10} - 40258 x^{9} + 573705 x^{8} - 365916 x^{7} + 4002937 x^{6} - 3216606 x^{5} + 17344149 x^{4} - 10599756 x^{3} + 31588815 x^{2} - 10143966 x + 34082749$ | $-\,3^{27}\cdot 7^{12}\cdot 13^{9}$ | $C_6 \times C_3$ (as 18T2) | $[2, 10, 1580]$ |
| 18.0.126...499.8 | $x^{18} - 9 x^{17} + 51 x^{16} - 196 x^{15} + 804 x^{14} - 3012 x^{13} + 12898 x^{12} - 46452 x^{11} + 170676 x^{10} - 511402 x^{9} + 1574124 x^{8} - 3865668 x^{7} + 9988128 x^{6} - 19346514 x^{5} + 40437777 x^{4} - 56155537 x^{3} + 89390700 x^{2} - 70039875 x + 77095313$ | $-\,3^{24}\cdot 7^{12}\cdot 19^{9}$ | $C_6 \times C_3$ (as 18T2) | $[18, 558]$ |
| 18.0.177...903.2 | $x^{18} - 9 x^{17} + 72 x^{16} - 372 x^{15} + 1908 x^{14} - 7560 x^{13} + 30192 x^{12} - 97146 x^{11} + 320526 x^{10} - 855266 x^{9} + 2391597 x^{8} - 5261490 x^{7} + 12570585 x^{6} - 22062519 x^{5} + 44899785 x^{4} - 57927960 x^{3} + 99243441 x^{2} - 73205505 x + 103239849$ | $-\,3^{44}\cdot 23^{9}$ | $C_{18}$ (as 18T1) | $[37449]$ |
| 18.0.200...000.16 | $x^{18} + 15 x^{16} - 8 x^{15} + 333 x^{14} + 24 x^{13} + 5655 x^{12} + 2670 x^{11} + 69687 x^{10} + 43582 x^{9} + 674097 x^{8} + 378498 x^{7} + 4862043 x^{6} + 2018526 x^{5} + 23403354 x^{4} + 6369416 x^{3} + 65929308 x^{2} + 9405912 x + 82566296$ | $-\,2^{18}\cdot 3^{24}\cdot 5^{9}\cdot 7^{12}$ | $C_6 \times C_3$ (as 18T2) | $[6, 6, 6, 6, 18]$ |
| 18.0.293...000.1 | $x^{18} + 68 x^{16} + 1627 x^{14} + 19505 x^{12} + 131697 x^{10} + 516410 x^{8} + 1146558 x^{6} + 1326597 x^{4} + 683179 x^{2} + 102185$ | $-\,2^{30}\cdot 5^{3}\cdot 37^{6}\cdot 107^{3}\cdot 191^{3}$ | $S_4^3.D_6$ (as 18T837) | $[2, 2, 2, 1444]$ |
| 18.0.319...008.1 | $x^{18} + 93 x^{16} + 3519 x^{14} + 70211 x^{12} + 806046 x^{10} + 5497452 x^{8} + 22162597 x^{6} + 50450268 x^{4} + 57830979 x^{2} + 24303817$ | $-\,2^{18}\cdot 3^{24}\cdot 73^{3}\cdot 577^{4}$ | $S_4^3.C_6$ (as 18T765) | $[2, 2, 10388]$ |
| 18.0.435...559.1 | $x^{18} - x^{17} + 96 x^{16} - 96 x^{15} + 3896 x^{14} - 3896 x^{13} + 87021 x^{12} - 87021 x^{11} + 1167646 x^{10} - 1167646 x^{9} + 9658271 x^{8} - 9658271 x^{7} + 48845771 x^{6} - 48845771 x^{5} + 146814521 x^{4} - 146814521 x^{3} + 258142646 x^{2} - 258142646 x + 295252021$ | $-\,3^{9}\cdot 7^{9}\cdot 19^{17}$ | $C_{18}$ (as 18T1) | $[2, 2, 2, 6632]$ |
| 18.0.485...448.1 | $x^{18} + 84 x^{16} + 2772 x^{14} + 47040 x^{12} + 451584 x^{10} + 2540160 x^{8} + 8354304 x^{6} + 15410304 x^{4} + 14224896 x^{2} + 4741632$ | $-\,2^{27}\cdot 3^{27}\cdot 7^{15}$ | $C_6 \times C_3$ (as 18T2) | $[2, 2, 28, 364]$ |
| 18.0.529...128.1 | $x^{18} + 93 x^{16} + 3423 x^{14} + 65693 x^{12} + 725662 x^{10} + 4768100 x^{8} + 18358829 x^{6} + 38317027 x^{4} + 34600118 x^{2} + 4151567$ | $-\,2^{18}\cdot 7^{13}\cdot 593081^{3}$ | $S_4^3.C_6$ (as 18T765) | $[2, 22536]$ |
| 18.0.704...303.2 | $x^{18} - 9 x^{17} + 60 x^{16} - 268 x^{15} + 1272 x^{14} - 5004 x^{13} + 22294 x^{12} - 81192 x^{11} + 315630 x^{10} - 978324 x^{9} + 3218604 x^{8} - 8208228 x^{7} + 22683008 x^{6} - 45561114 x^{5} + 102647091 x^{4} - 147782137 x^{3} + 257711352 x^{2} - 208331724 x + 258264152$ | $-\,3^{24}\cdot 7^{12}\cdot 23^{9}$ | $C_6 \times C_3$ (as 18T2) | $[3, 6, 3942]$ |
| 18.0.762...951.1 | $x^{18} - 7 x^{17} + 76 x^{16} - 378 x^{15} + 2531 x^{14} - 9987 x^{13} + 50888 x^{12} - 164417 x^{11} + 687416 x^{10} - 1828199 x^{9} + 6495797 x^{8} - 13992021 x^{7} + 43041793 x^{6} - 71859458 x^{5} + 193370792 x^{4} - 226538639 x^{3} + 536835424 x^{2} - 336518414 x + 707215681$ | $-\,19^{16}\cdot 31^{9}$ | $C_{18}$ (as 18T1) | $[2, 39906]$ |
| 18.0.861...000.2 | $x^{18} + 9 x^{16} - 16 x^{15} + 360 x^{14} + 240 x^{13} + 3928 x^{12} - 1680 x^{11} + 49218 x^{10} + 47424 x^{9} + 559842 x^{8} + 375408 x^{7} + 3618320 x^{6} + 3283728 x^{5} + 27436416 x^{4} + 39093488 x^{3} + 139982661 x^{2} + 126029568 x + 236250749$ | $-\,2^{24}\cdot 3^{18}\cdot 5^{9}\cdot 7^{14}$ | $S_3 \times C_6$ (as 18T6) | $[6, 6, 378]$ |
| 18.0.123...375.1 | $x^{18} - 3 x^{17} - 2 x^{16} + 226 x^{14} - 314 x^{13} + 2056 x^{12} - 2712 x^{11} + 26144 x^{10} - 23076 x^{9} + 264952 x^{8} - 69734 x^{7} + 1914474 x^{6} - 24520 x^{5} + 9403275 x^{4} - 679057 x^{3} + 28645658 x^{2} - 1743720 x + 39701416$ | $-\,3^{9}\cdot 5^{9}\cdot 7^{12}\cdot 13^{12}$ | $C_6 \times C_3$ (as 18T2) | $[2, 2, 2, 20, 140]$ |
| 18.0.125...339.1 | $x^{18} - 6 x^{17} + 75 x^{16} - 299 x^{15} + 2178 x^{14} - 5913 x^{13} + 32653 x^{12} - 52812 x^{11} + 291324 x^{10} - 201688 x^{9} + 2166219 x^{8} - 907068 x^{7} + 15298582 x^{6} - 8508129 x^{5} + 75490509 x^{4} - 37914480 x^{3} + 173222787 x^{2} - 45736635 x + 210280141$ | $-\,3^{27}\cdot 7^{12}\cdot 17^{9}$ | $C_6 \times C_3$ (as 18T2) | $[2, 2, 13286]$ |
| 18.0.142...459.2 | $x^{18} - 3 x^{17} + 51 x^{16} - 145 x^{15} + 1377 x^{14} - 4017 x^{13} + 24968 x^{12} - 71760 x^{11} + 328884 x^{10} - 886259 x^{9} + 3240978 x^{8} - 7306587 x^{7} + 21644553 x^{6} - 36408891 x^{5} + 88661442 x^{4} - 102732573 x^{3} + 217719351 x^{2} - 173351430 x + 337293181$ | $-\,3^{24}\cdot 7^{15}\cdot 13^{9}$ | $C_6 \times C_3$ (as 18T2) | $[2, 2, 8246]$ |
| 18.0.148...424.3 | $x^{18} - 6 x^{17} + 33 x^{16} - 130 x^{15} + 633 x^{14} - 1870 x^{13} + 6342 x^{12} - 16970 x^{11} + 50908 x^{10} - 87252 x^{9} + 276223 x^{8} - 443116 x^{7} + 892387 x^{6} - 960518 x^{5} + 5324905 x^{4} + 4622682 x^{3} + 21350862 x^{2} + 11905764 x + 19683833$ | $-\,2^{27}\cdot 7^{15}\cdot 13^{12}$ | $C_6 \times C_3$ (as 18T2) | $[6, 6, 1092]$ |
| 18.0.211...008.2 | $x^{18} - 4 x^{17} + 20 x^{16} - 38 x^{15} - 56 x^{14} + 42 x^{13} - 1868 x^{12} - 2142 x^{11} - 766 x^{10} - 7126 x^{9} + 94236 x^{8} + 435918 x^{7} + 1272160 x^{6} + 4190046 x^{5} + 10123484 x^{4} + 18327094 x^{3} + 32238933 x^{2} + 42657746 x + 24890048$ | $-\,2^{18}\cdot 3^{6}\cdot 7^{15}\cdot 13^{12}$ | $S_3 \times C_6$ (as 18T6) | $[3, 3, 2184]$ |
| 18.0.238...816.1 | $x^{18} - 6 x^{17} + 27 x^{16} - 98 x^{15} + 441 x^{14} - 1194 x^{13} + 3092 x^{12} - 8442 x^{11} + 21552 x^{10} - 23424 x^{9} + 91239 x^{8} - 177996 x^{7} + 55755 x^{6} - 228654 x^{5} + 1834899 x^{4} + 3117170 x^{3} + 7609494 x^{2} + 4744224 x + 4634713$ | $-\,2^{27}\cdot 3^{27}\cdot 13^{12}$ | $C_6 \times C_3$ (as 18T2) | $[2, 2, 3458]$ |
| 18.0.260...151.1 | $x^{18} - 9 x^{17} + 90 x^{16} - 516 x^{15} + 3204 x^{14} - 14112 x^{13} + 66792 x^{12} - 238122 x^{11} + 919602 x^{10} - 2697362 x^{9} + 8749269 x^{8} - 20953674 x^{7} + 57705369 x^{6} - 108970803 x^{5} + 254607615 x^{4} - 347840628 x^{3} + 682386453 x^{2} - 523610901 x + 844617131$ | $-\,3^{44}\cdot 31^{9}$ | $C_{18}$ (as 18T1) | $[93339]$ |
| 18.0.290...531.2 | $x^{18} - 7 x^{17} + 15 x^{16} + 6 x^{15} + 41 x^{14} - 547 x^{13} + 2399 x^{12} - 6459 x^{11} + 19848 x^{10} - 51876 x^{9} + 153844 x^{8} - 309033 x^{7} + 710103 x^{6} - 1068295 x^{5} + 2318748 x^{4} - 2871539 x^{3} + 5252508 x^{2} - 3731965 x + 4399861$ | $-\,11^{9}\cdot 37^{16}$ | $C_{18}$ (as 18T1) | $[38, 342]$ |
| 18.0.295...443.1 | $x^{18} - 3 x^{17} + 60 x^{16} - 157 x^{15} + 1116 x^{14} - 1161 x^{13} + 3951 x^{12} + 16026 x^{11} + 7536 x^{10} - 5656 x^{9} + 654144 x^{8} + 635424 x^{7} + 1444480 x^{6} + 14185344 x^{5} + 24462336 x^{4} + 8265216 x^{3} + 41054208 x^{2} + 180725760 x + 207974400$ | $-\,3^{21}\cdot 521^{9}$ | $D_9$ (as 18T5) | $[85, 170]$ |
| 18.0.433...887.1 | $x^{18} + 70 x^{16} - 4 x^{15} + 1925 x^{14} - 210 x^{13} + 27573 x^{12} - 4025 x^{11} + 230055 x^{10} - 36104 x^{9} + 1167950 x^{8} - 164045 x^{7} + 3604930 x^{6} - 360675 x^{5} + 6472620 x^{4} - 293353 x^{3} + 6075300 x^{2} + 2299968$ | $-\,7^{12}\cdot 17^{9}\cdot 31^{9}$ | $S_3 \times C_3$ (as 18T3) | $[3, 3, 9, 9, 18]$ |
| 18.0.612...576.1 | $x^{18} + 74 x^{16} + 2072 x^{14} + 28120 x^{12} + 196544 x^{10} + 710400 x^{8} + 1323712 x^{6} + 1188736 x^{4} + 407296 x^{2} + 18944$ | $-\,2^{27}\cdot 37^{17}$ | $C_{18}$ (as 18T1) | $[17, 1190]$ |
| 18.0.744...000.1 | $x^{18} + 113 x^{16} + 4986 x^{14} + 109769 x^{12} + 1290015 x^{10} + 8207609 x^{8} + 29008613 x^{6} + 56338590 x^{4} + 55167918 x^{2} + 20511149$ | $-\,2^{30}\cdot 5^{12}\cdot 7^{12}\cdot 29^{5}$ | $A_4^2:C_2^2$ (as 18T176) | $[2, 2, 6, 1536]$ |
| 18.0.748...184.2 | $x^{18} + 57 x^{16} + 1211 x^{14} + 12568 x^{12} + 72546 x^{10} + 245270 x^{8} + 483426 x^{6} + 518415 x^{4} + 248454 x^{2} + 26001$ | $-\,2^{18}\cdot 3^{9}\cdot 53^{4}\cdot 107^{9}$ | $C_2\times A_4^3:S_4$ (as 18T781) | $[2, 5006]$ |
| 18.0.759...496.1 | $x^{18} - 3 x^{17} - 26 x^{16} + 56 x^{15} + 394 x^{14} - 320 x^{13} - 3426 x^{12} - 1474 x^{11} + 17675 x^{10} + 29459 x^{9} - 13188 x^{8} - 108234 x^{7} - 101914 x^{6} + 81772 x^{5} + 470828 x^{4} + 848520 x^{3} + 1385816 x^{2} + 1478304 x + 1159120$ | $-\,2^{26}\cdot 37^{6}\cdot 71^{6}\cdot 151^{3}$ | $D_6\times S_4$ (as 18T111) | $[3, 4344]$ |
| 18.0.785...723.2 | $x^{18} - x^{17} + 47 x^{16} + 32 x^{15} + 1551 x^{14} + 1282 x^{13} + 23855 x^{12} + 46050 x^{11} + 258875 x^{10} + 362877 x^{9} + 1037476 x^{8} + 1297357 x^{7} + 2797383 x^{6} + 2663843 x^{5} + 3326344 x^{4} + 1462041 x^{3} + 1415022 x^{2} + 277585 x + 519841$ | $-\,3^{9}\cdot 7^{12}\cdot 19^{16}$ | $C_{18}$ (as 18T1) | $[3, 3, 3, 657]$ |
| 18.0.798...616.1 | $x^{18} - 3 x^{17} + 33 x^{16} - 91 x^{15} + 972 x^{14} - 3216 x^{13} + 17387 x^{12} - 47466 x^{11} + 246777 x^{10} - 744566 x^{9} + 2781420 x^{8} - 5768394 x^{7} + 20679591 x^{6} - 45616323 x^{5} + 134273652 x^{4} - 125897574 x^{3} + 462427464 x^{2} - 1117528098 x + 2682840203$ | $-\,2^{12}\cdot 3^{18}\cdot 7^{15}\cdot 13^{9}$ | $S_3 \times C_6$ (as 18T6) | $[2, 2, 2, 2, 4, 468]$ |
| 18.0.870...504.1 | $x^{18} - 7 x^{17} + 21 x^{16} - 10 x^{15} - 25 x^{14} - 337 x^{13} + 3019 x^{12} - 11321 x^{11} + 32356 x^{10} - 81340 x^{9} + 216453 x^{8} - 535373 x^{7} + 1224513 x^{6} - 2351635 x^{5} + 4043761 x^{4} - 5640557 x^{3} + 6680809 x^{2} - 5296030 x + 2999263$ | $-\,2^{12}\cdot 11^{9}\cdot 37^{14}$ | $S_3 \times C_6$ (as 18T6) | $[2, 6, 24, 72]$ |
| 18.0.950...296.2 | $x^{18} - 6 x^{17} + 81 x^{16} - 370 x^{15} + 2577 x^{14} - 9226 x^{13} + 39726 x^{12} - 107954 x^{11} + 304596 x^{10} - 615760 x^{9} + 1620055 x^{8} - 2975076 x^{7} + 6181459 x^{6} - 8245054 x^{5} + 15664617 x^{4} - 17759238 x^{3} + 36433958 x^{2} - 26053208 x + 31314401$ | $-\,2^{27}\cdot 7^{12}\cdot 13^{15}$ | $C_6 \times C_3$ (as 18T2) | $[2, 2, 6, 6, 378]$ |
| 18.0.104...499.4 | $x^{18} - 3 x^{17} + 7 x^{16} - 24 x^{15} + 322 x^{14} - 530 x^{13} + 4726 x^{12} - 6396 x^{11} + 62002 x^{10} - 59326 x^{9} + 668982 x^{8} - 297270 x^{7} + 5328864 x^{6} - 804120 x^{5} + 29142209 x^{4} - 3014537 x^{3} + 98419102 x^{2} - 6470051 x + 152453839$ | $-\,7^{12}\cdot 13^{12}\cdot 19^{9}$ | $C_6 \times C_3$ (as 18T2) | $[18, 1638]$ |
| 18.0.144...223.2 | $x^{18} - 3 x^{17} + 18 x^{16} - 147 x^{15} + 822 x^{14} - 1827 x^{13} - 99 x^{12} + 6528 x^{11} + 29988 x^{10} - 74840 x^{9} - 40512 x^{8} + 12960 x^{7} + 1123200 x^{6} - 1445376 x^{5} - 829440 x^{4} + 1155072 x^{3} + 3244032 x^{2} - 4718592 x + 2097152$ | $-\,3^{30}\cdot 7^{15}\cdot 23^{6}$ | $S_3 \times C_6$ (as 18T6) | $[2, 2, 3192]$ |
| 18.0.165...000.4 | $x^{18} + 5 x^{16} - 16 x^{15} + 306 x^{14} + 172 x^{13} + 5100 x^{12} + 4488 x^{11} + 75533 x^{10} + 72264 x^{9} + 817621 x^{8} + 822724 x^{7} + 6632797 x^{6} + 5813816 x^{5} + 37070685 x^{4} + 21380228 x^{3} + 129463023 x^{2} + 35149140 x + 219558249$ | $-\,2^{18}\cdot 5^{9}\cdot 7^{12}\cdot 13^{12}$ | $C_6 \times C_3$ (as 18T2) | $[2, 2, 2, 18, 558]$ |
| 18.0.179...107.1 | $x^{18} - 7 x^{17} + 60 x^{16} - 170 x^{15} + 1392 x^{14} - 4613 x^{13} + 24354 x^{12} - 23677 x^{11} + 48833 x^{10} - 35038 x^{9} + 59244 x^{8} - 39753 x^{7} + 33797 x^{6} - 10244 x^{5} + 1771 x^{4} - 295 x^{3} + 43 x^{2} - 8 x + 1$ | $-\,37^{12}\cdot 67^{9}$ | $S_3 \times C_3$ (as 18T3) | $[2, 2, 2, 2, 8, 344]$ |
| 18.0.210...408.5 | $x^{18} - 2 x^{17} + 19 x^{16} + 38 x^{15} + 81 x^{14} + 826 x^{13} + 3336 x^{12} + 3902 x^{11} + 45764 x^{10} - 17244 x^{9} + 40103 x^{8} - 540496 x^{7} - 196809 x^{6} - 1431434 x^{5} - 69861 x^{4} - 50646490 x^{3} + 64290142 x^{2} + 55016416 x + 1769766817$ | $-\,2^{18}\cdot 7^{12}\cdot 157^{9}$ | $S_3 \times C_3$ (as 18T3) | $[6, 18, 126]$ |
| 18.0.215...000.1 | $x^{18} - 3 x^{17} + 47 x^{16} - 172 x^{15} + 1517 x^{14} - 5332 x^{13} + 22374 x^{12} - 75980 x^{11} + 148668 x^{10} + 42506 x^{9} - 580776 x^{8} + 29214 x^{7} + 5997076 x^{6} - 20620332 x^{5} + 41420961 x^{4} - 55016363 x^{3} + 52690863 x^{2} - 31834602 x + 13067109$ | $-\,2^{12}\cdot 5^{9}\cdot 11^{6}\cdot 19^{15}$ | $S_3 \times C_6$ (as 18T6) | $[2, 2, 4, 4312]$ |
| 18.0.231...488.1 | $x^{18} + 76 x^{16} + 2166 x^{14} + 29716 x^{12} + 209741 x^{10} + 768208 x^{8} + 1451581 x^{6} + 1344364 x^{4} + 521284 x^{2} + 54872$ | $-\,2^{33}\cdot 11^{6}\cdot 19^{15}$ | $S_3 \times C_6$ (as 18T6) | $[90, 180]$ |
| 18.0.243...000.5 | $x^{18} - 2375 x^{12} + 2291875 x^{6} + 421875$ | $-\,2^{12}\cdot 3^{21}\cdot 5^{12}\cdot 13^{12}$ | $C_3^2 : C_2$ (as 18T4) | $[3, 3, 6, 6, 6, 6]$ |
| 18.0.294...488.1 | $x^{18} - 6 x^{17} - 3 x^{16} + 77 x^{15} - 30 x^{14} - 611 x^{13} + 891 x^{12} + 1526 x^{11} - 2479 x^{10} - 5449 x^{9} + 19416 x^{8} - 30707 x^{7} + 50896 x^{6} - 68306 x^{5} + 113908 x^{4} - 133788 x^{3} + 112784 x^{2} - 59608 x + 176912$ | $-\,2^{12}\cdot 79^{6}\cdot 127^{3}\cdot 229^{6}$ | $D_6\times S_4$ (as 18T111) | $[19660]$ |
| 18.0.295...000.1 | $x^{18} - 2 x^{17} + 20 x^{16} - 58 x^{15} + 421 x^{14} - 516 x^{13} + 6419 x^{12} - 2572 x^{11} + 71211 x^{10} + 17826 x^{9} + 639262 x^{8} + 466198 x^{7} + 4295158 x^{6} + 3906398 x^{5} + 19859011 x^{4} + 16508326 x^{3} + 53966797 x^{2} + 27726080 x + 60112841$ | $-\,2^{24}\cdot 5^{9}\cdot 37^{14}$ | $S_3 \times C_6$ (as 18T6) | $[2, 2, 2, 4238]$ |
| 18.0.308...376.2 | $x^{18} - 9 x^{17} + 96 x^{16} - 518 x^{15} + 3228 x^{14} - 10782 x^{13} + 42574 x^{12} - 97176 x^{11} + 161823 x^{10} - 297157 x^{9} - 55194 x^{8} + 410082 x^{7} + 2610916 x^{6} - 4401372 x^{5} + 87864060 x^{4} - 169850772 x^{3} + 539250456 x^{2} - 713931504 x + 599486056$ | $-\,2^{12}\cdot 3^{21}\cdot 7^{14}\cdot 13^{9}$ | $S_3 \times C_6$ (as 18T6) | $[2, 2, 2, 4, 4, 468]$ |
| 18.0.330...344.1 | $x^{18} - 2 x^{17} + 50 x^{16} + 26 x^{15} + 958 x^{14} + 606 x^{13} + 11197 x^{12} + 636 x^{11} + 68077 x^{10} - 139670 x^{9} + 170189 x^{8} - 1801562 x^{7} + 93271 x^{6} - 6155838 x^{5} + 11588776 x^{4} + 36901748 x^{3} + 100260832 x^{2} + 145398680 x + 203590394$ | $-\,2^{18}\cdot 13^{2}\cdot 193^{6}\cdot 229^{6}$ | $C_2\times A_4^3:S_4$ (as 18T769) | $[2, 2, 2, 12460]$ |
| 18.0.344...983.1 | $x^{18} - 3 x^{17} - 17 x^{16} + 50 x^{15} + 157 x^{14} - 404 x^{13} - 675 x^{12} + 1712 x^{11} + 2751 x^{10} - 3844 x^{9} + 313 x^{8} - 6978 x^{7} + 27375 x^{6} - 1454 x^{5} + 34418 x^{4} - 57389 x^{3} + 38988 x^{2} + 39252 x + 133128$ | $-\,3^{6}\cdot 103^{3}\cdot 107^{6}\cdot 257^{6}$ | $D_6\times S_4$ (as 18T111) | $[2, 2, 2700]$ |