| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
| 18.4.613...408.1 |
$x^{18} - 18 x^{16} - 12 x^{15} + 117 x^{14} + 180 x^{13} - 210 x^{12} - 912 x^{11} - 1071 x^{10} + 1200 x^{9} + 5742 x^{8} + 5748 x^{7} - 921 x^{6} - 3468 x^{5} + 306 x^{4} + 984 x^{3} - 342 x^{2} + 24 x + 4$ |
$18$ |
[4,7] |
$-\,2^{46}\cdot 3^{26}\cdot 7^{3}$ |
$3$ |
$39.748770239$ |
|
|
|
|
$C_3^4:(C_6^2:C_4)$ (as 18T576) |
trivial |
trivial |
$2$ |
$10$ |
$537112098.848$ |
| 18.4.231...976.1 |
$x^{18} - 6 x^{16} - 36 x^{15} + 156 x^{13} + 456 x^{12} + 252 x^{11} - 627 x^{10} - 1148 x^{9} - 810 x^{8} + 888 x^{7} + 1188 x^{6} - 432 x^{5} - 408 x^{4} - 24 x^{3} + 18 x^{2} + 24 x + 4$ |
$18$ |
[4,7] |
$-\,2^{50}\cdot 3^{30}$ |
$2$ |
$42.7953441874$ |
|
|
|
|
$C_3^4:(C_6^2:C_4)$ (as 18T576) |
trivial |
trivial |
$2$ |
$10$ |
$631164608.461$ |
| 18.4.463...952.1 |
$x^{18} - 18 x^{16} - 12 x^{15} + 135 x^{14} + 180 x^{13} - 480 x^{12} - 1080 x^{11} + 495 x^{10} + 3080 x^{9} + 1782 x^{8} - 3420 x^{7} - 11343 x^{6} - 1404 x^{5} + 38412 x^{4} - 19200 x^{3} - 50328 x^{2} + 70560 x - 23264$ |
$18$ |
[4,7] |
$-\,2^{51}\cdot 3^{30}$ |
$2$ |
$44.47545627795355$ |
|
|
|
|
$C_3^4:(C_6^2:C_4)$ (as 18T576) |
trivial |
trivial |
$2$ |
$10$ |
$951668872.2302067$ |
| 18.6.727...712.1 |
$x^{18} - 18 x^{16} - x^{15} + 117 x^{14} - 27 x^{13} - 369 x^{12} + 366 x^{11} + 18 x^{10} - 768 x^{9} + 1332 x^{8} - 728 x^{6} + 1008 x^{5} - 432 x^{4} - 384 x^{3} + 192 x^{2} - 256$ |
$18$ |
[6,6] |
$2^{12}\cdot 3^{27}\cdot 13^{12}$ |
$3$ |
$45.6034235559$ |
$215.0532439469929$ |
|
|
|
$C_3^4:(C_6^2:C_4)$ (as 18T576) |
trivial |
trivial |
$2$ |
$11$ |
$289404566.926$ |
| 18.2.116...456.1 |
$x^{18} - 57 x^{16} - 56 x^{15} + 1017 x^{14} + 2532 x^{13} - 1491 x^{12} - 24102 x^{11} - 32877 x^{10} - 46124 x^{9} - 45630 x^{8} - 363246 x^{7} - 213343 x^{6} + 1137708 x^{5} + 5266716 x^{4} + 4425096 x^{3} + 1727856 x^{2} - 1314144 x + 4034368$ |
$18$ |
[2,8] |
$2^{12}\cdot 3^{33}\cdot 13^{15}$ |
$3$ |
$100.854455962$ |
|
|
|
|
$C_3^4:(C_6^2:C_4)$ (as 18T576) |
$[3]$ |
$[3]$ |
$2$ |
$9$ |
$51867970070.3$ |
| 18.6.122...872.1 |
$x^{18} - 6 x^{17} + 15 x^{16} - 48 x^{15} - 78 x^{14} + 1620 x^{13} - 2514 x^{12} - 10248 x^{11} + 22575 x^{10} + 5846 x^{9} - 43767 x^{8} - 2232 x^{7} + 60048 x^{6} - 19056 x^{5} - 23832 x^{4} + 17664 x^{3} - 2880 x^{2} - 768 x + 128$ |
$18$ |
[6,6] |
$2^{50}\cdot 3^{24}\cdot 1567^{3}$ |
$3$ |
$101.127111997$ |
|
|
|
|
$C_3^4:(C_6^2:C_4)$ (as 18T576) |
trivial |
$[2]$ |
$2$ |
$11$ |
$2048242703160$ |
| 18.6.117...344.1 |
$x^{18} + 36 x^{16} - 60 x^{15} - 54 x^{14} + 72 x^{13} - 3708 x^{12} - 864 x^{11} - 2088 x^{10} + 46624 x^{9} + 106272 x^{8} - 413280 x^{7} + 564336 x^{6} + 2044224 x^{5} - 5198112 x^{4} - 4331904 x^{3} + 12916800 x^{2} + 2135808 x - 13174912$ |
$18$ |
[6,6] |
$2^{46}\cdot 3^{30}\cdot 7^{6}\cdot 41^{3}$ |
$4$ |
$130.315965232$ |
|
|
|
|
$C_3^4:(C_6^2:C_4)$ (as 18T576) |
trivial |
trivial |
$2$ |
$11$ |
$29059847084900$ |
| 18.6.216...000.1 |
$x^{18} - 3 x^{17} - 15 x^{16} + 69 x^{15} - 846 x^{14} + 3867 x^{13} + 16107 x^{12} + 46644 x^{11} + 382065 x^{10} - 613030 x^{9} + 570666 x^{8} + 592680 x^{7} - 883320 x^{6} - 749160 x^{5} + 379680 x^{4} + 193200 x^{3} + 32400 x^{2} - 4800 x - 1600$ |
$18$ |
[6,6] |
$2^{12}\cdot 3^{24}\cdot 5^{12}\cdot 11^{6}\cdot 3511^{3}$ |
$5$ |
$174.126300443$ |
|
|
|
|
$C_3^4:(C_6^2:C_4)$ (as 18T576) |
trivial |
$[2]$ |
$2$ |
$11$ |
$49924278928300$ |
| 18.12.643...016.1 |
$x^{18} - 6 x^{17} - 165 x^{16} + 244 x^{15} + 8913 x^{14} + 40110 x^{13} + 108067 x^{12} - 1612512 x^{11} - 20151420 x^{10} - 63799976 x^{9} + 132918156 x^{8} + 1531504776 x^{7} + 2883604616 x^{6} - 8073105096 x^{5} - 27515405844 x^{4} - 2899211376 x^{3} + 3680958876 x^{2} + 55125836136 x + 318109808548$ |
$18$ |
[12,3] |
$-\,2^{49}\cdot 3^{20}\cdot 7^{6}\cdot 17^{6}\cdot 487^{3}$ |
$5$ |
$308.585668091$ |
$18541.079591966358$ |
|
|
|
$C_3^4:(C_6^2:C_4)$ (as 18T576) |
trivial |
$[2, 2]$ |
$2$ |
$14$ |
$148056327645000000$ |
| 18.18.220...000.1 |
$x^{18} - 19674 x^{16} - 236892 x^{15} + 141285519 x^{14} + 2591050644 x^{13} - 483401755344 x^{12} - 9309346836120 x^{11} + 919061549546175 x^{10} + 14739425235311240 x^{9} - 1067582767106931570 x^{8} - 10423786760736518700 x^{7} + 770353183144777007265 x^{6} + 1519419179629720980900 x^{5} - 315065054456543206397700 x^{4} + 1832965846899730969466400 x^{3} + 51184572251157572179388400 x^{2} - 717390367091535907200369600 x + 2636432883430939313935566400$ |
$18$ |
[18,0] |
$2^{12}\cdot 3^{30}\cdot 5^{15}\cdot 11^{7}\cdot 2339^{4}\cdot 34819^{4}$ |
$6$ |
$5512.08232413$ |
|
|
|
|
$C_3^4:(C_6^2:C_4)$ (as 18T576) |
not computed |
not computed |
$2$ |
$17$ |
|
| 18.12.194...875.1 |
$x^{18} - 17521 x^{16} - 569479 x^{15} + 33727551 x^{14} + 3197342900 x^{13} + 265333015838 x^{12} - 7939735674291 x^{11} - 1204369129097611 x^{10} + 29127829411331299 x^{9} + 1098666998941876650 x^{8} - 52371747880387279692 x^{7} + 570089624510888144453 x^{6} + 42318523694808649767048 x^{5} - 1020163773496403914837031 x^{4} - 19198186493168895404375756 x^{3} + 296594972428063792018539441 x^{2} + 4443767388805538134083741964 x + 10265976897589850970755619041$ |
$18$ |
[12,3] |
$-\,3^{8}\cdot 5^{13}\cdot 31^{6}\cdot 61^{6}\cdot 839^{3}\cdot 21167611^{6}$ |
$6$ |
$54736.9186683457$ |
|
|
|
? |
$C_3^4:(C_6^2:C_4)$ (as 18T576) |
not computed |
not computed |
$2$ |
$14$ |
|
