| 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 |
Unit signature rank |
| 18.4.169...264.1 |
$x^{18} - x^{14} + 3 x^{12} - 9 x^{10} - 2 x^{8} - 24 x^{6} - 9 x^{4} - x^{2} + 1$ |
$18$ |
(4, 7) |
$-\,2^{24}\cdot 3^{6}\cdot 7^{12}$ |
$3$ |
$13.2987995223$ |
$22.58643281430495$ |
|
|
? |
$A_4\times D_6$ (as 18T60) |
trivial |
trivial |
$2$ |
$10$ |
$727.594007806$ |
$4$ |
| 18.0.981...544.2 |
$x^{18} + 7 x^{16} + 19 x^{14} + 40 x^{12} + 90 x^{10} + 143 x^{8} + 123 x^{6} + 55 x^{4} + 12 x^{2} + 1$ |
$18$ |
(0, 9) |
$-\,2^{24}\cdot 37^{6}\cdot 151^{2}$ |
$3$ |
$14.6627619978$ |
|
|
|
? |
$S_4^3.D_6$ (as 18T836) |
trivial |
trivial |
$2$ |
$8$ |
$931.387150622$ |
$0$ |
| 18.0.439...464.1 |
$x^{18} + x^{16} + 3 x^{14} + 10 x^{12} + 14 x^{10} - 5 x^{8} + 39 x^{6} - 11 x^{4} + 1$ |
$18$ |
(0, 9) |
$-\,2^{24}\cdot 11^{6}\cdot 23^{6}$ |
$3$ |
$15.9372542574$ |
$56.68244639377905$ |
|
|
? |
$D_6\times S_4$ (as 18T111) |
trivial |
trivial |
$2$ |
$8$ |
$2949.86471196$ |
$0$ |
| 18.4.692...544.3 |
$x^{18} - 5 x^{14} + 3 x^{12} - x^{10} - 10 x^{8} + 4 x^{6} - x^{4} - 5 x^{2} + 1$ |
$18$ |
(4, 7) |
$-\,2^{24}\cdot 37^{6}\cdot 401^{2}$ |
$3$ |
$16.3435162508$ |
|
|
|
? |
$S_4^3.D_6$ (as 18T836) |
trivial |
trivial |
$2$ |
$10$ |
$5811.84459048$ |
$4$ |
| 18.6.148...144.2 |
$x^{18} + 4 x^{16} + 5 x^{14} - 53 x^{12} - 189 x^{10} - 210 x^{8} + 74 x^{6} + 243 x^{4} + 169 x^{2} - 151$ |
$18$ |
(6, 6) |
$2^{24}\cdot 37^{6}\cdot 151^{3}$ |
$3$ |
$19.376264761$ |
|
|
|
? |
$S_4^3.D_6$ (as 18T837) |
trivial |
$[2]$ |
$2$ |
$11$ |
$41435.2837652$ |
$5$ |
| 18.4.139...744.1 |
$x^{18} - 9 x^{14} - 5 x^{12} + 27 x^{10} + 30 x^{8} - 16 x^{6} - 45 x^{4} - 33 x^{2} + 1$ |
$18$ |
(4, 7) |
$-\,2^{24}\cdot 3^{18}\cdot 11^{8}$ |
$3$ |
$21.9450096257$ |
|
|
|
? |
$C_2^3:A_4^2:D_6$ (as 18T587) |
trivial |
trivial |
$2$ |
$10$ |
$98707.8441305$ |
$4$ |
| 18.0.159...976.2 |
$x^{18} - 8 x^{16} + 5 x^{14} + 123 x^{12} - 429 x^{10} + 110 x^{8} + 2474 x^{6} - 4089 x^{4} - 3395 x^{2} + 9409$ |
$18$ |
(0, 9) |
$-\,2^{24}\cdot 3^{6}\cdot 7^{12}\cdot 97^{2}$ |
$4$ |
$22.1087838649$ |
|
|
|
? |
$C_2^4:(A_4\times D_6)$ (as 18T366) |
$[2]$ |
$[2]$ |
$2$ |
$8$ |
$14900.3278891$ |
$0$ |
| 18.4.408...856.2 |
$x^{18} + x^{16} - 16 x^{14} - 4 x^{12} + 42 x^{10} - 90 x^{8} - 40 x^{6} + 28 x^{4} + 13 x^{2} + 1$ |
$18$ |
(4, 7) |
$-\,2^{24}\cdot 101^{6}\cdot 479^{2}$ |
$3$ |
$23.2967591165$ |
|
|
|
? |
$S_4^3.D_6$ (as 18T836) |
trivial |
trivial |
$2$ |
$10$ |
$147343.219205$ |
$4$ |
| 18.12.115...424.3 |
$x^{18} - 2 x^{16} - 15 x^{14} + 43 x^{12} + 11 x^{10} - 108 x^{8} + 62 x^{6} + 17 x^{4} - 11 x^{2} + 1$ |
$18$ |
(12, 3) |
$-\,2^{24}\cdot 37^{6}\cdot 16361^{2}$ |
$3$ |
$24.6779073517$ |
|
|
|
? |
$S_4^3.D_6$ (as 18T836) |
trivial |
$[2]$ |
$2$ |
$14$ |
$1251722.42276$ |
$11$ |
| 18.0.133...344.1 |
$x^{18} + 7 x^{16} - 8 x^{15} + 37 x^{14} + 16 x^{13} + 96 x^{12} + 58 x^{11} + 72 x^{10} + 346 x^{9} + 303 x^{8} + 172 x^{7} + 457 x^{6} + 418 x^{5} + 103 x^{4} + 36 x^{3} + 82 x^{2} + 48 x + 9$ |
$18$ |
(0, 9) |
$-\,2^{24}\cdot 3^{12}\cdot 107^{6}$ |
$3$ |
$24.8837267261$ |
$84.02744441921831$ |
|
|
? |
$C_2\times C_6^2:D_6$ (as 18T228) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$8$ |
$105207.891383$ |
$0$ |
| 18.0.223...744.1 |
$x^{18} - 4 x^{17} + 15 x^{16} - 42 x^{15} + 92 x^{14} - 162 x^{13} + 248 x^{12} - 386 x^{11} + 594 x^{10} - 806 x^{9} + 1014 x^{8} - 662 x^{7} - 936 x^{6} + 1698 x^{5} + 428 x^{4} - 5774 x^{3} + 14953 x^{2} - 12726 x + 7151$ |
$18$ |
(0, 9) |
$-\,2^{24}\cdot 37^{6}\cdot 151^{4}$ |
$3$ |
$25.6049737522$ |
|
|
|
? |
$S_4^3.D_6$ (as 18T837) |
trivial |
trivial |
$2$ |
$8$ |
$131955.070418$ |
$0$ |
| 18.0.223...744.2 |
$x^{18} - 4 x^{17} + 11 x^{16} + 6 x^{15} - 35 x^{14} + 60 x^{13} - 116 x^{12} + 482 x^{11} - 1052 x^{10} + 674 x^{9} + 2187 x^{8} - 7202 x^{7} + 11603 x^{6} - 12444 x^{5} + 11069 x^{4} - 7876 x^{3} + 5784 x^{2} - 2412 x + 823$ |
$18$ |
(0, 9) |
$-\,2^{24}\cdot 37^{6}\cdot 151^{4}$ |
$3$ |
$25.6049737522$ |
|
|
|
? |
$S_4^3.D_6$ (as 18T837) |
trivial |
trivial |
$2$ |
$8$ |
$166207.337751$ |
$0$ |
| 18.0.188...000.1 |
$x^{18} + 19 x^{16} + 131 x^{14} + 388 x^{12} + 390 x^{10} - 269 x^{8} - 477 x^{6} + 723 x^{4} + 1440 x^{2} + 625$ |
$18$ |
(0, 9) |
$-\,2^{24}\cdot 5^{6}\cdot 23^{4}\cdot 37^{6}$ |
$4$ |
$28.8206268696$ |
|
|
|
? |
$C_2\times A_4^3:S_4$ (as 18T782) |
$[2]$ |
$[2]$ |
$2$ |
$8$ |
$260551.446568$ |
$0$ |
| 18.6.337...344.1 |
$x^{18} - 6 x^{17} - 10 x^{16} + 130 x^{15} - 127 x^{14} - 794 x^{13} + 1313 x^{12} + 2040 x^{11} - 169 x^{10} - 17522 x^{9} + 608 x^{8} + 79544 x^{7} - 40194 x^{6} - 182348 x^{5} + 181489 x^{4} + 110636 x^{3} - 150405 x^{2} - 21308 x + 25843$ |
$18$ |
(6, 6) |
$2^{24}\cdot 37^{6}\cdot 151^{5}$ |
$3$ |
$33.83596833220094$ |
|
|
|
? |
$S_4^3.D_6$ (as 18T836) |
trivial |
$[2]$ |
$2$ |
$11$ |
$5460543.05351946$ |
$5$ |
| 18.6.337...344.2 |
$x^{18} - 6 x^{17} + 15 x^{16} - 42 x^{15} + 37 x^{14} + 50 x^{13} + 40 x^{12} + 1744 x^{11} - 3162 x^{10} + 3406 x^{9} - 26087 x^{8} + 9740 x^{7} + 4635 x^{6} + 98104 x^{5} + 94695 x^{4} - 276626 x^{3} - 66366 x^{2} - 226376 x + 374323$ |
$18$ |
(6, 6) |
$2^{24}\cdot 37^{6}\cdot 151^{5}$ |
$3$ |
$33.83596833220094$ |
|
|
|
? |
$S_4^3.D_6$ (as 18T836) |
trivial |
$[2]$ |
$2$ |
$11$ |
$8976145.395520251$ |
$5$ |
| 18.12.188...064.1 |
$x^{18} - 2 x^{17} - 12 x^{16} + 30 x^{15} - 43 x^{14} - 274 x^{13} + 411 x^{12} + 3842 x^{11} + 4641 x^{10} - 25884 x^{9} - 44398 x^{8} + 66212 x^{7} + 128668 x^{6} - 42920 x^{5} - 126227 x^{4} - 31720 x^{3} + 1733 x^{2} + 446 x - 1$ |
$18$ |
(12, 3) |
$-\,2^{24}\cdot 37^{6}\cdot 16361^{3}$ |
$3$ |
$42.3066732557$ |
|
|
|
? |
$S_4^3.D_6$ (as 18T837) |
trivial |
$[2, 2]$ |
$2$ |
$14$ |
$177208946.916$ |
$10$ |
| 18.12.188...064.2 |
$x^{18} + 8 x^{16} - 91 x^{14} - 409 x^{12} + 3051 x^{10} - 1142 x^{8} - 21910 x^{6} + 53243 x^{4} - 49083 x^{2} + 16361$ |
$18$ |
(12, 3) |
$-\,2^{24}\cdot 37^{6}\cdot 16361^{3}$ |
$3$ |
$42.3066732557$ |
|
|
|
? |
$S_4^3.D_6$ (as 18T837) |
trivial |
$[2, 2]$ |
$2$ |
$14$ |
$209394213.452$ |
$10$ |
| 18.12.594...000.1 |
$x^{18} - 27 x^{16} + 185 x^{14} - 218 x^{12} - 624 x^{10} + 951 x^{8} + 639 x^{6} - 839 x^{4} - 178 x^{2} + 25$ |
$18$ |
(12, 3) |
$-\,2^{24}\cdot 5^{6}\cdot 197^{8}$ |
$3$ |
$45.0947616907$ |
$111.84239039608109$ |
|
|
? |
$C_2\times S_4^2$ (as 18T266) |
trivial |
$[2, 2]$ |
$2$ |
$14$ |
$497716786.103$ |
$10$ |
| 18.0.594...000.1 |
$x^{18} + 25 x^{16} + 241 x^{14} + 1154 x^{12} + 2972 x^{10} + 4263 x^{8} + 3403 x^{6} + 1461 x^{4} + 310 x^{2} + 25$ |
$18$ |
(0, 9) |
$-\,2^{24}\cdot 5^{6}\cdot 197^{8}$ |
$3$ |
$45.0947616907$ |
$111.84239039608109$ |
✓ |
|
? |
$D_6\times S_4$ (as 18T111) |
$[2, 36]$ |
$[2, 36]$ |
$2$ |
$8$ |
$634998.037914$ |
$0$ |
| 18.4.248...000.2 |
$x^{18} - 2 x^{17} + 23 x^{16} - 82 x^{15} + 381 x^{14} - 1648 x^{13} + 4904 x^{12} - 19718 x^{11} + 47256 x^{10} - 148740 x^{9} + 254869 x^{8} - 533192 x^{7} + 570705 x^{6} - 840100 x^{5} + 582705 x^{4} - 345452 x^{3} + 365092 x^{2} + 144240 x - 2425$ |
$18$ |
(4, 7) |
$-\,2^{24}\cdot 5^{8}\cdot 23^{6}\cdot 37^{6}$ |
$4$ |
$48.82810271744431$ |
|
|
|
? |
$C_2\times A_4^3:S_4$ (as 18T769) |
$[2, 2]$ |
$[2, 2, 2]$ |
$2$ |
$10$ |
$37694695.79612323$ |
$3$ |
| 18.0.220...000.1 |
$x^{18} + 36 x^{16} + 419 x^{14} + 2155 x^{12} + 5331 x^{10} + 6514 x^{8} + 3808 x^{6} + 959 x^{4} + 71 x^{2} + 1$ |
$18$ |
(0, 9) |
$-\,2^{24}\cdot 5^{8}\cdot 7^{8}\cdot 197^{6}$ |
$4$ |
$71.1947332391$ |
$409.2654977989979$ |
✓ |
|
? |
$C_2\times C_6^2:D_6$ (as 18T228) |
$[3, 180]$ |
$[3, 180]$ |
$2$ |
$8$ |
$7558593.60312$ |
$0$ |
| 18.12.308...104.1 |
$x^{18} - 14 x^{16} - 44 x^{15} - 743 x^{14} - 1480 x^{13} + 855 x^{12} + 526 x^{11} + 96135 x^{10} + 414476 x^{9} + 749878 x^{8} + 474770 x^{7} - 5371642 x^{6} - 18533510 x^{5} - 17049463 x^{4} + 5017936 x^{3} + 11592525 x^{2} + 720632 x - 1893607$ |
$18$ |
(12, 3) |
$-\,2^{24}\cdot 37^{6}\cdot 16361^{4}$ |
$3$ |
$72.52862150985621$ |
|
|
|
? |
$S_4^3.D_6$ (as 18T836) |
$[2]$ |
$[2, 2, 2]$ |
$2$ |
$14$ |
$10725750047.524626$ |
$10$ |
| 18.12.308...104.2 |
$x^{18} - 2 x^{17} - 71 x^{16} + 194 x^{15} + 1457 x^{14} - 6670 x^{13} - 5720 x^{12} + 88884 x^{11} - 93558 x^{10} - 531424 x^{9} + 814857 x^{8} + 2195904 x^{7} - 2393225 x^{6} - 9685134 x^{5} + 7065733 x^{4} + 28119616 x^{3} - 24179846 x^{2} - 29683498 x + 29810509$ |
$18$ |
(12, 3) |
$-\,2^{24}\cdot 37^{6}\cdot 16361^{4}$ |
$3$ |
$72.52862150985621$ |
|
|
|
? |
$S_4^3.D_6$ (as 18T836) |
$[2]$ |
$[2, 2, 2]$ |
$2$ |
$14$ |
$9118621852.757816$ |
$10$ |
| 18.12.431...624.1 |
$x^{18} - 131 x^{16} - 172 x^{15} + 7028 x^{14} + 18636 x^{13} - 185680 x^{12} - 792908 x^{11} + 2039902 x^{10} + 16130092 x^{9} + 7737010 x^{8} - 141852516 x^{7} - 361190300 x^{6} + 92662532 x^{5} + 1932933080 x^{4} + 3989871708 x^{3} + 3965722697 x^{2} + 1987694596 x + 394525193$ |
$18$ |
(12, 3) |
$-\,2^{24}\cdot 7^{12}\cdot 43^{2}\cdot 4129^{2}\cdot 242689^{2}$ |
$5$ |
$140.077363067$ |
|
|
|
? |
$S_3^3.S_3\wr C_3$ (as 18T807) |
$[3]$ |
$[3]$ |
$2$ |
$14$ |
$2931643563430$ |
$12$ |
