| 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 |
Max $p$ |
| 16.4.683...256.1 |
$x^{16} - 10 x^{14} - 16 x^{12} - 16 x^{10} + x^{8} + 16 x^{6} - 16 x^{4} + 10 x^{2} + 1$ |
$16$ |
(4, 6) |
$2^{12}\cdot 3^{12}\cdot 11^{12}$ |
$3$ |
$23.155701991215324$ |
$27.53692556083594$ |
|
|
? |
$C_2^3.D_4$ (as 16T146) |
trivial |
$[2]$ |
$2$ |
$9$ |
$48716.98632119528$ |
$3$ |
$11$ |
| 16.0.171...576.1 |
$x^{16} - 2 x^{15} + 4 x^{14} + 2 x^{13} - 26 x^{12} + 58 x^{11} + 52 x^{10} - 230 x^{9} + 43 x^{8} + 320 x^{7} - 268 x^{6} - 144 x^{5} + 290 x^{4} - 52 x^{3} - 68 x^{2} + 36 x + 20$ |
$16$ |
(0, 8) |
$2^{16}\cdot 11^{12}\cdot 17^{4}$ |
$3$ |
$24.529389527091844$ |
$55.9075725658252$ |
|
|
|
$C_2^4:S_4$ (as 16T751) |
trivial |
trivial |
$2$ |
$7$ |
$143252.4904745427$ |
$0$ |
$17$ |
| 16.8.279...576.1 |
$x^{16} - 4 x^{14} - 47 x^{12} - 340 x^{10} + 751 x^{8} + 116 x^{6} - 449 x^{4} - 28 x^{2} + 64$ |
$16$ |
(8, 4) |
$2^{24}\cdot 3^{12}\cdot 11^{12}$ |
$3$ |
$38.94309359419253$ |
$77.88618718838507$ |
|
|
|
$D_4^2:D_4$ (as 16T819) |
$[2]$ |
$[2, 2]$ |
$2$ |
$11$ |
$106386824.93550292$ |
$7$ |
$11$ |
| 16.4.279...576.1 |
$x^{16} + 24 x^{14} + 179 x^{12} + 396 x^{10} - 384 x^{8} - 2244 x^{6} - 1933 x^{4} - 24 x^{2} + 1$ |
$16$ |
(4, 6) |
$2^{24}\cdot 3^{12}\cdot 11^{12}$ |
$3$ |
$38.9430935942$ |
$77.88618718838507$ |
|
|
|
$D_4^2:D_4$ (as 16T879) |
$[2]$ |
$[2, 2]$ |
$2$ |
$9$ |
$10059141.9071$ |
$3$ |
$11$ |
| 16.0.998...625.1 |
$x^{16} - 8 x^{15} + 34 x^{14} - 98 x^{13} + 221 x^{12} - 416 x^{11} + 802 x^{10} - 1579 x^{9} + 2937 x^{8} - 4562 x^{7} + 3493 x^{6} + 1048 x^{5} - 2724 x^{4} + 451 x^{3} + 291 x^{2} + 109 x + 256$ |
$16$ |
(0, 8) |
$5^{12}\cdot 11^{12}\cdot 19^{4}$ |
$3$ |
$42.16580707489076$ |
$88.03367207503597$ |
|
|
? |
$D_4^2:C_4$ (as 16T482) |
$[2, 8]$ |
$[2, 8]$ |
$2$ |
$7$ |
$652724.5225870877$ |
$0$ |
$19$ |
| 16.8.842...000.1 |
$x^{16} - 4 x^{15} - 24 x^{14} + 112 x^{13} + 150 x^{12} - 964 x^{11} - 584 x^{10} + 4212 x^{9} + 6512 x^{8} - 23956 x^{7} - 33268 x^{6} + 122356 x^{5} + 76296 x^{4} - 355456 x^{3} - 155680 x^{2} + 826712 x - 459106$ |
$16$ |
(8, 4) |
$2^{36}\cdot 5^{8}\cdot 11^{12}$ |
$3$ |
$64.2461350483$ |
$102.52058353174812$ |
|
|
? |
$C_2^4.Q_{16}$ (as 16T698) |
$[2]$ |
$[2, 2]$ |
$2$ |
$11$ |
$352676089.385$ |
$7$ |
$11$ |
| 16.4.343...888.1 |
$x^{16} - 28 x^{14} - 48 x^{13} + 258 x^{12} + 876 x^{11} - 214 x^{10} - 4176 x^{9} - 5327 x^{8} - 276 x^{7} - 1002 x^{6} + 5712 x^{5} + 21732 x^{4} - 19692 x^{3} - 15138 x^{2} - 2232 x - 369$ |
$16$ |
(4, 6) |
$2^{36}\cdot 3^{13}\cdot 11^{12}$ |
$3$ |
$70.14924861706373$ |
$143.89931378928603$ |
|
|
|
$(C_2\times C_4^3):\SD_{16}$ (as 16T1450) |
$[2]$ |
$[2, 2, 2]$ |
$2$ |
$9$ |
$718287624.978213$ |
$2$ |
$11$ |
| 16.4.215...000.1 |
$x^{16} - 8 x^{14} - 56 x^{13} - 140 x^{12} + 512 x^{11} + 2040 x^{10} + 1024 x^{9} - 15864 x^{8} - 47232 x^{7} + 57120 x^{6} + 564112 x^{5} + 1486616 x^{4} + 1801024 x^{3} + 478000 x^{2} - 468704 x - 65116$ |
$16$ |
(4, 6) |
$2^{44}\cdot 5^{8}\cdot 11^{12}$ |
$3$ |
$90.85775551536167$ |
$94.88037201489196$ |
|
|
|
$C_2^4.C_2^4$ (as 16T494) |
$[4]$ |
$[2, 4]$ |
$2$ |
$9$ |
$1966100209.5258443$ |
$3$ |
$11$ |
| 18.8.684...516.1 |
$x^{18} - 5 x^{17} - 56 x^{16} + 529 x^{15} - 993 x^{14} - 6588 x^{13} + 39046 x^{12} - 156362 x^{11} + 503773 x^{10} - 141490 x^{9} - 1831205 x^{8} + 3754441 x^{7} - 5390900 x^{6} + 9893445 x^{5} - 13123755 x^{4} + 8353882 x^{3} - 1149308 x^{2} - 592664 x - 31121$ |
$18$ |
(8, 5) |
$-\,2^{2}\cdot 3^{12}\cdot 11^{12}\cdot 29^{13}$ |
$4$ |
$126.463948011$ |
$524.2201359616707$ |
|
|
? |
$C_2^9.\PSU(3,2)$ (as 18T690) |
$[3]$ |
$[6]$ |
$2$ |
$12$ |
$7013849905720$ |
$7$ |
$29$ |
| 18.8.684...516.3 |
$x^{18} - 3 x^{17} - 46 x^{16} + 104 x^{15} + 1358 x^{14} + 1656 x^{13} - 12573 x^{12} - 42659 x^{11} - 11159 x^{10} + 124464 x^{9} + 149214 x^{8} - 84897 x^{7} - 276673 x^{6} - 122952 x^{5} + 96574 x^{4} + 69489 x^{3} + 30535 x^{2} - 776 x - 6699$ |
$18$ |
(8, 5) |
$-\,2^{2}\cdot 3^{12}\cdot 11^{12}\cdot 29^{13}$ |
$4$ |
$126.463948011$ |
$524.2201359616707$ |
|
|
? |
$C_2^9.\PSU(3,2)$ (as 18T690) |
$[3]$ |
$[6]$ |
$2$ |
$12$ |
$6352908523040$ |
$7$ |
$29$ |
| 18.12.151...656.1 |
$x^{18} - 95 x^{16} + 2371 x^{14} - 6968 x^{12} - 168309 x^{10} + 483207 x^{8} + 379738 x^{6} - 82568 x^{4} - 47126 x^{2} + 5041$ |
$18$ |
(12, 3) |
$-\,2^{8}\cdot 3^{12}\cdot 11^{12}\cdot 29^{12}$ |
$4$ |
$132.149563928$ |
$631.1247260669011$ |
|
|
? |
$C_2^9.\PSU(3,2)$ (as 18T690) |
$[3]$ |
$[6]$ |
$2$ |
$14$ |
$6137013978930$ |
$11$ |
$29$ |
| 18.2.151...656.1 |
$x^{18} + 55 x^{16} + 984 x^{14} + 6534 x^{12} + 20477 x^{10} + 32487 x^{8} + 24685 x^{6} + 6560 x^{4} - 438 x^{2} - 1$ |
$18$ |
(2, 8) |
$2^{8}\cdot 3^{12}\cdot 11^{12}\cdot 29^{12}$ |
$4$ |
$132.149563928$ |
$486.663692361498$ |
|
|
? |
$C_2^8.\PSU(3,2)$ (as 18T628) |
$[3, 42]$ |
$[3, 42]$ |
$2$ |
$9$ |
$87795099108.1$ |
$2$ |
$29$ |
| 18.14.151...656.1 |
$x^{18} - 8 x^{17} - 58 x^{16} + 489 x^{15} + 1486 x^{14} - 11256 x^{13} - 25695 x^{12} + 122249 x^{11} + 318624 x^{10} - 617457 x^{9} - 2310497 x^{8} + 533145 x^{7} + 8063130 x^{6} + 6485006 x^{5} - 7875198 x^{4} - 15861689 x^{3} - 9730477 x^{2} - 2358898 x - 144768$ |
$18$ |
(14, 2) |
$2^{8}\cdot 3^{12}\cdot 11^{12}\cdot 29^{12}$ |
$4$ |
$132.149563928$ |
$486.663692361498$ |
|
|
? |
$C_2^8.\PSU(3,2)$ (as 18T628) |
$[3]$ |
$[6]$ |
$2$ |
$15$ |
$45922068284500$ |
$13$ |
$29$ |
| 18.10.151...656.2 |
$x^{18} + 13 x^{16} - 802 x^{14} - 521 x^{12} + 100829 x^{10} + 61861 x^{8} - 3516424 x^{6} - 7177007 x^{4} + 8854889 x^{2} - 336400$ |
$18$ |
(10, 4) |
$2^{8}\cdot 3^{12}\cdot 11^{12}\cdot 29^{12}$ |
$4$ |
$132.149563928$ |
$486.663692361498$ |
|
|
? |
$C_2^8.\PSU(3,2)$ (as 18T628) |
$[3]$ |
$[6]$ |
$2$ |
$13$ |
$26060768294400$ |
$9$ |
$29$ |
| 18.14.151...656.2 |
$x^{18} - 54 x^{16} + 906 x^{14} - 2106 x^{12} - 78507 x^{10} + 624588 x^{8} - 351795 x^{6} - 7002873 x^{4} + 9260529 x^{2} - 65536$ |
$18$ |
(14, 2) |
$2^{8}\cdot 3^{12}\cdot 11^{12}\cdot 29^{12}$ |
$4$ |
$132.149563928$ |
$486.663692361498$ |
|
|
? |
$C_2^8.\PSU(3,2)$ (as 18T628) |
$[3]$ |
$[6]$ |
$2$ |
$15$ |
$62823503274400$ |
$13$ |
$29$ |
| 18.10.151...656.3 |
$x^{18} + 23 x^{16} - 224 x^{14} - 3832 x^{12} + 438 x^{10} + 52686 x^{8} - 28277 x^{6} - 187471 x^{4} + 216505 x^{2} - 37249$ |
$18$ |
(10, 4) |
$2^{8}\cdot 3^{12}\cdot 11^{12}\cdot 29^{12}$ |
$4$ |
$132.149563928$ |
$344.1231970260991$ |
|
|
? |
$C_2^8.\PSU(3,2)$ (as 18T628) |
$[3]$ |
$[6]$ |
$2$ |
$13$ |
$34734399614900$ |
$9$ |
$29$ |
| 18.12.183...640.1 |
$x^{18} - 9 x^{17} + 58 x^{16} - 260 x^{15} + 726 x^{14} - 1246 x^{13} - 24 x^{12} + 7164 x^{11} - 18809 x^{10} + 22369 x^{9} + 5166 x^{8} - 67676 x^{7} + 76918 x^{6} + 12858 x^{5} - 63156 x^{4} + 24784 x^{3} + 1633 x^{2} - 497 x - 34$ |
$18$ |
(12, 3) |
$-\,2^{48}\cdot 3\cdot 5\cdot 7^{12}\cdot 11^{12}$ |
$5$ |
$133.581261913$ |
|
|
|
? |
$C_2^9.\PSU(3,2)$ (as 18T690) |
$[3]$ |
$[6]$ |
$2$ |
$14$ |
$19144721986200$ |
$11$ |
$11$ |
| 18.10.205...548.1 |
$x^{18} - 5 x^{17} - 57 x^{16} + 99 x^{15} + 1570 x^{14} + 2639 x^{13} - 16412 x^{12} - 67516 x^{11} - 62639 x^{10} + 290841 x^{9} + 898817 x^{8} + 954929 x^{7} - 936364 x^{6} - 4183151 x^{5} - 4654110 x^{4} - 1494656 x^{3} + 875783 x^{2} + 638708 x + 100156$ |
$18$ |
(10, 4) |
$2^{2}\cdot 3^{13}\cdot 11^{12}\cdot 29^{13}$ |
$4$ |
$134.422965483$ |
$524.2201359616707$ |
|
|
? |
$C_2^9.\PSU(3,2)$ (as 18T690) |
$[3]$ |
$[2, 6]$ |
$2$ |
$13$ |
$9126393544610$ |
$8$ |
$29$ |
| 18.16.453...968.1 |
$x^{18} - 91 x^{16} + 3071 x^{14} - 45448 x^{12} + 241549 x^{10} + 256189 x^{8} - 2426452 x^{6} + 3016330 x^{4} - 1208276 x^{2} + 141267$ |
$18$ |
(16, 1) |
$-\,2^{8}\cdot 3^{13}\cdot 11^{12}\cdot 29^{12}$ |
$4$ |
$140.466406038$ |
$486.663692361498$ |
|
|
? |
$C_2^9.\PSU(3,2)$ (as 18T690) |
$[3]$ |
$[2, 6]$ |
$2$ |
$16$ |
$37653279465100$ |
$14$ |
$29$ |
| 18.6.453...968.2 |
$x^{18} - 7 x^{17} - 21 x^{16} + 465 x^{15} - 1681 x^{14} - 1047 x^{13} + 24178 x^{12} - 32045 x^{11} - 236790 x^{10} + 1221854 x^{9} - 1651942 x^{8} - 3544935 x^{7} + 21154455 x^{6} - 39458815 x^{5} + 39125493 x^{4} + 1429096 x^{3} - 913520 x^{2} + 2427 x + 1324$ |
$18$ |
(6, 6) |
$2^{8}\cdot 3^{13}\cdot 11^{12}\cdot 29^{12}$ |
$4$ |
$140.466406038$ |
$631.1247260669011$ |
|
|
? |
$C_2^9.\PSU(3,2)$ (as 18T690) |
$[3]$ |
$[2, 6]$ |
$2$ |
$11$ |
$19594143470400$ |
$4$ |
$29$ |
| 18.14.453...968.2 |
$x^{18} - 41 x^{16} + 439 x^{14} + 547 x^{12} - 25340 x^{10} + 84661 x^{8} - 4613 x^{6} - 41336 x^{4} + 16087 x^{2} - 1452$ |
$18$ |
(14, 2) |
$2^{8}\cdot 3^{13}\cdot 11^{12}\cdot 29^{12}$ |
$4$ |
$140.466406038$ |
$631.1247260669011$ |
|
|
? |
$C_2^9.\PSU(3,2)$ (as 18T690) |
$[3]$ |
$[2, 6]$ |
$2$ |
$15$ |
$31455900915300$ |
$12$ |
$29$ |
| 18.16.586...448.1 |
$x^{18} - 77 x^{16} + 1640 x^{14} - 4136 x^{12} - 173160 x^{10} + 1497096 x^{8} - 3486304 x^{6} + 2410592 x^{4} - 39920 x^{2} + 48$ |
$18$ |
(16, 1) |
$-\,2^{52}\cdot 3\cdot 7^{12}\cdot 11^{12}$ |
$4$ |
$142.498216745$ |
|
|
|
? |
$C_2^9.\PSU(3,2)$ (as 18T690) |
$[3]$ |
$[2, 6]$ |
$2$ |
$16$ |
$49026424228400$ |
$14$ |
$11$ |
| 18.6.604...624.1 |
$x^{18} + 30 x^{16} - 237 x^{14} - 12894 x^{12} - 104793 x^{10} - 78105 x^{8} + 1522764 x^{6} + 3430704 x^{4} + 30912 x^{2} - 256$ |
$18$ |
(6, 6) |
$2^{10}\cdot 3^{12}\cdot 11^{12}\cdot 29^{12}$ |
$4$ |
$142.729423511$ |
$631.1247260669011$ |
|
|
? |
$C_2^8.\PSU(3,2)$ (as 18T628) |
$[3]$ |
$[6]$ |
$2$ |
$11$ |
$8242915852130$ |
$5$ |
$29$ |
| 18.2.234...792.1 |
$x^{18} + 77 x^{16} + 1640 x^{14} + 4136 x^{12} - 173160 x^{10} - 1497096 x^{8} - 3486304 x^{6} - 2410592 x^{4} - 39920 x^{2} - 48$ |
$18$ |
(2, 8) |
$2^{54}\cdot 3\cdot 7^{12}\cdot 11^{12}$ |
$4$ |
$153.90658677$ |
|
|
|
? |
$C_2^9.\PSU(3,2)$ (as 18T690) |
$[3, 12]$ |
$[6, 12]$ |
$2$ |
$9$ |
$553203991177$ |
$1$ |
$11$ |
| 18.10.438...024.1 |
$x^{18} - 10 x^{16} - 2655 x^{14} - 17862 x^{12} + 652964 x^{10} - 1810503 x^{8} + 175189 x^{6} + 586612 x^{4} - 62379 x^{2} - 1421$ |
$18$ |
(10, 4) |
$2^{8}\cdot 3^{12}\cdot 11^{12}\cdot 29^{13}$ |
$4$ |
$159.334590151$ |
$881.6296662679675$ |
|
|
? |
$C_2^8.\PSU(3,2)$ (as 18T629) |
$[3]$ |
$[6]$ |
$2$ |
$13$ |
$9431395188650$ |
$9$ |
$29$ |
| 18.14.438...024.1 |
$x^{18} - 9 x^{17} - 62 x^{16} + 694 x^{15} + 500 x^{14} - 15604 x^{13} + 18825 x^{12} + 122872 x^{11} - 440805 x^{10} + 43304 x^{9} + 4274724 x^{8} - 5042555 x^{7} - 23848782 x^{6} + 20759615 x^{5} + 75149206 x^{4} - 9596057 x^{3} - 98968582 x^{2} - 57724356 x - 10472017$ |
$18$ |
(14, 2) |
$2^{8}\cdot 3^{12}\cdot 11^{12}\cdot 29^{13}$ |
$4$ |
$159.334590151$ |
$486.663692361498$ |
|
|
? |
$C_2^8.\PSU(3,2)$ (as 18T629) |
$[6]$ |
$[2, 6]$ |
$2$ |
$15$ |
$23205342141900$ |
$13$ |
$29$ |
| 18.2.438...024.2 |
$x^{18} - 7 x^{17} - 40 x^{16} + 487 x^{15} - 567 x^{14} - 8258 x^{13} + 34163 x^{12} - 3442 x^{11} - 388690 x^{10} + 1484310 x^{9} - 1401896 x^{8} - 8816713 x^{7} + 41958877 x^{6} - 75861973 x^{5} - 36623786 x^{4} + 515197554 x^{3} - 1148085330 x^{2} + 1186373686 x - 529433279$ |
$18$ |
(2, 8) |
$2^{8}\cdot 3^{12}\cdot 11^{12}\cdot 29^{13}$ |
$4$ |
$159.334590151$ |
$486.663692361498$ |
|
|
? |
$C_2^8.\PSU(3,2)$ (as 18T629) |
$[2, 6]$ |
$[2, 6]$ |
$2$ |
$9$ |
$554821629344$ |
$2$ |
$29$ |
| 18.6.438...024.2 |
$x^{18} + 24 x^{16} - 1844 x^{14} - 54485 x^{12} - 187710 x^{10} + 58202 x^{8} + 679992 x^{6} + 177219 x^{4} - 472903 x^{2} - 134096$ |
$18$ |
(6, 6) |
$2^{8}\cdot 3^{12}\cdot 11^{12}\cdot 29^{13}$ |
$4$ |
$159.334590151$ |
$881.6296662679675$ |
|
|
? |
$C_2^8.\PSU(3,2)$ (as 18T629) |
$[3]$ |
$[6]$ |
$2$ |
$11$ |
$12753359805900$ |
$5$ |
$29$ |
| 18.0.386...936.1 |
$x^{18} + 73 x^{16} + 2140 x^{14} + 32332 x^{12} + 268908 x^{10} + 1228530 x^{8} + 2988007 x^{6} + 3692137 x^{4} + 2029159 x^{2} + 310249$ |
$18$ |
(0, 9) |
$-\,2^{16}\cdot 3^{12}\cdot 11^{12}\cdot 29^{12}$ |
$4$ |
$179.82780512$ |
|
✓ |
|
? |
$C_2^9.\PSU(3,2)$ (as 18T690) |
$[2, 144534]$ |
$[2, 144534]$ |
$2$ |
$8$ |
$190811408.266$ |
$0$ |
$29$ |
| 18.18.116...808.1 |
$x^{18} - 98 x^{16} + 3703 x^{14} - 67268 x^{12} + 595810 x^{10} - 2338934 x^{8} + 3657487 x^{6} - 2192564 x^{4} + 469207 x^{2} - 19200$ |
$18$ |
(18, 0) |
$2^{16}\cdot 3^{13}\cdot 11^{12}\cdot 29^{12}$ |
$4$ |
$191.145280697$ |
|
|
|
? |
$C_2^9.\PSU(3,2)$ (as 18T690) |
$[3]$ |
$[2, 2, 6]$ |
$2$ |
$17$ |
$1051681723050000$ |
$15$ |
$29$ |
| 18.18.154...744.1 |
$x^{18} - 73 x^{16} + 2140 x^{14} - 32332 x^{12} + 268908 x^{10} - 1228530 x^{8} + 2988007 x^{6} - 3692137 x^{4} + 2029159 x^{2} - 310249$ |
$18$ |
(18, 0) |
$2^{18}\cdot 3^{12}\cdot 11^{12}\cdot 29^{12}$ |
$4$ |
$194.224772244$ |
|
|
|
? |
$C_2^8.\PSU(3,2)$ (as 18T628) |
$[3]$ |
$[2, 6]$ |
$2$ |
$17$ |
$2279395348120000$ |
$16$ |
$29$ |
| 18.18.425...296.1 |
$x^{18} - 108 x^{16} + 4789 x^{14} - 111720 x^{12} + 1455570 x^{10} - 10319559 x^{8} + 35603881 x^{6} - 47212314 x^{4} + 15533215 x^{2} - 257499$ |
$18$ |
(18, 0) |
$2^{16}\cdot 3^{12}\cdot 11^{13}\cdot 29^{12}$ |
$4$ |
$205.452766098$ |
|
|
|
? |
$C_2^9.\PSU(3,2)$ (as 18T690) |
$[3]$ |
$[2, 2, 6]$ |
$2$ |
$17$ |
$1142178547210000$ |
$15$ |
$29$ |
