| 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 $p$ |
| 18.4.466...832.1 |
$x^{18} - 3 x^{17} + 6 x^{16} - 12 x^{15} + 27 x^{14} - 39 x^{13} + 21 x^{12} + 39 x^{11} - 135 x^{10} + 299 x^{9} - 531 x^{8} + 651 x^{7} - 438 x^{6} + 291 x^{4} - 267 x^{3} + 114 x^{2} - 24 x + 2$ |
$18$ |
(4, 7) |
$-\,2^{12}\cdot 3^{24}\cdot 7^{9}$ |
$3$ |
$18.1717752482$ |
$31.418004901678522$ |
|
|
|
$S_3\times S_4$ (as 18T69) |
trivial |
trivial |
$2$ |
$10$ |
$73198.8164752$ |
$4$ |
$7$ |
| 18.2.140...496.1 |
$x^{18} - 3 x^{17} + 9 x^{15} - 3 x^{14} - 12 x^{13} - 3 x^{12} + 75 x^{11} - 27 x^{10} - 100 x^{9} + 3 x^{8} + 111 x^{7} + 15 x^{6} - 33 x^{4} + 45 x^{3} - 18 x^{2} + 3 x + 1$ |
$18$ |
(2, 8) |
$2^{12}\cdot 3^{25}\cdot 7^{9}$ |
$3$ |
$19.3154172029$ |
$31.418004901678522$ |
|
|
|
$S_3\times S_4$ (as 18T70) |
trivial |
$[2]$ |
$2$ |
$9$ |
$51512.6268208$ |
$1$ |
$7$ |
| 18.6.173...808.1 |
$x^{18} - 8 x^{16} + 37 x^{14} - 137 x^{12} + 371 x^{10} - 798 x^{8} + 1274 x^{6} - 1421 x^{4} + 1029 x^{2} - 343$ |
$18$ |
(6, 6) |
$2^{24}\cdot 7^{9}\cdot 37^{6}$ |
$3$ |
$22.2155083539$ |
|
|
|
? |
$C_2^3:A_4^2:D_6$ (as 18T587) |
trivial |
trivial |
$2$ |
$11$ |
$187171.044254$ |
$6$ |
$37$ |
| 18.6.478...968.1 |
$x^{18} - 6 x^{17} + 12 x^{16} - 18 x^{15} + 30 x^{14} + 6 x^{13} - 99 x^{12} + 90 x^{11} + 78 x^{10} + 154 x^{9} - 276 x^{8} + 90 x^{7} + 531 x^{6} - 474 x^{5} + 42 x^{4} + 630 x^{3} - 216 x^{2} - 216 x + 87$ |
$18$ |
(6, 6) |
$2^{22}\cdot 3^{24}\cdot 7^{9}$ |
$3$ |
$26.707684868128254$ |
$104.1620784659052$ |
|
|
? |
$C_2^5.S_4^2$ (as 18T623) |
trivial |
$[2]$ |
$2$ |
$11$ |
$3785079.187402965$ |
$5$ |
$7$ |
| 18.0.143...904.1 |
$x^{18} + 12 x^{16} + 96 x^{14} + 531 x^{12} + 1974 x^{10} + 5124 x^{8} + 9261 x^{6} + 10584 x^{4} + 6174 x^{2} + 1029$ |
$18$ |
(0, 9) |
$-\,2^{22}\cdot 3^{25}\cdot 7^{9}$ |
$3$ |
$28.3885348958$ |
|
|
|
? |
$C_2^5.S_4^2$ (as 18T623) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$8$ |
$225010.312142$ |
$0$ |
$7$ |
| 18.6.764...488.2 |
$x^{18} - 12 x^{16} + 72 x^{14} - 309 x^{12} + 756 x^{10} - 1386 x^{8} + 1323 x^{6} + 1470 x^{4} - 343$ |
$18$ |
(6, 6) |
$2^{26}\cdot 3^{24}\cdot 7^{9}$ |
$3$ |
$31.15528997851923$ |
|
|
|
? |
$C_2^7:S_3^2$ (as 18T461) |
trivial |
$[2]$ |
$2$ |
$11$ |
$15781234.409074862$ |
$5$ |
$7$ |
| 18.0.229...464.1 |
$x^{18} + 24 x^{16} + 174 x^{14} + 237 x^{12} - 1638 x^{10} - 3318 x^{8} + 2205 x^{6} + 8820 x^{4} + 6174 x^{2} + 1029$ |
$18$ |
(0, 9) |
$-\,2^{26}\cdot 3^{25}\cdot 7^{9}$ |
$3$ |
$33.116050347$ |
|
|
|
? |
$C_2^7:S_3^2$ (as 18T461) |
$[2, 2]$ |
$[2, 2]$ |
$2$ |
$8$ |
$1108870.57618$ |
$0$ |
$7$ |
| 18.6.229...464.1 |
$x^{18} - 12 x^{16} + 54 x^{14} - 195 x^{12} + 924 x^{10} - 4242 x^{8} + 11907 x^{6} - 13230 x^{4} + 6174 x^{2} - 1029$ |
$18$ |
(6, 6) |
$2^{26}\cdot 3^{25}\cdot 7^{9}$ |
$3$ |
$33.116050347$ |
$96.90637454417673$ |
|
|
? |
$S_4^2$ (as 18T187) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$18636657.3177$ |
$4$ |
$7$ |
| 18.6.229...464.2 |
$x^{18} - 12 x^{16} + 96 x^{14} - 531 x^{12} + 1974 x^{10} - 5124 x^{8} + 9261 x^{6} - 10584 x^{4} + 6174 x^{2} - 1029$ |
$18$ |
(6, 6) |
$2^{26}\cdot 3^{25}\cdot 7^{9}$ |
$3$ |
$33.116050347$ |
|
|
|
? |
$C_2^4.S_4^2$ (as 18T546) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$18946965.7706$ |
$4$ |
$7$ |
| 18.6.305...952.1 |
$x^{18} + 12 x^{16} + 42 x^{14} - 15 x^{12} - 336 x^{10} - 420 x^{8} + 441 x^{6} + 882 x^{4} - 343$ |
$18$ |
(6, 6) |
$2^{28}\cdot 3^{24}\cdot 7^{9}$ |
$3$ |
$33.6495743593$ |
$104.1620784659052$ |
|
|
? |
$C_2\times S_4^2$ (as 18T266) |
trivial |
$[2]$ |
$2$ |
$11$ |
$34521438.5567$ |
$5$ |
$7$ |
| 18.4.709...000.1 |
$x^{18} - 7 x^{17} + 2 x^{16} + 24 x^{15} + 36 x^{14} - 204 x^{13} + 84 x^{12} + 484 x^{11} - 390 x^{10} - 774 x^{9} + 724 x^{8} + 808 x^{7} - 648 x^{6} - 656 x^{5} + 328 x^{4} + 344 x^{3} - 50 x^{2} - 98 x - 4$ |
$18$ |
(4, 7) |
$-\,2^{52}\cdot 5^{8}\cdot 7^{9}$ |
$3$ |
$40.0723272139$ |
|
|
|
|
$C_2^8.F_9:C_2$ (as 18T693) |
trivial |
trivial |
$2$ |
$10$ |
$167304913.044$ |
$4$ |
$7$ |
| 18.4.992...648.2 |
$x^{18} - 6 x^{15} + 44 x^{9} - 24 x^{6} - 48 x^{3} + 32$ |
$18$ |
(4, 7) |
$-\,2^{14}\cdot 3^{36}\cdot 7^{9}$ |
$3$ |
$40.8249790476$ |
|
|
|
? |
$C_3^6:(C_2\times S_4)$ (as 18T680) |
trivial |
trivial |
$2$ |
$10$ |
$134503197.937$ |
$4$ |
$7$ |
| 18.4.992...648.3 |
$x^{18} - 3 x^{15} - 3 x^{12} + 11 x^{9} - 6 x^{3} + 2$ |
$18$ |
(4, 7) |
$-\,2^{14}\cdot 3^{36}\cdot 7^{9}$ |
$3$ |
$40.82497904764348$ |
|
|
|
✓ |
$C_3^6:(C_2\times S_4)$ (as 18T680) |
trivial |
trivial |
$2$ |
$10$ |
$89390108.1214179$ |
$4$ |
$7$ |
| 18.6.262...384.1 |
$x^{18} - 27 x^{16} + 180 x^{14} - 270 x^{13} - 633 x^{12} + 2250 x^{11} + 3516 x^{10} + 5512 x^{9} + 23415 x^{8} + 31770 x^{7} + 39825 x^{6} + 113874 x^{5} + 191892 x^{4} + 229320 x^{3} + 262134 x^{2} + 197172 x + 59322$ |
$18$ |
(6, 6) |
$2^{26}\cdot 3^{24}\cdot 7^{12}$ |
$3$ |
$43.09049381891572$ |
$104.1620784659052$ |
|
|
? |
$C_2^4.S_4^2$ (as 18T545) |
trivial |
$[2, 2]$ |
$2$ |
$11$ |
$217086717.51119798$ |
$4$ |
$7$ |
| 18.4.396...592.1 |
$x^{18} - 6 x^{15} + 36 x^{9} - 96 x^{3} + 64$ |
$18$ |
(4, 7) |
$-\,2^{16}\cdot 3^{36}\cdot 7^{9}$ |
$3$ |
$44.0934162105$ |
|
|
|
? |
$S_3\times C_3^3:S_4$ (as 18T446) |
trivial |
trivial |
$2$ |
$10$ |
$132122594.291$ |
$4$ |
$7$ |
| 18.4.567...000.1 |
$x^{18} - 2 x^{17} - 13 x^{16} + 32 x^{15} + 36 x^{14} - 208 x^{13} + 304 x^{12} + 416 x^{11} - 1356 x^{10} + 616 x^{9} + 716 x^{8} - 2512 x^{7} + 192 x^{6} - 800 x^{5} + 752 x^{4} + 5184 x^{3} + 4408 x^{2} - 3568 x - 4792$ |
$18$ |
(4, 7) |
$-\,2^{55}\cdot 5^{8}\cdot 7^{9}$ |
$3$ |
$44.979666485$ |
|
|
|
? |
$C_2^8.F_9:C_2$ (as 18T694) |
$[2]$ |
$[4]$ |
$2$ |
$10$ |
$463320517.67$ |
$3$ |
$7$ |
| 18.4.408...168.1 |
$x^{18} - 30 x^{15} - 108 x^{14} + 198 x^{13} + 66 x^{12} + 1890 x^{11} - 1458 x^{10} - 7016 x^{9} + 5832 x^{8} - 3024 x^{7} + 8184 x^{6} + 13068 x^{5} - 25848 x^{4} + 26952 x^{3} - 35424 x^{2} + 2052 x + 11596$ |
$18$ |
(4, 7) |
$-\,2^{16}\cdot 3^{37}\cdot 7^{12}$ |
$3$ |
$64.823153928$ |
|
|
|
? |
$C_3^5:(C_2\times S_4)$ (as 18T579) |
$[2]$ |
$[2, 2]$ |
$2$ |
$10$ |
$2111608232.77$ |
$3$ |
$7$ |
| 18.6.130...000.2 |
$x^{18} - 30 x^{16} - 20 x^{15} + 369 x^{14} + 492 x^{13} - 2752 x^{12} - 5832 x^{11} + 12636 x^{10} + 43200 x^{9} - 10368 x^{8} - 161856 x^{7} - 157008 x^{6} + 165312 x^{5} + 490560 x^{4} + 476672 x^{3} + 241920 x^{2} + 64512 x + 7168$ |
$18$ |
(6, 6) |
$2^{12}\cdot 3^{27}\cdot 5^{3}\cdot 7^{14}\cdot 17^{3}$ |
$5$ |
$78.5663979433$ |
|
|
|
|
$C_3^5:\SOPlus(4,2)$ (as 18T600) |
$[3]$ |
$[6]$ |
$2$ |
$11$ |
$24567917072.0$ |
$5$ |
$17$ |
| 18.18.176...328.1 |
$x^{18} - 6 x^{17} - 519 x^{16} + 3756 x^{15} + 88872 x^{14} - 737148 x^{13} - 5797908 x^{12} + 57465132 x^{11} + 87691578 x^{10} - 1579826968 x^{9} + 2273909790 x^{8} + 6201928740 x^{7} - 19005134448 x^{6} + 12267519804 x^{5} + 13274970588 x^{4} - 25904627196 x^{3} + 16722340749 x^{2} - 4954977954 x + 565527201$ |
$18$ |
(18, 0) |
$2^{36}\cdot 3^{31}\cdot 7^{10}\cdot 2213^{2}\cdot 17333^{2}$ |
$5$ |
$544.400232925$ |
|
|
|
? |
$C_3^6.\GL(2,\mathbb{Z}/4)$ (as 18T752) |
trivial |
$[2, 2]$ |
$2$ |
$17$ |
$75186462196700000000$ |
$16$ |
$17333$ |
| 20.0.444...352.1 |
$x^{20} - 8 x^{19} + 16 x^{18} + 48 x^{17} - 276 x^{16} + 336 x^{15} + 744 x^{14} - 2928 x^{13} + 3291 x^{12} + 1168 x^{11} - 9884 x^{10} + 21496 x^{9} - 31062 x^{8} + 18024 x^{7} + 39012 x^{6} - 118104 x^{5} + 163479 x^{4} - 142872 x^{3} + 91072 x^{2} - 40832 x + 13840$ |
$20$ |
(0, 10) |
$2^{38}\cdot 3^{34}\cdot 7^{13}$ |
$3$ |
$85.5809002804$ |
|
|
|
|
$A_6^2.D_4.C_2$ (as 20T996) |
$[2]$ |
$[2]$ |
$2$ |
$9$ |
$446181242355$ |
$0$ |
$7$ |
