| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
| 18.2.380...000.1 |
$x^{18} - 2 x^{17} + 2 x^{16} - 3 x^{15} + 2 x^{14} - 4 x^{13} + 2 x^{12} - 10 x^{11} + 2 x^{10} - 3 x^{9} - 2 x^{8} - 10 x^{7} - 2 x^{6} - 4 x^{5} - 2 x^{4} - 3 x^{3} - 2 x^{2} - 2 x - 1$ |
$18$ |
[2,8] |
$2^{12}\cdot 5^{9}\cdot 41^{6}$ |
$3$ |
$12.2395735055$ |
$22.728124217737328$ |
|
|
? |
$\SOPlus(4,2)$ (as 18T34) |
trivial |
$2$ |
$9$ |
$225.62524734$ |
| 18.0.661...947.1 |
$x^{18} - 3 x^{17} + 6 x^{16} - 9 x^{15} + 15 x^{14} - 21 x^{13} + 24 x^{12} - 24 x^{11} + 27 x^{10} - 29 x^{9} + 27 x^{8} - 24 x^{7} + 24 x^{6} - 21 x^{5} + 15 x^{4} - 9 x^{3} + 6 x^{2} - 3 x + 1$ |
$18$ |
[0,9] |
$-\,3^{21}\cdot 43^{6}$ |
$2$ |
$12.6220805982$ |
$24.357295210976567$ |
|
|
? |
$\SOPlus(4,2)$ (as 18T34) |
trivial |
$6$ |
$8$ |
$893.183574652$ |
| 18.2.111...312.1 |
$x^{18} - 4 x^{17} + 8 x^{16} - 8 x^{15} + x^{14} + 8 x^{13} - 10 x^{12} + 2 x^{11} + 6 x^{10} - 4 x^{9} - 4 x^{8} + 10 x^{7} - 6 x^{6} + 4 x^{5} + x^{4} + 2 x^{2} + 1$ |
$18$ |
[2,8] |
$2^{27}\cdot 97^{6}$ |
$2$ |
$12.9957766336$ |
$27.85677655436824$ |
|
|
|
$\SOPlus(4,2)$ (as 18T34) |
trivial |
$2$ |
$9$ |
$473.705580838$ |
| 18.0.129...427.1 |
$x^{18} - x^{17} + x^{16} + 4 x^{15} - x^{14} + x^{13} + 7 x^{12} + 3 x^{11} + 4 x^{10} - 2 x^{9} + 10 x^{8} + 2 x^{6} - 5 x^{5} + 4 x^{4} + x^{3} + 2 x^{2} - x + 1$ |
$18$ |
[0,9] |
$-\,3^{9}\cdot 433^{6}$ |
$2$ |
$13.1035788428$ |
$36.0416425818802$ |
|
|
? |
$\SOPlus(4,2)$ (as 18T34) |
trivial |
$6$ |
$8$ |
$979.022125559$ |
| 18.6.390...125.1 |
$x^{18} - 2 x^{15} - 5 x^{14} - 5 x^{13} - 25 x^{12} - 10 x^{11} - 10 x^{10} + 5 x^{9} + 10 x^{8} - 10 x^{7} + 25 x^{6} - 5 x^{5} + 5 x^{4} - 2 x^{3} - 1$ |
$18$ |
[6,6] |
$5^{15}\cdot 71^{6}$ |
$2$ |
$15.8329237356$ |
$32.21841549588632$ |
|
|
? |
$\SOPlus(4,2)$ (as 18T34) |
trivial |
$2$ |
$11$ |
$6472.48552936$ |
| 18.6.423...288.1 |
$x^{18} - 6 x^{17} + 16 x^{16} - 20 x^{15} + 2 x^{14} + 12 x^{13} + x^{12} + 14 x^{11} - 124 x^{10} + 224 x^{9} - 124 x^{8} + 14 x^{7} + x^{6} + 12 x^{5} + 2 x^{4} - 20 x^{3} + 16 x^{2} - 6 x + 1$ |
$18$ |
[6,6] |
$2^{24}\cdot 3^{9}\cdot 71^{6}$ |
$3$ |
$18.0725764746$ |
$36.775884711001936$ |
|
|
? |
$\SOPlus(4,2)$ (as 18T34) |
trivial |
$2$ |
$11$ |
$43907.4332716$ |
| 18.18.667...125.1 |
$x^{18} - 34 x^{16} + 441 x^{14} - 2812 x^{12} + 9602 x^{10} - 17803 x^{8} + 17336 x^{6} - 8330 x^{4} + 1725 x^{2} - 125$ |
$18$ |
[18,0] |
$5^{9}\cdot 3881^{6}$ |
$2$ |
$35.1398213925$ |
$139.30183056945089$ |
|
|
? |
$\SOPlus(4,2)$ (as 18T34) |
trivial |
$2$ |
$17$ |
$113560017.765$ |
| 18.18.119...352.1 |
$x^{18} - 32 x^{16} - 14 x^{15} + 350 x^{14} + 254 x^{13} - 1599 x^{12} - 1462 x^{11} + 3065 x^{10} + 3262 x^{9} - 2369 x^{8} - 2968 x^{7} + 677 x^{6} + 1160 x^{5} - 30 x^{4} - 190 x^{3} - 13 x^{2} + 10 x + 1$ |
$18$ |
[18,0] |
$2^{27}\cdot 2113^{6}$ |
$2$ |
$36.294834954$ |
$130.01538370516005$ |
|
|
|
$\SOPlus(4,2)$ (as 18T34) |
trivial |
$2$ |
$17$ |
$179925968.916$ |
