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 |
18.2.785...448.1 |
$x^{18} - 6 x^{16} - 12 x^{14} - 24 x^{13} + 60 x^{12} + 96 x^{11} + 147 x^{10} + 200 x^{9} + 78 x^{8} - 216 x^{7} - 618 x^{6} - 528 x^{5} + 288 x^{4} + 456 x^{3} + 54 x^{2} + 48 x + 68$ |
$18$ |
[2,8] |
$2^{51}\cdot 3^{20}$ |
$2$ |
$24.1575589791$ |
$29.715621574744997$ |
|
|
|
$\PSU(3,2)$ (as 18T35) |
trivial |
$2$ |
$9$ |
$1297121.60548$ |
18.2.117...672.1 |
$x^{18} - 6 x^{17} + 21 x^{16} - 48 x^{15} + 78 x^{14} - 108 x^{13} + 198 x^{12} - 576 x^{11} + 1674 x^{10} - 3780 x^{9} + 6498 x^{8} - 8208 x^{7} + 7614 x^{6} - 4860 x^{5} + 1782 x^{4} - 351 x^{2} + 162 x - 27$ |
$18$ |
[2,8] |
$2^{50}\cdot 3^{21}$ |
$2$ |
$24.7079034867$ |
$29.715621574744997$ |
|
|
|
$\PSU(3,2)$ (as 18T35) |
trivial |
$2$ |
$9$ |
$1938173.05938$ |
18.18.932...125.1 |
$x^{18} - 3 x^{17} - 63 x^{16} + 198 x^{15} + 1503 x^{14} - 4947 x^{13} - 16878 x^{12} + 57978 x^{11} + 91992 x^{10} - 321677 x^{9} - 256524 x^{8} + 779346 x^{7} + 512415 x^{6} - 768105 x^{5} - 588846 x^{4} + 180750 x^{3} + 224865 x^{2} + 48300 x + 2095$ |
$18$ |
[18,0] |
$3^{20}\cdot 5^{13}\cdot 23^{12}$ |
$3$ |
$87.6526306183$ |
$130.44222925812892$ |
|
|
|
$\PSU(3,2)$ (as 18T35) |
trivial |
$2$ |
$17$ |
$2264806866520$ |
18.18.128...125.1 |
$x^{18} - 3 x^{17} - 84 x^{16} + 273 x^{15} + 2358 x^{14} - 8727 x^{13} - 25149 x^{12} + 118758 x^{11} + 67869 x^{10} - 693201 x^{9} + 318291 x^{8} + 1574322 x^{7} - 1444974 x^{6} - 1310592 x^{5} + 1609968 x^{4} + 345060 x^{3} - 589545 x^{2} - 19575 x + 63075$ |
$18$ |
[18,0] |
$3^{21}\cdot 5^{12}\cdot 23^{13}$ |
$3$ |
$101.412519039$ |
$130.44222925812892$ |
|
|
|
$\PSU(3,2)$ (as 18T35) |
trivial |
$2$ |
$17$ |
$15141979627900$ |