| 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 $p$ |
| 18.0.714...752.1 |
$x^{18} - 2 x^{17} - x^{16} + 2 x^{15} + 2 x^{14} + 2 x^{13} + 2 x^{12} - 18 x^{11} + 20 x^{10} + 6 x^{9} - 30 x^{7} + 54 x^{6} - 62 x^{5} + 62 x^{4} - 50 x^{3} + 27 x^{2} - 8 x + 1$ |
$18$ |
(0, 9) |
$-\,2^{18}\cdot 3^{9}\cdot 7^{12}$ |
$3$ |
$12.6762068204$ |
$18.725839469079336$ |
|
|
? |
$C_3\times S_4$ (as 18T30) |
trivial |
trivial |
$2$ |
$8$ |
$218.30650371$ |
$0$ |
$7$ |
| 18.0.242...752.1 |
$x^{18} + 3 x^{16} - 11 x^{12} - 24 x^{10} - 6 x^{8} + 64 x^{6} + 96 x^{4} + 48 x^{2} + 8$ |
$18$ |
(0, 9) |
$-\,2^{33}\cdot 3^{24}$ |
$2$ |
$15.4187795211$ |
$29.106779845745038$ |
|
|
? |
$C_3\times S_4$ (as 18T30) |
trivial |
trivial |
$2$ |
$8$ |
$1397.78740667$ |
$0$ |
$3$ |
| 18.6.148...000.1 |
$x^{18} - 3 x^{17} - 3 x^{16} + 21 x^{15} - 33 x^{14} - 75 x^{13} + 162 x^{12} + 183 x^{11} - 114 x^{10} + 63 x^{9} + 285 x^{8} + 255 x^{7} + 240 x^{6} + 114 x^{5} + 168 x^{4} + 147 x^{3} + 12 x^{2} + 15 x + 1$ |
$18$ |
(6, 6) |
$2^{12}\cdot 3^{32}\cdot 5^{9}$ |
$3$ |
$25.0257573825$ |
$37.4222358010528$ |
|
|
? |
$C_3\times S_4$ (as 18T30) |
trivial |
trivial |
$2$ |
$11$ |
$481845.912362$ |
$6$ |
$5$ |
| 18.6.456...733.1 |
$x^{18} - 3 x^{17} + 5 x^{16} - 11 x^{15} - 38 x^{14} + 126 x^{13} - 232 x^{12} + 539 x^{11} - 326 x^{10} - 845 x^{9} + 1726 x^{8} - 3000 x^{7} + 6144 x^{6} - 2419 x^{5} - 4313 x^{4} + 7814 x^{3} - 8884 x^{2} - 3258 x - 419$ |
$18$ |
(6, 6) |
$7^{12}\cdot 53^{9}$ |
$2$ |
$26.6401476874$ |
$71.87959071301479$ |
|
|
? |
$C_3\times S_4$ (as 18T30) |
trivial |
$[2]$ |
$2$ |
$11$ |
$511646.143485$ |
$5$ |
$53$ |
| 18.18.348...064.1 |
$x^{18} - 9 x^{17} + 186 x^{15} - 288 x^{14} - 1332 x^{13} + 2631 x^{12} + 4608 x^{11} - 9063 x^{10} - 8983 x^{9} + 13797 x^{8} + 9882 x^{7} - 9111 x^{6} - 5535 x^{5} + 2250 x^{4} + 1488 x^{3} - 81 x^{2} - 135 x - 17$ |
$18$ |
(18, 0) |
$2^{33}\cdot 3^{39}$ |
$2$ |
$38.5168749816$ |
$72.71017779983123$ |
|
|
? |
$C_3\times S_4$ (as 18T30) |
trivial |
$[2]$ |
$2$ |
$17$ |
$433776737.943$ |
$17$ |
$3$ |
| 18.18.455...256.1 |
$x^{18} - 3 x^{17} - 54 x^{16} + 39 x^{15} + 1062 x^{14} + 876 x^{13} - 7833 x^{12} - 13659 x^{11} + 19524 x^{10} + 58964 x^{9} + 6090 x^{8} - 83943 x^{7} - 59961 x^{6} + 20367 x^{5} + 28668 x^{4} + 1902 x^{3} - 3390 x^{2} - 420 x + 19$ |
$18$ |
(18, 0) |
$2^{12}\cdot 3^{31}\cdot 23^{9}$ |
$3$ |
$50.4962827918$ |
$139.32681210085573$ |
|
|
? |
$C_3\times S_4$ (as 18T30) |
trivial |
$[2, 2]$ |
$2$ |
$17$ |
$5162525491.39$ |
$16$ |
$23$ |
