| 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 |
| 15.3.632...441.1 |
$x^{15} - 9 x^{13} - 5 x^{12} + 9 x^{11} - 12 x^{10} - 12 x^{9} - 36 x^{8} - 39 x^{7} + 137 x^{6} - 189 x^{5} + 255 x^{4} - 42 x^{3} - 288 x^{2} + 234 x - 55$ |
$15$ |
[3,6] |
$3^{22}\cdot 17^{10}$ |
$2$ |
$33.1189928328$ |
|
|
|
? |
$C_3^4:F_5$ (as 15T42) |
trivial |
$2$ |
$8$ |
$585049.61015$ |
| 15.3.196...104.1 |
$x^{15} - 3 x^{13} - 8 x^{12} + 36 x^{11} - 96 x^{10} + 48 x^{9} + 234 x^{8} - 705 x^{7} + 498 x^{6} + 837 x^{5} - 660 x^{4} + 2612 x^{3} - 162 x^{2} - 5478 x - 2270$ |
$15$ |
[3,6] |
$2^{12}\cdot 3^{20}\cdot 13^{10}$ |
$3$ |
$41.6499583098$ |
$104.4102771283633$ |
|
|
? |
$C_3^4:F_5$ (as 15T42) |
trivial |
$2$ |
$8$ |
$6739975.37814$ |
| 15.15.197...376.1 |
$x^{15} - 38 x^{13} - 24 x^{12} + 510 x^{11} + 632 x^{10} - 2806 x^{9} - 5244 x^{8} + 4716 x^{7} + 15360 x^{6} + 3732 x^{5} - 13992 x^{4} - 11836 x^{3} - 1224 x^{2} + 1712 x + 488$ |
$15$ |
[15,0] |
$2^{18}\cdot 3^{16}\cdot 53^{10}$ |
$3$ |
$104.636349444$ |
$410.65812890181047$ |
|
|
? |
$C_3^4:F_5$ (as 15T42) |
trivial |
$2$ |
$14$ |
$80612912136.0$ |
| 15.15.759...000.1 |
$x^{15} - 5 x^{14} - 65 x^{13} + 200 x^{12} + 1855 x^{11} - 1901 x^{10} - 25345 x^{9} - 12110 x^{8} + 140785 x^{7} + 212285 x^{6} - 130655 x^{5} - 431210 x^{4} - 230470 x^{3} - 6800 x^{2} + 14680 x + 1132$ |
$15$ |
[15,0] |
$2^{12}\cdot 3^{16}\cdot 5^{16}\cdot 7^{10}$ |
$4$ |
$114.477472662$ |
$395.4607923134719$ |
|
|
? |
$C_3^4:F_5$ (as 15T42) |
trivial |
$2$ |
$14$ |
$273937438532$ |
