| 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 |
| 15.3.861...125.1 |
$x^{15} - 6 x^{10} - 9 x^{5} - 3$ |
$15$ |
[3,6] |
$3^{24}\cdot 5^{15}$ |
$2$ |
$28.997730674$ |
|
|
|
✓ |
$C_5^3:C_{12}$ (as 15T38) |
trivial |
$2$ |
$8$ |
$145365.373746$ |
| 15.3.861...125.2 |
$x^{15} - 6 x^{10} + 9 x^{5} - 3$ |
$15$ |
[3,6] |
$3^{24}\cdot 5^{15}$ |
$2$ |
$28.997730674$ |
|
|
|
✓ |
$C_5^3:C_{12}$ (as 15T38) |
trivial |
$2$ |
$8$ |
$148937.278666$ |
| 15.3.861...125.3 |
$x^{15} - 9 x^{5} - 9$ |
$15$ |
[3,6] |
$3^{24}\cdot 5^{15}$ |
$2$ |
$28.99773067397644$ |
|
|
|
? |
$C_5^3:C_{12}$ (as 15T38) |
trivial |
$2$ |
$8$ |
$143399.2032501699$ |
| 15.15.430...000.1 |
$x^{15} - 35 x^{13} + 425 x^{11} - 76 x^{10} - 2350 x^{9} + 820 x^{8} + 6225 x^{7} - 2580 x^{6} - 7880 x^{5} + 2750 x^{4} + 4525 x^{3} - 500 x^{2} - 1100 x - 200$ |
$15$ |
[15,0] |
$2^{12}\cdot 5^{17}\cdot 13^{10}$ |
$3$ |
$59.6511612956$ |
$290.113545079841$ |
|
|
? |
$C_5^3:C_{12}$ (as 15T38) |
trivial |
$2$ |
$14$ |
$633057748.364$ |
| 15.15.100...000.1 |
$x^{15} - 40 x^{13} + 605 x^{11} - 92 x^{10} - 4450 x^{9} + 1870 x^{8} + 16825 x^{7} - 12460 x^{6} - 29575 x^{5} + 32500 x^{4} + 14105 x^{3} - 26650 x^{2} + 5980 x + 1352$ |
$15$ |
[15,0] |
$2^{12}\cdot 5^{15}\cdot 7^{10}\cdot 13^{4}$ |
$4$ |
$63.1312305754$ |
|
|
|
? |
$C_5^3:C_{12}$ (as 15T38) |
trivial |
$2$ |
$14$ |
$557433481.465$ |
