| 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 |
| 15.3.351730374981194881.1 |
$x^{15} - 2 x^{14} + x^{12} - 6 x^{11} + 27 x^{9} - 37 x^{8} + 44 x^{7} - 34 x^{6} + 14 x^{5} - 15 x^{4} - 8 x^{3} + 9 x - 1$ |
$15$ |
[3,6] |
$7^{12}\cdot 71^{4}$ |
$2$ |
$14.7824808479$ |
$153.19868787917656$ |
|
|
? |
$C_5^3:C_6$ (as 15T30) |
trivial |
$2$ |
$8$ |
$694.485336338$ |
| 15.3.893...961.2 |
$x^{15} - 3 x^{14} + 4 x^{13} - 9 x^{12} - 179 x^{11} - 399 x^{10} - 1436 x^{9} - 1321 x^{8} - 2904 x^{7} - 1881 x^{6} - 2687 x^{5} - 1411 x^{4} - 1282 x^{3} - 707 x^{2} - 228 x - 167$ |
$15$ |
[3,6] |
$7^{12}\cdot 71^{8}$ |
$2$ |
$46.0697884494$ |
$153.19868787917656$ |
|
|
? |
$C_5^3:C_6$ (as 15T30) |
trivial |
$2$ |
$8$ |
$4324309.87704$ |
| 15.15.304...625.1 |
$x^{15} - 55 x^{13} - 60 x^{12} + 945 x^{11} + 1656 x^{10} - 5375 x^{9} - 11115 x^{8} + 10925 x^{7} + 27215 x^{6} - 6172 x^{5} - 24600 x^{4} - 820 x^{3} + 5330 x^{2} - 1025 x + 41$ |
$15$ |
[15,0] |
$5^{18}\cdot 7^{10}\cdot 41^{4}$ |
$3$ |
$67.9576564585$ |
$787.932519799391$ |
|
|
? |
$C_5^3:C_6$ (as 15T30) |
trivial |
$2$ |
$14$ |
$1104951237.88$ |
| 15.15.860...625.1 |
$x^{15} - 190 x^{13} - 225 x^{12} + 11395 x^{11} + 21517 x^{10} - 250100 x^{9} - 633040 x^{8} + 1695760 x^{7} + 6430440 x^{6} + 1502486 x^{5} - 17230250 x^{4} - 28602215 x^{3} - 19903040 x^{2} - 6446635 x - 774941$ |
$15$ |
[15,0] |
$5^{18}\cdot 7^{10}\cdot 41^{8}$ |
$3$ |
$182.9422806$ |
$787.932519799391$ |
|
|
? |
$C_5^3:C_6$ (as 15T30) |
trivial |
$2$ |
$14$ |
$1909494312040$ |
