| 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 |
| 15.5.450...947.1 |
$x^{15} - 2 x^{12} - 5 x^{9} + 13 x^{6} - 7 x^{3} + 1$ |
$15$ |
[5,5] |
$-\,3^{15}\cdot 11^{12}$ |
$2$ |
$20.4284493826$ |
$34.90644688215396$ |
|
|
✓ |
$C_3^4:C_{10}$ (as 15T33) |
trivial |
$2$ |
$9$ |
$9289.39400206$ |
| 15.5.450...947.2 |
$x^{15} - 10 x^{12} + 29 x^{9} - 25 x^{6} + 3 x^{3} + 1$ |
$15$ |
[5,5] |
$-\,3^{15}\cdot 11^{12}$ |
$2$ |
$20.4284493826$ |
$34.90644688215396$ |
|
|
? |
$C_3^4:C_{10}$ (as 15T33) |
trivial |
$2$ |
$9$ |
$8686.79947771$ |
| 15.5.450...947.3 |
$x^{15} - 3 x^{12} - 3 x^{9} + 15 x^{6} - 10 x^{3} - 1$ |
$15$ |
[5,5] |
$-\,3^{15}\cdot 11^{12}$ |
$2$ |
$20.428449382566903$ |
$34.90644688215396$ |
|
|
✓ |
$C_3^4:C_{10}$ (as 15T33) |
trivial |
$2$ |
$9$ |
$10031.504095520013$ |
| 15.5.450...947.4 |
$x^{15} - 3 x^{12} - 3 x^{9} + 15 x^{6} - 10 x^{3} - 1$ |
$15$ |
[5,5] |
$-\,3^{15}\cdot 11^{12}$ |
$2$ |
$20.428449382566903$ |
$34.90644688215396$ |
|
|
✓ |
$C_3^4:C_{10}$ (as 15T33) |
trivial |
$2$ |
$9$ |
$10031.504095520013$ |
| 15.15.138...697.1 |
$x^{15} - 75 x^{13} - 123 x^{12} + 1854 x^{11} + 5532 x^{10} - 15374 x^{9} - 79524 x^{8} - 19527 x^{7} + 386911 x^{6} + 652257 x^{5} - 170775 x^{4} - 1591761 x^{3} - 1909161 x^{2} - 991875 x - 197317$ |
$15$ |
[15,0] |
$3^{15}\cdot 11^{13}\cdot 23^{4}$ |
$3$ |
$55.3081337984$ |
$358.80911756371285$ |
|
|
? |
$C_3^4:C_{10}$ (as 15T33) |
trivial |
$2$ |
$14$ |
$164409576.613$ |
| 15.15.138...697.2 |
$x^{15} - 60 x^{13} - 63 x^{12} + 1341 x^{11} + 2727 x^{10} - 12674 x^{9} - 40869 x^{8} + 31254 x^{7} + 243271 x^{6} + 196857 x^{5} - 393162 x^{4} - 847458 x^{3} - 566559 x^{2} - 111090 x + 12167$ |
$15$ |
[15,0] |
$3^{15}\cdot 11^{13}\cdot 23^{4}$ |
$3$ |
$55.3081337984$ |
$358.80911756371285$ |
|
|
? |
$C_3^4:C_{10}$ (as 15T33) |
trivial |
$2$ |
$14$ |
$181222525.173$ |
