| 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 |
| 15.3.59463924292145152.1 |
$x^{15} - x^{14} - 6 x^{13} + 15 x^{12} - 9 x^{11} - 13 x^{10} + 30 x^{9} - 31 x^{8} + 24 x^{7} - 14 x^{6} + 10 x^{5} - 18 x^{4} + 27 x^{3} - 21 x^{2} + 8 x - 1$ |
$15$ |
[3,6] |
$2^{12}\cdot 13^{9}\cdot 37^{2}$ |
$3$ |
$13.1305697532$ |
$132.357735064494$ |
|
|
? |
$C_3\wr F_5$ (as 15T56) |
trivial |
$2$ |
$8$ |
$226.669584518$ |
| 15.3.193...968.1 |
$x^{15} - 4 x^{14} + 7 x^{13} - 15 x^{12} + 18 x^{11} - 24 x^{10} + 36 x^{9} - 16 x^{8} + 71 x^{7} + 69 x^{5} + 67 x^{4} + 17 x^{3} + 48 x^{2} + 27 x + 5$ |
$15$ |
[3,6] |
$2^{12}\cdot 13^{9}\cdot 211^{2}$ |
$3$ |
$16.5612966065$ |
$422.4770749541333$ |
|
|
? |
$C_3\wr F_5$ (as 15T56) |
trivial |
$2$ |
$8$ |
$2104.10568096$ |
| 15.15.239...032.1 |
$x^{15} - 24 x^{13} - 27 x^{12} + 167 x^{11} + 341 x^{10} - 181 x^{9} - 864 x^{8} - 357 x^{7} + 621 x^{6} + 583 x^{5} + 16 x^{4} - 170 x^{3} - 81 x^{2} - 15 x - 1$ |
$15$ |
[15,0] |
$2^{16}\cdot 3^{4}\cdot 37^{2}\cdot 53^{9}$ |
$4$ |
$49.2028298634$ |
$2377.988328757685$ |
|
|
? |
$C_3\wr F_5$ (as 15T56) |
trivial |
$2$ |
$14$ |
$122000230.472$ |
| 15.15.930...648.1 |
$x^{15} - 60 x^{13} - 36 x^{12} + 1440 x^{11} + 1728 x^{10} - 17044 x^{9} - 31104 x^{8} + 95184 x^{7} + 254000 x^{6} - 146880 x^{5} - 870528 x^{4} - 488292 x^{3} + 744192 x^{2} + 965808 x + 311392$ |
$15$ |
[15,0] |
$2^{16}\cdot 3^{16}\cdot 53^{9}$ |
$3$ |
$73.2138967047$ |
$410.65812890181047$ |
|
|
? |
$C_3\wr F_5$ (as 15T56) |
trivial |
$2$ |
$14$ |
$1919192855.56$ |
