| 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 |
| 15.3.124...288.1 |
$x^{15} - 5 x^{14} + 16 x^{13} - 39 x^{12} + 65 x^{11} - 91 x^{10} + 78 x^{9} - 39 x^{8} - 26 x^{7} + 78 x^{6} - 78 x^{5} + 52 x^{4} - 13 x^{3} - 9 x^{2} + 6 x - 1$ |
$15$ |
[3,6] |
$2^{12}\cdot 13^{13}$ |
$2$ |
$16.0783533395$ |
$18.278423529398573$ |
|
|
? |
$F_5\times C_3$ (as 15T8) |
trivial |
$2$ |
$8$ |
$1735.38854006$ |
| 15.3.132...125.1 |
$x^{15} - 14 x^{10} + 35 x^{5} + 7$ |
$15$ |
[3,6] |
$5^{9}\cdot 7^{14}$ |
$2$ |
$16.1487969276$ |
$20.558227794588174$ |
|
|
? |
$F_5\times C_3$ (as 15T8) |
trivial |
$2$ |
$8$ |
$1272.85837366$ |
| 15.15.173...000.1 |
$x^{15} - 30 x^{13} + 360 x^{11} - 12 x^{10} - 2200 x^{9} + 240 x^{8} + 7200 x^{7} - 1680 x^{6} - 11980 x^{5} + 4800 x^{4} + 7800 x^{3} - 4800 x^{2} + 400 x + 104$ |
$15$ |
[15,0] |
$2^{12}\cdot 5^{15}\cdot 7^{12}$ |
$3$ |
$41.2926193649$ |
$56.09031360603209$ |
|
|
? |
$F_5\times C_3$ (as 15T8) |
trivial |
$2$ |
$14$ |
$22293487.2915$ |
| 15.15.150...125.1 |
$x^{15} - 35 x^{13} + 455 x^{11} - 70 x^{10} - 2800 x^{9} + 1225 x^{8} + 8575 x^{7} - 6475 x^{6} - 11375 x^{5} + 12250 x^{4} + 3500 x^{3} - 6125 x^{2} + 875$ |
$15$ |
[15,0] |
$3^{6}\cdot 5^{15}\cdot 7^{14}$ |
$3$ |
$47.7064034771$ |
$67.78510966855065$ |
|
|
? |
$F_5\times C_3$ (as 15T8) |
trivial |
$2$ |
$14$ |
$63554489.595$ |
