| 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 |
| 15.5.154972454814106259.1 |
$x^{15} - x^{14} - 2 x^{13} + x^{12} + x^{11} - x^{10} + 2 x^{9} - 15 x^{8} + 8 x^{7} + 28 x^{6} - 34 x^{5} - 7 x^{4} + 27 x^{3} - 7 x^{2} - 3 x + 1$ |
$15$ |
[5,5] |
$-\,11^{13}\cdot 67^{2}$ |
$2$ |
$13.9964200427$ |
$142.76988787487005$ |
|
|
? |
$C_7^3:C_6$ (as 15T44) |
trivial |
$2$ |
$9$ |
$492.79424719$ |
| 15.5.695...651.1 |
$x^{15} - x^{14} - 6 x^{13} + 29 x^{12} - 66 x^{11} - 32 x^{10} + 34 x^{9} + 100 x^{8} + 122 x^{7} + 56 x^{6} + 12 x^{5} + 11 x^{4} - 9 x^{3} + 7 x^{2} - 6 x + 1$ |
$15$ |
[5,5] |
$-\,11^{13}\cdot 67^{4}$ |
$2$ |
$24.5184836613$ |
$142.76988787487005$ |
|
|
? |
$C_7^3:C_6$ (as 15T44) |
trivial |
$2$ |
$9$ |
$47044.8303705$ |
| 15.15.262...593.1 |
$x^{15} - 36 x^{13} - 27 x^{12} + 459 x^{11} + 540 x^{10} - 2560 x^{9} - 3357 x^{8} + 7287 x^{7} + 8848 x^{6} - 11637 x^{5} - 9867 x^{4} + 10811 x^{3} + 3105 x^{2} - 4623 x + 989$ |
$15$ |
[15,0] |
$3^{15}\cdot 11^{13}\cdot 23^{2}$ |
$3$ |
$36.4103868594$ |
$358.80911756371285$ |
|
|
? |
$C_7^3:C_6$ (as 15T44) |
trivial |
$2$ |
$14$ |
$6722708.12403$ |
| 15.15.196...617.1 |
$x^{15} - 48 x^{13} - 32 x^{12} + 882 x^{11} + 1176 x^{10} - 7303 x^{9} - 15390 x^{8} + 21330 x^{7} + 81960 x^{6} + 35883 x^{5} - 123750 x^{4} - 208680 x^{3} - 143280 x^{2} - 47760 x - 6368$ |
$15$ |
[15,0] |
$3^{15}\cdot 11^{13}\cdot 199^{2}$ |
$3$ |
$48.5484451457$ |
$1525.9508812936347$ |
|
|
? |
$C_7^3:C_6$ (as 15T44) |
trivial |
$2$ |
$14$ |
$63974103.6431$ |
