| 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 |
| 15.3.148...624.1 |
$x^{15} - 3 x^{14} + 5 x^{13} - 2 x^{12} + 3 x^{11} + 11 x^{10} + x^{9} + 22 x^{8} + 13 x^{7} + 9 x^{6} + 5 x^{5} - 12 x^{4} - 14 x^{3} - 12 x^{2} - 8 x - 2$ |
$15$ |
[3,6] |
$2^{12}\cdot 3^{6}\cdot 89^{6}$ |
$3$ |
$16.2715341149$ |
$28.44982682753188$ |
|
|
? |
$S_5$ (as 15T10) |
trivial |
$2$ |
$8$ |
$2917.47210187$ |
| 15.3.185...944.1 |
$x^{15} - 2 x^{14} + 13 x^{12} - 18 x^{11} + 38 x^{9} - 58 x^{8} + 38 x^{7} - 12 x^{6} - 58 x^{5} + 110 x^{4} - 77 x^{3} + 22 x^{2} - 1$ |
$15$ |
[3,6] |
$2^{12}\cdot 277^{6}$ |
$2$ |
$16.5126168606$ |
$28.97769793904893$ |
|
|
? |
$S_5$ (as 15T10) |
trivial |
$2$ |
$8$ |
$2752.96294871$ |
| 15.3.222...000.1 |
$x^{15} - 5 x^{14} + 9 x^{13} - 11 x^{12} + 17 x^{11} - 17 x^{10} - 3 x^{9} + 13 x^{8} - x^{7} + 21 x^{6} - 25 x^{5} - 5 x^{4} - 13 x^{3} - 3 x^{2} - x - 1$ |
$15$ |
[3,6] |
$2^{28}\cdot 3^{12}\cdot 5^{6}$ |
$3$ |
$16.7188986112$ |
$24.1776264427508$ |
|
|
? |
$S_5$ (as 15T10) |
trivial |
$2$ |
$8$ |
$6480.35807094$ |
| 15.3.137...464.1 |
$x^{15} - x^{14} - 2 x^{13} - 2 x^{12} + 5 x^{11} + 7 x^{10} - 42 x^{9} + 132 x^{8} - 204 x^{7} + 180 x^{6} - 114 x^{5} + 108 x^{3} - 108 x^{2} + 72 x - 36$ |
$15$ |
[3,6] |
$2^{12}\cdot 3^{12}\cdot 43^{6}$ |
$3$ |
$18.8759310611$ |
$27.49509522275834$ |
|
|
? |
$S_5$ (as 15T10) |
$[2]$ |
$2$ |
$8$ |
$6571.39436311$ |
| 15.3.119...625.1 |
$x^{15} - 5 x^{12} + 25 x^{9} - 155 x^{6} + 265 x^{3} - 8$ |
$15$ |
[3,6] |
$3^{22}\cdot 5^{18}$ |
$2$ |
$34.557462503212804$ |
$42.105893506402914$ |
|
|
? |
$S_5$ (as 15T10) |
$[3]$ |
$2$ |
$8$ |
$1074187.3969807$ |
| 15.15.342...000.1 |
$x^{15} - 25 x^{13} - 2 x^{12} + 229 x^{11} + 40 x^{10} - 981 x^{9} - 228 x^{8} + 2103 x^{7} + 546 x^{6} - 2175 x^{5} - 568 x^{4} + 923 x^{3} + 198 x^{2} - 120 x - 8$ |
$15$ |
[15,0] |
$2^{18}\cdot 5^{6}\cdot 307^{6}$ |
$3$ |
$43.2194610327$ |
$110.81516141756055$ |
|
|
|
$S_5$ (as 15T10) |
trivial |
$2$ |
$14$ |
$34611808.3905$ |
| 15.15.365...000.1 |
$x^{15} - 3 x^{14} - 27 x^{13} + 85 x^{12} + 201 x^{11} - 751 x^{10} - 255 x^{9} + 2109 x^{8} - 473 x^{7} - 2181 x^{6} + 883 x^{5} + 715 x^{4} - 261 x^{3} - 69 x^{2} + 19 x - 1$ |
$15$ |
[15,0] |
$2^{16}\cdot 5^{6}\cdot 17^{6}\cdot 23^{6}$ |
$4$ |
$43.4067596623$ |
$99.2601763557667$ |
|
|
? |
$S_5$ (as 15T10) |
trivial |
$2$ |
$14$ |
$84519303.959$ |
