| 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 |
| 15.3.893...961.1 |
$x^{15} - 5 x^{14} + 20 x^{13} - 36 x^{12} - 42 x^{11} + 56 x^{10} + 532 x^{9} - 700 x^{8} + 2030 x^{7} + 868 x^{6} - 9408 x^{5} + 8918 x^{4} - 17640 x^{3} + 7840 x^{2} - 2205 x - 1421$ |
$15$ |
[3,6] |
$7^{12}\cdot 71^{8}$ |
$2$ |
$46.0697884494$ |
$153.19868787917656$ |
|
|
|
$(C_5^2 : C_3):C_2$ (as 15T12) |
trivial |
$2$ |
$8$ |
$9078479.24352$ |
| 15.3.227...441.1 |
$x^{15} - 3 x^{14} - 81 x^{13} + 482 x^{12} + 1855 x^{11} - 20398 x^{10} - 17885 x^{9} + 216818 x^{8} - 344645 x^{7} - 1939966 x^{6} - 1313053 x^{5} + 4806214 x^{4} - 16258641 x^{3} - 76618654 x^{2} - 46619874 x + 86089913$ |
$15$ |
[3,6] |
$7^{12}\cdot 71^{12}$ |
$2$ |
$143.577078138$ |
$153.19868787917656$ |
|
|
|
$(C_5^2 : C_3):C_2$ (as 15T12) |
$[5, 5]$ |
$2$ |
$8$ |
$1666688074.98$ |
| 15.15.860...625.2 |
$x^{15} - 190 x^{13} - 295 x^{12} + 11170 x^{11} + 29483 x^{10} - 198850 x^{9} - 614795 x^{8} + 922090 x^{7} + 4387410 x^{6} + 1717736 x^{5} - 7816650 x^{4} - 9556485 x^{3} - 2437450 x^{2} + 647185 x - 21853$ |
$15$ |
[15,0] |
$5^{18}\cdot 7^{10}\cdot 41^{8}$ |
$3$ |
$182.9422806$ |
$748.3796765914713$ |
|
|
? |
$(C_5^2 : C_3):C_2$ (as 15T12) |
trivial |
$2$ |
$14$ |
$1691423909070$ |
| 15.15.243...625.1 |
$x^{15} - 615 x^{13} - 1230 x^{12} + 142680 x^{11} + 519839 x^{10} - 15801400 x^{9} - 78738040 x^{8} + 868413005 x^{7} + 5416669490 x^{6} - 21713100456 x^{5} - 172685011550 x^{4} + 170114602855 x^{3} + 2260510932180 x^{2} + 245238148250 x - 9370162894441$ |
$15$ |
[15,0] |
$5^{18}\cdot 7^{10}\cdot 41^{12}$ |
$3$ |
$492.481344638$ |
$748.3796765914713$ |
|
|
? |
$(C_5^2 : C_3):C_2$ (as 15T12) |
$[5]$ |
$2$ |
$14$ |
$676079996900000$ |
