| 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 |
| 14.2.282...000.1 |
$x^{14} - 3 x^{13} - 5 x^{12} + 31 x^{11} - 50 x^{10} + 127 x^{9} - 55 x^{8} + 1003 x^{7} - 5194 x^{6} + 13043 x^{5} + 6647 x^{4} - 129703 x^{3} + 382419 x^{2} - 490216 x + 319344$ |
$14$ |
[2,6] |
$2^{20}\cdot 3^{14}\cdot 5^{10}\cdot 7^{8}$ |
$4$ |
$77.5071129459$ |
$2342.2158414001506$ |
|
|
|
$A_{14}$ (as 14T62) |
trivial |
$2$ |
$7$ |
$874877246.508$ |
| 14.6.272...000.1 |
$x^{14} - 6 x^{13} - 9 x^{12} + 404 x^{11} + 756 x^{10} - 744 x^{9} - 31226 x^{8} - 178104 x^{7} - 129651 x^{6} + 191106 x^{5} - 447273 x^{4} - 2482812 x^{3} + 1375542 x^{2} + 2905308 x - 1000188$ |
$14$ |
[6,4] |
$2^{28}\cdot 3^{14}\cdot 5^{12}\cdot 7^{2}\cdot 11^{6}$ |
$5$ |
$175.929162324$ |
|
|
|
|
$A_{14}$ (as 14T62) |
trivial |
$2$ |
$9$ |
$1461564547240$ |
| 14.2.930...736.1 |
$x^{14} - 52416 x^{5} - 1053696 x - 5061888$ |
$14$ |
[2,6] |
$2^{16}\cdot 3^{12}\cdot 7^{14}\cdot 13^{14}$ |
$4$ |
$515.27224336$ |
|
|
|
? |
$A_{14}$ (as 14T62) |
trivial |
$2$ |
$7$ |
$136382579473000$ |
| 14.14.120...000.1 |
$x^{14} - 2900730 x^{12} - 287910000 x^{11} + 3313325898225 x^{10} + 597401557200000 x^{9} - 1855964346085631250 x^{8} - 447630993322011000000 x^{7} + 517062546566176619531250 x^{6} + 144716607884926457572500000 x^{5} - 63938673030863212150078125000 x^{4} - 18637303238230533691855781250000 x^{3} + 2587399700316109318860370458984375 x^{2} + 773043792817583070706838466796875000 x + 40095511130962225240189804491943359375$ |
$14$ |
[14,0] |
$2^{14}\cdot 3^{22}\cdot 5^{12}\cdot 7^{14}\cdot 19^{6}\cdot 197^{6}\cdot 199^{6}\cdot 2593^{6}\cdot 34963^{6}\cdot 560233^{6}\cdot 1072255949^{2}\cdot 6488895781911832501^{2}$ |
$12$ |
$729476162501000.0$ |
|
|
|
? |
$A_{14}$ (as 14T62) |
not computed |
$2$ |
$13$ |
|
| 14.10.103...000.1 |
$x^{14} - 75054 x^{12} - 1377936 x^{11} + 2221160193 x^{10} + 73963665216 x^{9} - 32146732228590 x^{8} - 1435876427859264 x^{7} + 229281249311034354 x^{6} + 12030481855773499104 x^{5} - 708298583106976109136 x^{4} - 40091843709134882829360 x^{3} + 666759835809172158276111 x^{2} + 43071240857705358819374952 x + 414212142950309582401202559$ |
$14$ |
[10,2] |
$2^{14}\cdot 3^{22}\cdot 5^{6}\cdot 7^{14}\cdot 23^{2}\cdot 211^{2}\cdot 68389^{6}\cdot 119737^{2}\cdot 67580323^{6}\cdot 332926921^{6}\cdot 65049457057236257^{2}$ |
$11$ |
$850323339437000.0$ |
|
|
|
? |
$A_{14}$ (as 14T62) |
not computed |
$2$ |
$11$ |
|
