| 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 |
| 34.0.770...296.1 |
$x^{34} - 2 x^{17} + 2$ |
$34$ |
[0,17] |
$-\,2^{50}\cdot 17^{34}$ |
$2$ |
$47.1129275253$ |
$55.08022815278142$ |
|
|
✓ |
$C_2\times F_{17}$ (as 34T9) |
trivial |
$4$ |
$16$ |
$2332460652781060.5$ |
| 34.0.380...067.1 |
$x^{34} - 3 x^{17} + 3$ |
$34$ |
[0,17] |
$-\,3^{33}\cdot 17^{34}$ |
$2$ |
$49.3784209847$ |
$57.728840819705006$ |
|
|
✓ |
$C_2\times F_{17}$ (as 34T9) |
trivial |
$6$ |
$16$ |
$6031882093114950.0$ |
| 34.0.100...312.1 |
$x^{34} + 2$ |
$34$ |
[0,17] |
$-\,2^{67}\cdot 17^{34}$ |
$2$ |
$66.6277410694$ |
$77.89520567226786$ |
|
|
✓ |
$C_2\times F_{17}$ (as 34T9) |
trivial |
$2$ |
$16$ |
$585226461963806300$ |
| 34.2.100...312.1 |
$x^{34} - 2$ |
$34$ |
[2,16] |
$2^{67}\cdot 17^{34}$ |
$2$ |
$66.6277410694$ |
$77.89520567226786$ |
|
|
✓ |
$C_2\times F_{17}$ (as 34T9) |
trivial |
$2$ |
$17$ |
$504347647410496830$ |
| 34.2.796...125.1 |
$x^{34} - 5$ |
$34$ |
[2,16] |
$5^{33}\cdot 17^{34}$ |
$2$ |
$81.0701514633$ |
$94.77998234304803$ |
|
|
? |
$C_2\times F_{17}$ (as 34T9) |
trivial |
$2$ |
$17$ |
$10116155297585506000$ |
| 34.2.653...328.1 |
$x^{34} - 3$ |
$34$ |
[2,16] |
$2^{34}\cdot 3^{33}\cdot 17^{34}$ |
$3$ |
$98.7568419694$ |
$115.45768163941001$ |
|
|
✓ |
$C_2\times F_{17}$ (as 34T9) |
trivial |
$2$ |
$17$ |
$520979448668698900000$ |
| 34.0.136...000.1 |
$x^{34} + 5$ |
$34$ |
[0,17] |
$-\,2^{34}\cdot 5^{33}\cdot 17^{34}$ |
$3$ |
$162.140302927$ |
$189.55996468609607$ |
|
|
✓ |
$C_2\times F_{17}$ (as 34T9) |
not computed |
$2$ |
$16$ |
|
