| 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 |
| 17.1.239...153.1 |
$x^{17} - 34 x^{12} + 17 x^{11} + 85 x^{10} + 102 x^{9} - 170 x^{8} - 272 x^{7} - 68 x^{6} + 255 x^{5} + 255 x^{4} + 68 x^{3} + 17 x^{2} + 17 x + 4$ |
$17$ |
[1,8] |
$17^{19}$ |
$1$ |
$23.7250763118$ |
$27.737240813400426$ |
|
|
? |
$F_{17}$ (as 17T5) |
trivial |
$2$ |
$8$ |
$195995.113671$ |
| 17.1.604...088.1 |
$x^{17} - 2 x^{16} + 8 x^{13} + 16 x^{12} - 16 x^{11} + 64 x^{9} - 32 x^{8} - 80 x^{7} + 32 x^{6} + 40 x^{5} + 80 x^{4} + 16 x^{3} - 128 x^{2} - 2 x + 68$ |
$17$ |
[1,8] |
$2^{79}$ |
$1$ |
$25.0555590588$ |
$30.64330498235436$ |
|
|
? |
$F_{17}$ (as 17T5) |
trivial |
$2$ |
$8$ |
$600164.932841$ |
| 17.1.542...872.1 |
$x^{17} - 2$ |
$17$ |
[1,8] |
$2^{16}\cdot 17^{17}$ |
$2$ |
$32.6415873531$ |
$38.16162936825564$ |
|
|
✓ |
$F_{17}$ (as 17T5) |
trivial |
$2$ |
$8$ |
$2966240.41128$ |
| 17.1.323...625.1 |
$x^{17} + 17 x^{15} + 119 x^{13} + 442 x^{11} + 935 x^{9} + 1122 x^{7} + 714 x^{5} + 204 x^{3} + 17 x - 1$ |
$17$ |
[1,8] |
$5^{8}\cdot 17^{17}$ |
$2$ |
$36.2556739236$ |
$44.44158735609407$ |
|
|
✓ |
$F_{17}$ (as 17T5) |
trivial |
$2$ |
$8$ |
$7413165.64743$ |
| 17.1.356...617.1 |
$x^{17} - 3$ |
$17$ |
[1,8] |
$3^{16}\cdot 17^{17}$ |
$2$ |
$47.8084011557$ |
$55.893313822619575$ |
|
|
✓ |
$F_{17}$ (as 17T5) |
trivial |
$2$ |
$8$ |
$76477842.2049$ |
| 17.1.126...625.1 |
$x^{17} - 5$ |
$17$ |
[1,8] |
$5^{16}\cdot 17^{17}$ |
$2$ |
$77.3219936269$ |
$90.39797087345524$ |
|
|
✓ |
$F_{17}$ (as 17T5) |
trivial |
$2$ |
$8$ |
$4452069250.85$ |
| 17.1.233...712.1 |
$x^{17} - 6$ |
$17$ |
[1,8] |
$2^{16}\cdot 3^{16}\cdot 17^{17}$ |
$3$ |
$91.7965942667$ |
$107.32038150548227$ |
|
|
✓ |
$F_{17}$ (as 17T5) |
trivial |
$2$ |
$8$ |
$19074539557.9$ |
| 17.1.274...377.1 |
$x^{17} - 7$ |
$17$ |
[1,8] |
$7^{16}\cdot 17^{17}$ |
$2$ |
$106.129302988$ |
$124.07690477638815$ |
|
|
✓ |
$F_{17}$ (as 17T5) |
trivial |
$2$ |
$8$ |
$70086534327.5$ |
| 17.17.597...272.1 |
$x^{17} - 51 x^{15} + 1071 x^{13} - 11934 x^{11} + 75735 x^{9} - 272646 x^{7} + 520506 x^{5} - 446148 x^{3} + 111537 x - 22482$ |
$17$ |
[17,0] |
$2^{24}\cdot 3^{16}\cdot 17^{17}$ |
$3$ |
$127.200185081$ |
$158.09016490784836$ |
|
|
? |
$F_{17}$ (as 17T5) |
trivial |
$2$ |
$16$ |
$13029132161200$ |
| 17.17.827...000.1 |
$x^{17} - 85 x^{15} + 2975 x^{13} - 55250 x^{11} + 584375 x^{9} - 3506250 x^{7} + 11156250 x^{5} - 15937500 x^{3} + 6640625 x - 1737500$ |
$17$ |
[17,0] |
$2^{16}\cdot 5^{16}\cdot 17^{17}$ |
$3$ |
$148.465447605$ |
$180.79594174691047$ |
|
|
? |
$F_{17}$ (as 17T5) |
trivial |
$2$ |
$16$ |
$48080253767000$ |
