| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
| 9.1.79082438656.1 |
$ x^{9} - 3 x^{8} + 12 x^{6} - 14 x^{5} - 2 x^{4} + 12 x^{2} + \cdots + 1 $ |
$9$ |
[1,4] |
$2^{14}\cdot 13^{6}$ |
$2$ |
$16.2516620874$ |
|
|
not computed |
$\PSL(2,8)$ (as 9T27) |
trivial |
$2$ |
$4$ |
$188.995903531$ |
| 9.1.1450463739904.1 |
$ x^{9} - x^{8} + 12 x^{6} - 12 x^{5} - 28 x^{4} + 48 x^{3} + \cdots - 1 $ |
$9$ |
[1,4] |
$2^{14}\cdot 97^{4}$ |
$2$ |
$22.453215355$ |
|
|
not computed |
$\PSL(2,8)$ (as 9T27) |
$[7]$ |
$2$ |
$4$ |
$195.876560311$ |
| 9.1.2312735309824.1 |
$ x^{9} - x^{8} - 16 x^{6} + 36 x^{5} - 12 x^{4} - 8 x^{3} - 3 x - 1 $ |
$9$ |
[1,4] |
$2^{14}\cdot 109^{4}$ |
$2$ |
$23.6478558892$ |
|
|
not computed |
$\PSL(2,8)$ (as 9T27) |
$[7]$ |
$2$ |
$4$ |
$214.443775555$ |
| 9.1.2671367962624.1 |
$ x^{9} + 4 x^{7} - 10 x^{5} - 12 x^{4} + 12 x^{2} + 10 x + 4 $ |
$9$ |
[1,4] |
$2^{14}\cdot 113^{4}$ |
$2$ |
$24.0296912297$ |
|
|
not computed |
$\PSL(2,8)$ (as 9T27) |
$[7]$ |
$2$ |
$4$ |
$253.76613554$ |
| 9.1.4169931445681.1 |
$ x^{9} + x^{7} - 4 x^{6} - 12 x^{4} - x^{3} - 7 x^{2} - x - 1 $ |
$9$ |
[1,4] |
$1429^{4}$ |
$1$ |
$25.2485560505$ |
|
|
not computed |
$\PSL(2,8)$ (as 9T27) |
$[7]$ |
$2$ |
$4$ |
$417.372043196$ |
| 9.1.4262209798144.1 |
$ x^{9} - x^{8} + 8 x^{7} - 18 x^{6} + 28 x^{5} - 56 x^{4} + 68 x^{3} + \cdots - 6 $ |
$9$ |
[1,4] |
$2^{14}\cdot 127^{4}$ |
$2$ |
$25.3100357227$ |
|
|
not computed |
$\PSL(2,8)$ (as 9T27) |
$[7]$ |
$2$ |
$4$ |
$496.58271455$ |
| 9.1.6029426229121.1 |
$ x^{9} - 2 x^{8} + 10 x^{7} - 25 x^{6} + 34 x^{5} - 40 x^{4} + \cdots - 4 $ |
$9$ |
[1,4] |
$1567^{4}$ |
$1$ |
$26.3045371903$ |
|
|
not computed |
$\PSL(2,8)$ (as 9T27) |
$[7]$ |
$2$ |
$4$ |
$401.146444514$ |
| 9.1.6116164255744.1 |
$ x^{9} + 8 x^{7} - 16 x^{6} + 30 x^{5} - 64 x^{4} + 80 x^{3} + \cdots - 4 $ |
$9$ |
[1,4] |
$2^{14}\cdot 139^{4}$ |
$2$ |
$26.346316485$ |
|
|
not computed |
$\PSL(2,8)$ (as 9T27) |
$[7]$ |
$2$ |
$4$ |
$272.110121765$ |
| 9.1.6347497291776.1 |
$ x^{9} - 6 x^{6} + 18 x^{5} - 18 x^{4} + 36 x^{3} + 18 x^{2} + \cdots + 22 $ |
$9$ |
[1,4] |
$2^{14}\cdot 3^{18}$ |
$2$ |
$26.455220861$ |
|
|
not computed |
$\PSL(2,8)$ (as 9T27) |
$[7]$ |
$2$ |
$4$ |
$445.942248354$ |
| 9.1.6769201929361.1 |
$ x^{9} - 2 x^{8} + 6 x^{6} - 8 x^{5} - 12 x^{4} + 12 x^{3} + \cdots + 1 $ |
$9$ |
[1,4] |
$1613^{4}$ |
$1$ |
$26.6449723803$ |
|
|
not computed |
$\PSL(2,8)$ (as 9T27) |
$[7]$ |
$2$ |
$4$ |
$181.163320861$ |
| 9.1.8075418025984.1 |
$ x^{9} - 4 x^{8} + 10 x^{5} + 20 x^{4} - 72 x^{3} - 8 x^{2} + \cdots - 128 $ |
$9$ |
[1,4] |
$2^{14}\cdot 149^{4}$ |
$2$ |
$27.1724905184$ |
|
|
not computed |
$\PSL(2,8)$ (as 9T27) |
$[7]$ |
$2$ |
$4$ |
$511.492125327$ |
| 9.1.8215383330001.1 |
$ x^{9} - 18 x^{7} - 2 x^{6} + 85 x^{5} + 24 x^{4} - 8 x^{3} + \cdots - 14 $ |
$9$ |
[1,4] |
$1693^{4}$ |
$1$ |
$27.2244207464$ |
|
|
not computed |
$\PSL(2,8)$ (as 9T27) |
$[7]$ |
$2$ |
$4$ |
$341.001921505$ |
| 9.1.8517805686784.1 |
$ x^{9} - 2 x^{8} + 2 x^{7} + 10 x^{6} - 18 x^{5} + 30 x^{4} + \cdots + 152 $ |
$9$ |
[1,4] |
$2^{14}\cdot 151^{4}$ |
$2$ |
$27.3339931307$ |
|
|
not computed |
$\PSL(2,8)$ (as 9T27) |
$[7]$ |
$2$ |
$4$ |
$797.666486981$ |
| 9.1.15904215784081.1 |
$ x^{9} - 3 x^{8} + 4 x^{6} + 5 x^{5} - 18 x^{4} + 23 x^{3} + \cdots - 4 $ |
$9$ |
[1,4] |
$1997^{4}$ |
$1$ |
$29.2977787843$ |
|
|
not computed |
$\PSL(2,8)$ (as 9T27) |
$[7]$ |
$2$ |
$4$ |
$498.973946432$ |
| 9.1.114290809913344.1 |
$ x^{9} + 34 x^{5} - 136 x^{4} + 272 x^{3} - 340 x^{2} + \cdots - 68 $ |
$9$ |
[1,4] |
$2^{14}\cdot 17^{8}$ |
$2$ |
$36.4755002403$ |
|
|
not computed |
$\PSL(2,8)$ (as 9T27) |
$[7]$ |
$2$ |
$4$ |
$1876.43825915$ |
| 9.1.514147280633856.1 |
$ x^{9} - 12 x^{6} - 18 x^{5} + 36 x^{2} - 27 x - 128 $ |
$9$ |
[1,4] |
$2^{14}\cdot 3^{22}$ |
$2$ |
$43.1087353613$ |
|
|
not computed |
$\PSL(2,8)$ (as 9T27) |
$[7]$ |
$2$ |
$4$ |
$3190.27571115$ |
| 9.1.41645929731342336.1 |
$ x^{9} - 36 x^{6} - 54 x^{5} + 432 x^{3} + 324 x^{2} + \cdots - 1152 $ |
$9$ |
[1,4] |
$2^{14}\cdot 3^{26}$ |
$2$ |
$70.2456076334$ |
|
|
not computed |
$\PSL(2,8)$ (as 9T27) |
$[7]$ |
$2$ |
$4$ |
$63858.3966428$ |
| 9.1.41645929731342336.2 |
$ x^{9} - 36 x^{6} - 54 x^{5} - 324 x^{4} - 216 x^{3} + \cdots - 2124 $ |
$9$ |
[1,4] |
$2^{14}\cdot 3^{26}$ |
$2$ |
$70.2456076334$ |
|
|
not computed |
$\PSL(2,8)$ (as 9T27) |
$[7]$ |
$2$ |
$4$ |
$45869.9703414$ |
| 9.1.180...376.1 |
$ x^{9} - 444 x^{6} - 4662 x^{5} - 27972 x^{4} + \cdots - 26643404 $ |
$9$ |
[1,4] |
$2^{14}\cdot 3^{22}\cdot 37^{8}$ |
$3$ |
$1067.87979791$ |
|
|
not computed |
$\PSL(2,8)$ (as 9T27) |
$[63]$ |
$2$ |
$4$ |
$893886967.791$ |
| 9.9.163...809.1 |
$ x^{9} - 3 x^{8} - 12000 x^{7} - 295072 x^{6} + \cdots - 1186350537195 $ |
$9$ |
[9,0] |
$3^{4}\cdot 37^{6}\cdot 2977717^{4}$ |
$3$ |
$13639.6500292$ |
|
|
|
$\PSL(2,8)$ (as 9T27) |
$[21]$ |
$2$ |
$8$ |
$13435625715600000$ |
| 9.9.823...136.1 |
$ x^{9} - x^{8} - 46044 x^{7} + 2290792 x^{6} + \cdots + 75\!\cdots\!91 $ |
$9$ |
[9,0] |
$2^{6}\cdot 7^{10}\cdot 37^{8}\cdot 263^{4}\cdot 1283^{4}$ |
$5$ |
$97861.4241849$ |
|
|
|
$\PSL(2,8)$ (as 9T27) |
$[9]$ |
$2$ |
$8$ |
$33057799402800000000$ |
