| 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 |
| 23.1.875...368.1 |
$x^{23} - 2$ |
$23$ |
[1,11] |
$-\,2^{22}\cdot 23^{23}$ |
$2$ |
$44.6343866265$ |
$50.83747447492002$ |
|
|
✓ |
$F_{23}$ (as 23T4) |
trivial |
$2$ |
$11$ |
$14787749883.9$ |
| 23.1.101...875.1 |
$x^{23} + 23 x^{21} + 230 x^{19} + 1311 x^{17} + 4692 x^{15} + 10948 x^{13} + 16744 x^{11} + 16445 x^{9} + 9867 x^{7} + 3289 x^{5} + 506 x^{3} + 23 x - 1$ |
$23$ |
[1,11] |
$-\,5^{11}\cdot 23^{23}$ |
$2$ |
$49.6612718765$ |
$58.57701468324603$ |
|
|
✓ |
$F_{23}$ (as 23T4) |
trivial |
$2$ |
$11$ |
$53144954646.2$ |
| 23.1.655...303.1 |
$x^{23} - 3$ |
$23$ |
[1,11] |
$-\,3^{22}\cdot 23^{23}$ |
$2$ |
$65.781638742$ |
$74.92367730844663$ |
|
|
✓ |
$F_{23}$ (as 23T4) |
trivial |
$2$ |
$11$ |
$1289649122770$ |
| 23.1.497...375.1 |
$x^{23} - 5$ |
$23$ |
[1,11] |
$-\,5^{22}\cdot 23^{23}$ |
$2$ |
$107.227909756$ |
$122.1299660918339$ |
|
|
✓ |
$F_{23}$ (as 23T4) |
trivial |
$2$ |
$11$ |
$364622659737000$ |
| 23.1.274...112.1 |
$x^{23} - 6$ |
$23$ |
[1,11] |
$-\,2^{22}\cdot 3^{22}\cdot 23^{23}$ |
$3$ |
$127.657525936$ |
$145.39879915059288$ |
|
|
✓ |
$F_{23}$ (as 23T4) |
trivial |
$2$ |
$11$ |
$2659711570670000$ |
| 23.1.816...783.1 |
$x^{23} - 7$ |
$23$ |
[1,11] |
$-\,7^{22}\cdot 23^{23}$ |
$2$ |
$147.938933317$ |
$168.49882601279793$ |
|
|
✓ |
$F_{23}$ (as 23T4) |
trivial |
$2$ |
$11$ |
$14416124790000000$ |
| 23.23.208...000.1 |
$x^{23} - 115 x^{21} + 5750 x^{19} - 163875 x^{17} + 2932500 x^{15} - 34212500 x^{13} + 261625000 x^{11} - 1284765625 x^{9} + 3854296875 x^{7} - 6423828125 x^{5} + 4941406250 x^{3} - 1123046875 x - 218280250$ |
$23$ |
[23,0] |
$2^{22}\cdot 5^{22}\cdot 23^{23}$ |
$3$ |
$208.089216574$ |
$244.2599321836678$ |
|
|
? |
$F_{23}$ (as 23T4) |
trivial |
$2$ |
$22$ |
$108577580716000000000$ |
| 23.23.281...792.1 |
$x^{23} - 299 x^{21} + 38870 x^{19} - 2880267 x^{17} + 134008212 x^{15} - 4064915764 x^{13} + 80820089896 x^{11} - 1031899362065 x^{9} + 8048815024107 x^{7} - 34878198437797 x^{5} + 69756396875594 x^{3} - 41219689062851 x - 12722733426052$ |
$23$ |
[23,0] |
$2^{22}\cdot 13^{22}\cdot 23^{23}$ |
$3$ |
$519.015829516$ |
$609.2327772055112$ |
|
|
? |
$F_{23}$ (as 23T4) |
trivial |
$2$ |
$22$ |
$3930853533530000000000000$ |
