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 |
21.3.445...007.1 |
$x^{21} - 7 x^{14} + 7 x^{7} + 7$ |
$21$ |
[3,9] |
$-\,7^{41}$ |
$1$ |
$44.6635579203$ |
$59.36850199103005$ |
|
|
|
$C_7:F_7$ (as 21T19) |
trivial |
$2$ |
$11$ |
$2576323425.69$ |
21.3.445...007.2 |
$x^{21} - 21 x^{14} + 35 x^{7} - 7$ |
$21$ |
[3,9] |
$-\,7^{41}$ |
$1$ |
$44.6635579203$ |
$59.36850199103005$ |
|
|
|
$C_7:F_7$ (as 21T19) |
trivial |
$2$ |
$11$ |
$2078079445.0$ |
21.21.231...952.1 |
$x^{21} - 133 x^{19} + 7238 x^{17} - 211995 x^{15} - 8844 x^{14} + 3686319 x^{13} + 529074 x^{12} - 39442403 x^{11} - 12480468 x^{10} + 258905465 x^{9} + 147566874 x^{8} - 994440486 x^{7} - 914967690 x^{6} + 1920581572 x^{5} + 2791657596 x^{4} - 763121359 x^{3} - 3207628788 x^{2} - 1974848148 x - 392454504$ |
$21$ |
[21,0] |
$2^{18}\cdot 7^{35}\cdot 13^{12}$ |
$3$ |
$200.937734939$ |
$523.5407564581101$ |
|
|
|
$C_7:F_7$ (as 21T19) |
trivial |
$2$ |
$20$ |
$773095802604000000$ |
21.21.351...472.1 |
$x^{21} - 217 x^{19} + 19544 x^{17} - 959637 x^{15} - 33706 x^{14} + 28285005 x^{13} + 3493224 x^{12} - 517708667 x^{11} - 143018778 x^{10} + 5859384083 x^{9} + 2942499210 x^{8} - 39262594646 x^{7} - 31779062112 x^{6} + 138562884152 x^{5} + 168986405644 x^{4} - 168971552743 x^{3} - 345735927544 x^{2} - 146449603860 x - 6727656872$ |
$21$ |
[21,0] |
$2^{18}\cdot 7^{35}\cdot 29^{12}$ |
$3$ |
$317.817965147$ |
$1041.419982801981$ |
|
|
|
$C_7:F_7$ (as 21T19) |
trivial |
$2$ |
$20$ |
$100927220322000000000$ |