| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
| 20.8.172...000.1 |
$x^{20} + 10 x^{18} - 19 x^{16} - 324 x^{14} - 82 x^{12} + 1684 x^{10} + 466 x^{8} - 1940 x^{6} - 983 x^{4} + 42 x^{2} + 9$ |
$20$ |
[8,6] |
$2^{28}\cdot 3^{2}\cdot 5^{14}\cdot 43^{8}$ |
$4$ |
$40.9091545909$ |
|
|
|
? |
$C_2^9.F_5$ (as 20T429) |
trivial |
$[2]$ |
$2$ |
$13$ |
$539927092.339$ |
| 20.8.180...000.1 |
$x^{20} - 10 x^{19} + 35 x^{18} - 385 x^{16} + 1058 x^{15} - 60 x^{14} - 3950 x^{13} + 3375 x^{12} + 8310 x^{11} - 10375 x^{10} - 10660 x^{9} + 14945 x^{8} + 8660 x^{7} - 11600 x^{6} - 3864 x^{5} + 6175 x^{4} - 960 x^{3} - 2055 x^{2} + 870 x + 359$ |
$20$ |
[8,6] |
$2^{28}\cdot 5^{22}\cdot 7^{10}$ |
$3$ |
$41.0070019335$ |
$82.32356195675848$ |
|
|
? |
$C_2\wr F_5$ (as 20T134) |
trivial |
$[2]$ |
$2$ |
$13$ |
$526854946.66$ |
| 20.12.658...000.2 |
$x^{20} - 4 x^{19} - 9 x^{18} + 46 x^{17} - 93 x^{16} - 358 x^{15} + 1366 x^{14} + 3416 x^{13} - 535 x^{12} + 9002 x^{11} + 39897 x^{10} - 63890 x^{9} - 379411 x^{8} - 327670 x^{7} + 565752 x^{6} + 1165256 x^{5} + 259669 x^{4} - 793320 x^{3} - 509915 x^{2} + 54050 x + 69775$ |
$20$ |
[12,4] |
$2^{28}\cdot 5^{11}\cdot 3469^{5}$ |
$3$ |
$49.0824882484$ |
|
|
|
? |
$C_2^9.D_5\wr C_2$ (as 20T771) |
trivial |
$[2, 2]$ |
$2$ |
$15$ |
$5534015418.29$ |
| 20.12.658...000.3 |
$x^{20} + 2 x^{18} - 263 x^{16} + 840 x^{14} + 7642 x^{12} - 14024 x^{10} - 34594 x^{8} + 80288 x^{6} - 22531 x^{4} - 34690 x^{2} + 17345$ |
$20$ |
[12,4] |
$2^{28}\cdot 5^{11}\cdot 3469^{5}$ |
$3$ |
$49.0824882484$ |
|
|
|
? |
$C_2^9.D_5\wr C_2$ (as 20T771) |
trivial |
$[2, 2]$ |
$2$ |
$15$ |
$6395502933.06$ |
| 20.8.737...744.5 |
$x^{20} + 12 x^{18} - 12 x^{16} - 204 x^{14} + 208 x^{12} + 700 x^{10} - 704 x^{8} - 448 x^{6} + 272 x^{4} + 160 x^{2} + 16$ |
$20$ |
[8,6] |
$2^{28}\cdot 13^{14}\cdot 17^{8}$ |
$3$ |
$49.36076809853314$ |
|
|
|
? |
$C_2^9.S_5$ (as 20T663) |
trivial |
trivial |
$2$ |
$13$ |
$3616897874.7391453$ |
