| 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 |
| 20.0.820...808.1 |
$x^{20} - 3 x^{19} + 5 x^{18} - 5 x^{17} + 4 x^{16} - 5 x^{15} + 11 x^{14} - 21 x^{13} + 30 x^{12} - 35 x^{11} + 37 x^{10} - 35 x^{9} + 30 x^{8} - 21 x^{7} + 11 x^{6} - 5 x^{5} + 4 x^{4} - 5 x^{3} + 5 x^{2} - 3 x + 1$ |
$20$ |
[0,10] |
$2^{16}\cdot 277^{7}$ |
$2$ |
$12.4649894626$ |
$28.97769793904893$ |
|
|
? |
$S_5$ (as 20T30) |
trivial |
$2$ |
$9$ |
$351.863063149$ |
| 20.0.279...169.1 |
$x^{20} - 5 x^{19} + 12 x^{18} - 21 x^{17} + 36 x^{16} - 63 x^{15} + 103 x^{14} - 143 x^{13} + 166 x^{12} - 170 x^{11} + 169 x^{10} - 170 x^{9} + 166 x^{8} - 143 x^{7} + 103 x^{6} - 63 x^{5} + 36 x^{4} - 21 x^{3} + 12 x^{2} - 5 x + 1$ |
$20$ |
[0,10] |
$1609^{7}$ |
$1$ |
$13.2524024297$ |
$40.11234224026316$ |
|
|
? |
$S_5$ (as 20T30) |
trivial |
$2$ |
$9$ |
$751.110855868$ |
| 20.6.766...792.1 |
$x^{20} - x^{19} - 3 x^{18} + 5 x^{17} + 4 x^{16} - 11 x^{15} - 13 x^{14} + 21 x^{13} - 10 x^{12} - 25 x^{11} + 21 x^{10} - 25 x^{9} - 10 x^{8} + 21 x^{7} - 13 x^{6} - 11 x^{5} + 4 x^{4} + 5 x^{3} - 3 x^{2} - x + 1$ |
$20$ |
[6,7] |
$-\,2^{16}\cdot 3^{16}\cdot 43^{7}$ |
$3$ |
$15.6399355752$ |
$27.49509522275834$ |
|
|
? |
$S_5$ (as 20T30) |
trivial |
$2$ |
$12$ |
$11415.5281685$ |
| 20.6.118...887.1 |
$x^{20} - x^{19} - 3 x^{18} + 11 x^{17} - 5 x^{16} - 23 x^{15} + 41 x^{14} + 21 x^{13} - 82 x^{12} + 32 x^{11} + 123 x^{10} - 148 x^{9} - 25 x^{8} + 156 x^{7} - 55 x^{6} - 11 x^{5} - 8 x^{4} + 2 x^{3} + 12 x^{2} - 7 x + 1$ |
$20$ |
[6,7] |
$-\,3^{16}\cdot 223^{7}$ |
$2$ |
$15.9809909602$ |
$35.962463598304126$ |
|
|
? |
$S_5$ (as 20T30) |
trivial |
$2$ |
$12$ |
$14563.3790161$ |
| 20.20.488...273.1 |
$x^{20} - 4 x^{19} - 25 x^{18} + 117 x^{17} + 180 x^{16} - 1199 x^{15} - 186 x^{14} + 5483 x^{13} - 2045 x^{12} - 12596 x^{11} + 7421 x^{10} + 15113 x^{9} - 9814 x^{8} - 9236 x^{7} + 5722 x^{6} + 2421 x^{5} - 1409 x^{4} - 79 x^{3} + 122 x^{2} - 20 x + 1$ |
$20$ |
[20,0] |
$61^{7}\cdot 397^{7}$ |
$2$ |
$34.2327761026$ |
$155.6181223379848$ |
|
|
? |
$S_5$ (as 20T30) |
trivial |
$2$ |
$19$ |
$694470597.337$ |
| 20.20.862...313.1 |
$x^{20} - 8 x^{19} - 5 x^{18} + 191 x^{17} - 373 x^{16} - 1121 x^{15} + 4398 x^{14} - 928 x^{13} - 14149 x^{12} + 17892 x^{11} + 7841 x^{10} - 27291 x^{9} + 9170 x^{8} + 12905 x^{7} - 9484 x^{6} - 736 x^{5} + 2234 x^{4} - 537 x^{3} - 12 x^{2} + 14 x - 1$ |
$20$ |
[20,0] |
$36497^{7}$ |
$1$ |
$39.5175497437$ |
$191.04188022525324$ |
|
|
? |
$S_5$ (as 20T30) |
trivial |
$2$ |
$19$ |
$2923694908.82$ |
