| 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 |
| 20.0.159...125.1 |
$x^{20} - 5 x^{19} + 25 x^{18} - 65 x^{17} + 155 x^{16} - 344 x^{15} + 735 x^{14} - 1155 x^{13} + 2515 x^{12} - 5995 x^{11} + 11436 x^{10} - 15605 x^{9} + 15660 x^{8} - 11360 x^{7} + 6125 x^{6} - 2544 x^{5} + 900 x^{4} - 255 x^{3} + 60 x^{2} - 10 x + 1$ |
$20$ |
[0,10] |
$5^{27}\cdot 11^{8}$ |
$2$ |
$22.9174651666$ |
$59.80309407631675$ |
✓ |
|
? |
$C_5:C_{20}$ (as 20T25) |
trivial |
$10$ |
$9$ |
$1031961.46725$ |
| 20.0.119...125.1 |
$x^{20} - 6 x^{19} + 30 x^{18} - 100 x^{17} + 285 x^{16} - 662 x^{15} + 1266 x^{14} - 1564 x^{13} + 1560 x^{12} - 2105 x^{11} + 4112 x^{10} - 6402 x^{9} + 7316 x^{8} - 5906 x^{7} + 3515 x^{6} - 1610 x^{5} + 643 x^{4} - 206 x^{3} + 52 x^{2} - 9 x + 1$ |
$20$ |
[0,10] |
$5^{15}\cdot 211^{8}$ |
$2$ |
$28.4407133632$ |
$241.90980283096022$ |
✓ |
|
? |
$C_5:C_{20}$ (as 20T25) |
$[11]$ |
$10$ |
$9$ |
$454775.127492$ |
| 20.20.167...000.1 |
$x^{20} - 35 x^{18} + 500 x^{16} - 3735 x^{14} + 15485 x^{12} - 34730 x^{10} + 37840 x^{8} - 16450 x^{6} + 2800 x^{4} - 200 x^{2} + 5$ |
$20$ |
[20,0] |
$2^{20}\cdot 5^{27}\cdot 11^{8}$ |
$3$ |
$45.8349303332$ |
$119.6061881526335$ |
|
|
? |
$C_5:C_{20}$ (as 20T25) |
trivial |
$2$ |
$19$ |
$21446337591.7$ |
| 20.20.282...125.1 |
$x^{20} - 5 x^{19} - 50 x^{18} + 225 x^{17} + 1140 x^{16} - 4174 x^{15} - 15180 x^{14} + 40885 x^{13} + 124360 x^{12} - 228115 x^{11} - 617264 x^{10} + 754985 x^{9} + 1778530 x^{8} - 1588305 x^{7} - 2831085 x^{6} + 2212556 x^{5} + 2195650 x^{4} - 1829365 x^{3} - 484030 x^{2} + 592885 x - 103589$ |
$20$ |
[20,0] |
$5^{27}\cdot 11^{14}$ |
$2$ |
$47.0526822423$ |
$76.00863310368105$ |
|
|
? |
$C_5:C_{20}$ (as 20T25) |
trivial |
$2$ |
$19$ |
$29332960138.8$ |
