| 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 |
| 20.0.289...989.1 |
$x^{20} - 4 x^{17} + 25 x^{16} - 31 x^{14} - 36 x^{13} + 184 x^{12} + 60 x^{11} - 157 x^{10} - 149 x^{9} + 445 x^{8} - 27 x^{7} - 180 x^{6} + 67 x^{5} + 156 x^{4} + 4 x^{3} - 3 x^{2} - 3 x + 1$ |
$20$ |
[0,10] |
$11^{16}\cdot 229^{5}$ |
$2$ |
$26.4894547313$ |
$103.04617822247701$ |
|
|
? |
$C_5\times S_4$ (as 20T34) |
trivial |
$2$ |
$9$ |
$957497.704734$ |
| 20.0.515...177.1 |
$x^{20} + 9 x^{18} - 4 x^{17} + 53 x^{16} - 20 x^{15} + 151 x^{14} - 68 x^{13} + 368 x^{12} - 76 x^{11} + 496 x^{10} - 166 x^{9} + 634 x^{8} - 55 x^{7} + 277 x^{6} + 61 x^{5} + 175 x^{4} + x^{3} + 12 x^{2} - 3 x + 1$ |
$20$ |
[0,10] |
$11^{16}\cdot 257^{5}$ |
$2$ |
$27.2644931779$ |
$109.16431898404717$ |
|
|
? |
$C_5\times S_4$ (as 20T34) |
trivial |
$2$ |
$9$ |
$831805.977332$ |
| 20.10.834...523.1 |
$x^{20} - 4 x^{17} - 25 x^{16} - 31 x^{14} + 36 x^{13} + 184 x^{12} + 60 x^{11} + 157 x^{10} - 149 x^{9} - 361 x^{8} + 27 x^{7} - 180 x^{6} - 69 x^{5} + 154 x^{4} + 4 x^{3} + 3 x^{2} - 3 x - 1$ |
$20$ |
[10,5] |
$-\,11^{16}\cdot 283^{5}$ |
$2$ |
$27.9293454037$ |
$114.55323701805673$ |
|
|
? |
$C_5\times S_4$ (as 20T34) |
trivial |
$2$ |
$14$ |
$11612148.1752$ |
| 20.10.182...811.1 |
$x^{20} - x^{19} + 5 x^{18} + 2 x^{17} + 12 x^{16} - 3 x^{15} - 81 x^{14} + 94 x^{13} - 79 x^{12} - 271 x^{11} + 174 x^{10} + 348 x^{9} + 350 x^{8} - 334 x^{7} - 473 x^{6} + 234 x^{5} + 74 x^{4} - 49 x^{3} + 18 x^{2} + 3 x - 1$ |
$20$ |
[10,5] |
$-\,11^{16}\cdot 331^{5}$ |
$2$ |
$29.0449843342$ |
$123.88768709435013$ |
|
|
? |
$C_5\times S_4$ (as 20T34) |
trivial |
$2$ |
$14$ |
$18726448.7284$ |
| 20.20.131...677.1 |
$x^{20} - 36 x^{18} - 4 x^{17} + 473 x^{16} + 80 x^{15} - 2859 x^{14} - 548 x^{13} + 8448 x^{12} + 1324 x^{11} - 12749 x^{10} - 1241 x^{9} + 9949 x^{8} + 445 x^{7} - 3988 x^{6} - 69 x^{5} + 780 x^{4} + 16 x^{3} - 63 x^{2} - 3 x + 1$ |
$20$ |
[20,0] |
$11^{16}\cdot 19^{5}\cdot 103^{5}$ |
$3$ |
$45.2909942405$ |
$301.2378650303931$ |
|
|
? |
$C_5\times S_4$ (as 20T34) |
trivial |
$2$ |
$19$ |
$13698434875.8$ |
| 20.20.758...777.1 |
$x^{20} - x^{19} - 39 x^{18} + 28 x^{17} + 593 x^{16} - 302 x^{15} - 4531 x^{14} + 1664 x^{13} + 18779 x^{12} - 5250 x^{11} - 42734 x^{10} + 10050 x^{9} + 52063 x^{8} - 11604 x^{7} - 32303 x^{6} + 7629 x^{5} + 8990 x^{4} - 2522 x^{3} - 785 x^{2} + 296 x - 23$ |
$20$ |
[20,0] |
$11^{16}\cdot 2777^{5}$ |
$2$ |
$49.4319926992$ |
$358.8410245617943$ |
|
|
? |
$C_5\times S_4$ (as 20T34) |
trivial |
$2$ |
$19$ |
$40125051391.3$ |
