| 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 |
| 20.0.174...736.1 |
$x^{20} - 4 x^{19} + 8 x^{18} - 8 x^{17} + 5 x^{16} + 2 x^{15} - 16 x^{14} + 30 x^{13} - 22 x^{12} - 4 x^{11} + 34 x^{10} - 66 x^{9} + 109 x^{8} - 136 x^{7} + 120 x^{6} - 76 x^{5} + 48 x^{4} - 40 x^{3} + 32 x^{2} - 16 x + 4$ |
$20$ |
[0,10] |
$2^{32}\cdot 67^{8}$ |
$2$ |
$16.2958836099$ |
$27.532135213818396$ |
|
|
? |
$C_2\times A_5$ (as 20T31) |
trivial |
$4$ |
$9$ |
$34612.1677943$ |
| 20.0.250...256.1 |
$x^{20} - 2 x^{19} + 2 x^{18} + 2 x^{17} - 5 x^{16} + 4 x^{15} + 4 x^{14} - 12 x^{13} + 7 x^{12} + 2 x^{11} - 14 x^{10} + 6 x^{9} + 5 x^{8} - 12 x^{7} + 8 x^{6} + 4 x^{5} - 4 x^{4} + 8 x^{3} + 4$ |
$20$ |
[0,10] |
$2^{32}\cdot 17^{12}$ |
$2$ |
$16.5927108803$ |
$22.238309660442344$ |
|
|
? |
$C_2\times A_5$ (as 20T31) |
trivial |
$4$ |
$9$ |
$30574.1646172$ |
| 20.4.250...000.1 |
$x^{20} - 5 x^{18} - 10 x^{17} + 5 x^{16} + 50 x^{15} + 55 x^{14} - 70 x^{13} - 180 x^{12} - 90 x^{11} + 88 x^{10} + 250 x^{9} + 290 x^{8} + 60 x^{7} - 195 x^{6} - 100 x^{5} + 30 x^{4} + 20 x^{3} + 15 x^{2} - 10 x + 1$ |
$20$ |
[4,8] |
$2^{24}\cdot 5^{26}$ |
$2$ |
$18.6164556664$ |
$22.91954538992328$ |
|
|
? |
$C_2\times A_5$ (as 20T31) |
trivial |
$2$ |
$11$ |
$94707.1867115$ |
| 20.4.721...184.1 |
$x^{20} - 4 x^{19} - x^{18} + 16 x^{17} - 16 x^{15} - 34 x^{14} + 2 x^{13} + 52 x^{12} + 60 x^{11} - 16 x^{10} - 54 x^{9} - 60 x^{8} - 10 x^{7} + 41 x^{6} + 4 x^{5} + 7 x^{4} + 10 x^{3} - 16 x^{2} + 2$ |
$20$ |
[4,8] |
$2^{24}\cdot 73^{10}$ |
$2$ |
$19.6289660947$ |
$24.166091947189145$ |
|
|
? |
$C_2\times A_5$ (as 20T31) |
trivial |
$2$ |
$11$ |
$363553.530459$ |
| 20.0.333...401.1 |
$x^{20} + 3 x^{18} - 19 x^{17} + 21 x^{16} - 159 x^{15} - 7 x^{14} + 354 x^{13} + 1233 x^{12} + 655 x^{11} - 2385 x^{10} + 2997 x^{9} + 15528 x^{8} + 15281 x^{7} - 4769 x^{6} - 14351 x^{5} - 1363 x^{4} + 4718 x^{3} + 3265 x^{2} - 9 x + 77$ |
$20$ |
[0,10] |
$19^{10}\cdot 293^{8}$ |
$2$ |
$42.27891647$ |
$74.61233142048303$ |
✓ |
|
? |
$C_2\times A_5$ (as 20T31) |
$[14]$ |
$2$ |
$9$ |
$7783721.02563$ |
| 20.0.164...016.1 |
$x^{20} + 32 x^{18} + 422 x^{16} + 2990 x^{14} + 12409 x^{12} + 30722 x^{10} + 43977 x^{8} + 33208 x^{6} + 10956 x^{4} + 1216 x^{2} + 4$ |
$20$ |
[0,10] |
$2^{32}\cdot 887^{8}$ |
$2$ |
$45.7949343742$ |
$100.17614206286586$ |
✓ |
|
? |
$C_2\times A_5$ (as 20T31) |
$[2, 4, 4]$ |
$4$ |
$9$ |
$18267764.1868$ |
| 20.20.589...249.1 |
$x^{20} - 10 x^{19} + 5 x^{18} + 240 x^{17} - 634 x^{16} - 1660 x^{15} + 7586 x^{14} + 1448 x^{13} - 34555 x^{12} + 17062 x^{11} + 80377 x^{10} - 61496 x^{9} - 107173 x^{8} + 88980 x^{7} + 85210 x^{6} - 61692 x^{5} - 38499 x^{4} + 18788 x^{3} + 7682 x^{2} - 1660 x - 101$ |
$20$ |
[20,0] |
$17^{10}\cdot 643^{8}$ |
$2$ |
$54.7657260763$ |
$104.55142275454696$ |
|
|
? |
$C_2\times A_5$ (as 20T31) |
trivial |
$2$ |
$19$ |
$94964848909.5$ |
| 20.20.791...209.1 |
$x^{20} - 45 x^{18} - 12 x^{17} + 851 x^{16} + 407 x^{15} - 8787 x^{14} - 5526 x^{13} + 54107 x^{12} + 38628 x^{11} - 204919 x^{10} - 149409 x^{9} + 477144 x^{8} + 320340 x^{7} - 658303 x^{6} - 352394 x^{5} + 484524 x^{4} + 150931 x^{3} - 142212 x^{2} + 2654 x + 3877$ |
$20$ |
[20,0] |
$19^{8}\cdot 293^{10}$ |
$2$ |
$55.5821383072$ |
$74.61233142048303$ |
|
|
? |
$C_2\times A_5$ (as 20T31) |
trivial |
$2$ |
$19$ |
$96962157521.7$ |
