| 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 |
| 20.0.172...632.1 |
$x^{20} - x^{19} + x^{18} - 4 x^{17} - 3 x^{16} + 15 x^{15} + 3 x^{14} - 28 x^{13} + 2 x^{12} + 19 x^{11} + 29 x^{10} - 56 x^{9} + 17 x^{8} - 3 x^{7} + 26 x^{6} - 34 x^{5} + 37 x^{4} - 35 x^{3} + 21 x^{2} - 7 x + 1$ |
$20$ |
[0,10] |
$2^{15}\cdot 47^{10}$ |
$2$ |
$11.5297907554$ |
$19.390719429665317$ |
|
|
? |
$C_5:D_4$ (as 20T11) |
trivial |
$2$ |
$9$ |
$143.606119616$ |
| 20.0.310...368.1 |
$x^{20} + 3 x^{18} - 3 x^{16} - 10 x^{14} + 25 x^{12} - 3 x^{10} + 50 x^{8} - 40 x^{6} - 24 x^{4} + 48 x^{2} + 32$ |
$20$ |
[0,10] |
$2^{15}\cdot 79^{10}$ |
$2$ |
$14.9481016472$ |
$25.13961017995307$ |
|
|
? |
$C_5:D_4$ (as 20T11) |
trivial |
$2$ |
$9$ |
$2246.68851207$ |
| 20.10.110...024.1 |
$x^{20} - 11 x^{18} + 20 x^{16} + 111 x^{14} - 325 x^{12} - 31 x^{10} + 325 x^{8} + 111 x^{6} - 20 x^{4} - 11 x^{2} - 1$ |
$20$ |
[10,5] |
$-\,2^{10}\cdot 401^{10}$ |
$2$ |
$28.319604517$ |
$40.049968789001575$ |
|
|
? |
$C_5:D_4$ (as 20T11) |
trivial |
$2$ |
$14$ |
$10069184.9066$ |
| 20.20.335...125.1 |
$x^{20} - 2 x^{19} - 27 x^{18} + 58 x^{17} + 272 x^{16} - 639 x^{15} - 1245 x^{14} + 3339 x^{13} + 2469 x^{12} - 8464 x^{11} - 1650 x^{10} + 9965 x^{9} + 827 x^{8} - 6081 x^{7} - 914 x^{6} + 1796 x^{5} + 510 x^{4} - 151 x^{3} - 63 x^{2} - x + 1$ |
$20$ |
[20,0] |
$5^{5}\cdot 401^{10}$ |
$2$ |
$29.9443360083$ |
$44.77722635447622$ |
|
|
? |
$C_5:D_4$ (as 20T11) |
trivial |
$2$ |
$19$ |
$151466349.639$ |
| 20.0.352...768.1 |
$x^{20} + 8 x^{18} - 12 x^{17} + 60 x^{16} - 150 x^{15} + 288 x^{14} - 666 x^{13} + 1043 x^{12} - 1854 x^{11} + 3542 x^{10} - 3928 x^{9} + 7725 x^{8} - 8380 x^{7} + 17188 x^{6} - 17644 x^{5} + 8749 x^{4} + 7050 x^{3} - 20666 x^{2} + 3320 x + 7907$ |
$20$ |
[0,10] |
$2^{15}\cdot 401^{10}$ |
$2$ |
$33.6778751857$ |
$56.639209034025185$ |
✓ |
|
? |
$C_5:D_4$ (as 20T11) |
$[7]$ |
$2$ |
$9$ |
$795087.603907$ |
| 20.20.360...432.1 |
$x^{20} - 44 x^{18} + 779 x^{16} - 7195 x^{14} + 37781 x^{12} - 116321 x^{10} + 211202 x^{8} - 221656 x^{6} + 125920 x^{4} - 32976 x^{2} + 2592$ |
$20$ |
[20,0] |
$2^{25}\cdot 401^{10}$ |
$2$ |
$47.6277078395$ |
$80.09993757800315$ |
|
|
? |
$C_5:D_4$ (as 20T11) |
trivial |
$2$ |
$19$ |
$16979295917.9$ |
| 20.10.650...176.1 |
$x^{20} - 33 x^{18} + 180 x^{16} + 2997 x^{14} - 26325 x^{12} - 7533 x^{10} + 236925 x^{8} + 242757 x^{6} - 131220 x^{4} - 216513 x^{2} - 59049$ |
$20$ |
[10,5] |
$-\,2^{10}\cdot 3^{10}\cdot 401^{10}$ |
$3$ |
$49.0509938737$ |
$69.3685807840985$ |
|
|
|
$C_5:D_4$ (as 20T11) |
trivial |
$2$ |
$14$ |
$3848976829.54$ |
| 20.0.177...224.1 |
$x^{20} - x^{19} + 17 x^{18} + 65 x^{17} + 90 x^{16} + 770 x^{15} + 2069 x^{14} + 3588 x^{13} + 16293 x^{12} + 15488 x^{11} + 105429 x^{10} + 223263 x^{9} + 472533 x^{8} + 888791 x^{7} + 682047 x^{6} + 1592904 x^{5} + 10772482 x^{4} + 8858817 x^{3} + 13596529 x^{2} + 5680831 x + 842147$ |
$20$ |
[0,10] |
$2^{10}\cdot 11^{5}\cdot 401^{10}$ |
$3$ |
$51.5745390853$ |
$132.83071933856263$ |
✓ |
|
? |
$C_5:D_4$ (as 20T11) |
$[382]$ |
$2$ |
$9$ |
$795087.603907$ |
