| 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 |
| 20.0.320...000.1 |
$x^{20} - 10 x^{18} + 55 x^{16} - 200 x^{14} + 485 x^{12} - 798 x^{10} + 865 x^{8} - 420 x^{6} + 35 x^{4} + 50 x^{2} + 5$ |
$20$ |
[0,10] |
$2^{30}\cdot 5^{25}$ |
$2$ |
$21.1474252688$ |
$22.91954538992328$ |
|
|
|
$D_{20}$ (as 20T10) |
trivial |
$4$ |
$9$ |
$665063.298986$ |
| 20.2.400...000.1 |
$x^{20} - 5 x^{18} + 15 x^{14} - 120 x^{12} + 371 x^{10} - 505 x^{8} + 420 x^{6} - 140 x^{4} - 80 x^{2} - 16$ |
$20$ |
[2,9] |
$-\,2^{28}\cdot 5^{26}$ |
$2$ |
$21.3846919998$ |
$22.91954538992328$ |
|
|
|
$D_{20}$ (as 20T10) |
trivial |
$2$ |
$10$ |
$320036.323885$ |
| 20.2.351...875.1 |
$x^{20} - 5 x^{18} + 15 x^{16} - 18 x^{15} + 70 x^{14} + 360 x^{13} + 205 x^{12} - 225 x^{11} - 312 x^{10} - 630 x^{9} - 260 x^{8} + 450 x^{7} + 550 x^{6} + 342 x^{5} + 90 x^{4} - 180 x^{3} - 170 x^{2} - 45 x + 1$ |
$20$ |
[2,9] |
$-\,5^{26}\cdot 11^{9}$ |
$2$ |
$23.8389824525$ |
$26.875549226221146$ |
|
|
|
$D_{20}$ (as 20T10) |
trivial |
$2$ |
$10$ |
$1089848.04881$ |
| 20.0.772...125.1 |
$x^{20} - 5 x^{17} + 25 x^{16} - 79 x^{15} + 120 x^{14} - 130 x^{13} + 160 x^{12} + 45 x^{11} - 39 x^{10} - 315 x^{9} + 810 x^{8} - 1330 x^{7} + 1810 x^{6} - 1714 x^{5} + 1445 x^{4} - 1055 x^{3} + 550 x^{2} - 255 x + 81$ |
$20$ |
[0,10] |
$5^{25}\cdot 11^{10}$ |
$2$ |
$24.7975541901$ |
$26.875549226221146$ |
|
|
|
$D_{20}$ (as 20T10) |
trivial |
$2$ |
$9$ |
$2264798.97636$ |
| 20.0.798...253.1 |
$x^{20} - 4 x^{19} + 19 x^{18} - 57 x^{17} + 133 x^{16} - 190 x^{15} + 171 x^{14} + 532 x^{13} - 1330 x^{12} + 3648 x^{11} - 3325 x^{10} + 2812 x^{9} + 3534 x^{8} - 9880 x^{7} + 14212 x^{6} - 15447 x^{5} + 10906 x^{4} - 6574 x^{3} + 4579 x^{2} - 840 x + 225$ |
$20$ |
[0,10] |
$7^{9}\cdot 19^{19}$ |
$2$ |
$39.36498034295749$ |
$43.38753139294459$ |
|
|
|
$D_{20}$ (as 20T10) |
trivial |
$2$ |
$9$ |
$259320806.1491311$ |
| 20.2.558...771.1 |
$x^{20} - 8 x^{19} + 38 x^{18} - 133 x^{17} + 323 x^{16} - 570 x^{15} + 608 x^{14} + 608 x^{13} - 2280 x^{12} + 5662 x^{11} - 2527 x^{10} + 4731 x^{9} + 8265 x^{8} - 6935 x^{7} + 27265 x^{6} - 20539 x^{5} + 29469 x^{4} - 20178 x^{3} + 16226 x^{2} - 6696 x + 729$ |
$20$ |
[2,9] |
$-\,7^{10}\cdot 19^{19}$ |
$2$ |
$43.3875313929$ |
$43.38753139294459$ |
|
|
|
$D_{20}$ (as 20T10) |
trivial |
$2$ |
$10$ |
$1336347065.64$ |
| 20.20.132...213.1 |
$x^{20} - 6 x^{19} - 26 x^{18} + 210 x^{17} + 139 x^{16} - 2755 x^{15} + 1437 x^{14} + 17203 x^{13} - 18778 x^{12} - 55009 x^{11} + 79884 x^{10} + 92609 x^{9} - 165018 x^{8} - 78936 x^{7} + 175998 x^{6} + 29276 x^{5} - 90960 x^{4} - 3681 x^{3} + 17377 x^{2} + 1089 x - 103$ |
$20$ |
[20,0] |
$13^{10}\cdot 277^{9}$ |
$2$ |
$45.298891252$ |
$60.00833275470999$ |
|
|
? |
$D_{20}$ (as 20T10) |
trivial |
$2$ |
$19$ |
$12870125339.9$ |
| 20.0.818...125.1 |
$x^{20} - 3 x^{19} + 5 x^{18} + 29 x^{17} + 2 x^{16} - 447 x^{15} + 1875 x^{14} - 2988 x^{13} - 797 x^{12} + 13317 x^{11} - 13069 x^{10} - 45010 x^{9} + 158294 x^{8} - 203394 x^{7} + 94740 x^{6} + 88164 x^{5} - 87665 x^{4} + 23262 x^{3} + 85694 x^{2} - 52120 x + 15161$ |
$20$ |
[0,10] |
$5^{15}\cdot 401^{9}$ |
$2$ |
$49.618367447$ |
$66.95757085563274$ |
✓ |
|
|
$D_{20}$ (as 20T10) |
$[404]$ |
$2$ |
$9$ |
$2526424.45141$ |
| 20.20.282...077.1 |
$x^{20} - 4 x^{19} - 42 x^{18} + 167 x^{17} + 590 x^{16} - 2576 x^{15} - 2936 x^{14} + 18115 x^{13} - 262 x^{12} - 56895 x^{11} + 34045 x^{10} + 71526 x^{9} - 65218 x^{8} - 32272 x^{7} + 41379 x^{6} + 787 x^{5} - 8208 x^{4} + 1108 x^{3} + 440 x^{2} - 113 x + 7$ |
$20$ |
[20,0] |
$13^{9}\cdot 277^{10}$ |
$2$ |
$52.7854700266$ |
$60.00833275470999$ |
|
|
? |
$D_{20}$ (as 20T10) |
trivial |
$2$ |
$19$ |
$84757731927.8$ |
| 20.0.328...125.1 |
$x^{20} - 4 x^{19} + 42 x^{18} - 108 x^{17} + 585 x^{16} - 1163 x^{15} + 4645 x^{14} - 10617 x^{13} + 31833 x^{12} - 75285 x^{11} + 168816 x^{10} - 330321 x^{9} + 666734 x^{8} - 1317875 x^{7} + 2500617 x^{6} - 4132047 x^{5} + 5546802 x^{4} - 5570593 x^{3} + 3798320 x^{2} - 1539672 x + 282861$ |
$20$ |
[0,10] |
$5^{15}\cdot 401^{10}$ |
$2$ |
$66.9575708556$ |
$66.95757085563274$ |
✓ |
|
|
$D_{20}$ (as 20T10) |
$[2, 808]$ |
$2$ |
$9$ |
$31495162.1453$ |
