| 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 |
| 20.0.117...792.1 |
$x^{20} - 9 x^{19} + 45 x^{18} - 163 x^{17} + 464 x^{16} - 1081 x^{15} + 2121 x^{14} - 3545 x^{13} + 5100 x^{12} - 6329 x^{11} + 6805 x^{10} - 6329 x^{9} + 5100 x^{8} - 3545 x^{7} + 2121 x^{6} - 1081 x^{5} + 464 x^{4} - 163 x^{3} + 45 x^{2} - 9 x + 1$ |
$20$ |
[0,10] |
$2^{16}\cdot 3^{10}\cdot 13^{13}$ |
$3$ |
$15.9752551367$ |
$20.646295463608727$ |
|
|
? |
$D_{10}:C_4$ (as 20T19) |
trivial |
$6$ |
$9$ |
$19012.2439561$ |
| 20.0.520...552.1 |
$x^{20} - 10 x^{19} + 48 x^{18} - 142 x^{17} + 289 x^{16} - 440 x^{15} + 548 x^{14} - 588 x^{13} + 510 x^{12} - 316 x^{11} + 176 x^{10} - 204 x^{9} + 246 x^{8} - 168 x^{7} + 36 x^{6} + 36 x^{5} - 3 x^{4} - 18 x^{3} + 2 x + 1$ |
$20$ |
[0,10] |
$2^{34}\cdot 13^{13}$ |
$2$ |
$17.2113196975$ |
$22.243775686467696$ |
|
|
? |
$D_{10}:C_4$ (as 20T19) |
trivial |
$4$ |
$9$ |
$49980.9250389$ |
| 20.0.819...000.1 |
$x^{20} - 6 x^{15} + 16 x^{10} + 12 x^{5} + 2$ |
$20$ |
[0,10] |
$2^{34}\cdot 5^{21}$ |
$2$ |
$17.60635673584025$ |
$20.6807601406833$ |
|
|
? |
$D_{10}:C_4$ (as 20T19) |
trivial |
$4$ |
$9$ |
$66422.84426665277$ |
| 20.4.200...125.1 |
$x^{20} - 12 x^{15} + 31 x^{10} + 30 x^{5} - 1$ |
$20$ |
[4,8] |
$5^{21}\cdot 29^{10}$ |
$2$ |
$29.1821646514$ |
$34.27792339979557$ |
|
|
|
$D_{10}:C_4$ (as 20T19) |
trivial |
$2$ |
$11$ |
$10784558.4809$ |
| 20.0.501...125.1 |
$x^{20} - 10 x^{18} + 80 x^{16} - 24 x^{15} - 280 x^{14} + 105 x^{13} + 870 x^{12} + 30 x^{11} - 2024 x^{10} - 165 x^{9} + 4525 x^{8} + 1095 x^{7} - 5325 x^{6} - 399 x^{5} + 5925 x^{4} + 2760 x^{3} + 115 x^{2} + 1395 x + 1646$ |
$20$ |
[0,10] |
$5^{23}\cdot 29^{10}$ |
$2$ |
$34.2779233998$ |
$34.27792339979557$ |
|
|
|
$D_{10}:C_4$ (as 20T19) |
$[8]$ |
$2$ |
$9$ |
$24284084.6035$ |
| 20.0.279...752.1 |
$x^{20} - 12 x^{18} + 48 x^{16} - 246 x^{14} + 1830 x^{12} - 5960 x^{10} + 8229 x^{8} - 4878 x^{6} + 3429 x^{4} - 720 x^{2} + 212$ |
$20$ |
[0,10] |
$2^{30}\cdot 53^{13}$ |
$2$ |
$37.3528985871$ |
$55.55867702757995$ |
|
|
? |
$D_{10}:C_4$ (as 20T19) |
$[2]$ |
$4$ |
$9$ |
$75297483.0313$ |
| 20.0.472...000.1 |
$x^{20} + 60 x^{16} - 400 x^{14} - 140 x^{13} + 1100 x^{12} + 960 x^{11} - 3960 x^{10} - 1800 x^{9} + 13600 x^{8} - 800 x^{7} - 18720 x^{6} + 2024 x^{5} + 9200 x^{4} - 160 x^{3} + 80 x + 8$ |
$20$ |
[0,10] |
$2^{34}\cdot 5^{21}\cdot 7^{8}$ |
$3$ |
$38.3449974467$ |
$54.71614825602517$ |
|
|
? |
$D_{10}:C_4$ (as 20T19) |
$[5]$ |
$4$ |
$9$ |
$32474897.1206$ |
| 20.0.118...000.1 |
$x^{20} + 160 x^{16} + 2080 x^{12} + 3520 x^{8} + 1920 x^{4} + 320$ |
$20$ |
[0,10] |
$2^{34}\cdot 5^{23}\cdot 7^{8}$ |
$3$ |
$45.04076037358156$ |
$54.71614825602517$ |
|
|
? |
$D_{10}:C_4$ (as 20T19) |
$[20]$ |
$2$ |
$9$ |
$59442903.78454278$ |
| 20.4.131...000.1 |
$x^{20} - 352 x^{15} - 6600 x^{10} - 1408 x^{5} + 16$ |
$20$ |
[4,8] |
$2^{16}\cdot 5^{21}\cdot 29^{10}$ |
$3$ |
$50.8090997509$ |
$59.68133104862686$ |
|
|
? |
$D_{10}:C_4$ (as 20T19) |
trivial |
$2$ |
$11$ |
$2214161388.52$ |
| 20.0.781...000.2 |
$x^{20} - 60 x^{15} + 1600 x^{10} + 12000 x^{5} + 20000$ |
$20$ |
[0,10] |
$2^{30}\cdot 5^{37}$ |
$2$ |
$55.54430046008365$ |
$65.24338750098681$ |
|
|
? |
$D_{10}:C_4$ (as 20T19) |
$[2]$ |
$4$ |
$9$ |
$3648614961.5519567$ |
| 20.4.783...125.5 |
$x^{20} + 5 x^{18} - 70 x^{16} - 8 x^{15} - 75 x^{14} - 75 x^{13} + 875 x^{12} - 835 x^{11} - 549 x^{10} - 1325 x^{9} - 4615 x^{8} + 3575 x^{7} - 11725 x^{6} + 9510 x^{5} - 15325 x^{4} + 4740 x^{3} - 7475 x^{2} + 4975 x - 371$ |
$20$ |
[4,8] |
$5^{29}\cdot 29^{10}$ |
$2$ |
$55.552742678807896$ |
$65.25330389102201$ |
|
|
|
$D_{10}:C_4$ (as 20T19) |
$[2]$ |
$2$ |
$11$ |
$3578043519.9864955$ |
| 20.0.210...000.1 |
$x^{20} + 262 x^{10} + 3125$ |
$20$ |
[0,10] |
$2^{20}\cdot 5^{21}\cdot 29^{10}$ |
$3$ |
$58.3643293027$ |
$68.55584679959114$ |
|
|
? |
$D_{10}:C_4$ (as 20T19) |
$[2]$ |
$2$ |
$9$ |
$3072223202.83$ |
| 20.0.373...048.1 |
$x^{20} - 6 x^{19} - 9 x^{18} + 108 x^{17} + 26 x^{16} - 1220 x^{15} + 1416 x^{14} + 5050 x^{13} - 8760 x^{12} - 18634 x^{11} + 60110 x^{10} - 34470 x^{9} - 71994 x^{8} + 135816 x^{7} + 8409 x^{6} - 349100 x^{5} + 806930 x^{4} - 839814 x^{3} + 332021 x^{2} - 294146 x + 971137$ |
$20$ |
[0,10] |
$2^{30}\cdot 17^{13}\cdot 37^{8}$ |
$3$ |
$75.616658507$ |
$144.0398122329659$ |
✓ |
|
? |
$D_{10}:C_4$ (as 20T19) |
$[4, 20]$ |
$2$ |
$9$ |
$431927236.362$ |
| 20.0.800...000.1 |
$x^{20} - 380 x^{10} + 78125$ |
$20$ |
[0,10] |
$2^{40}\cdot 5^{37}$ |
$2$ |
$78.55150302317644$ |
$92.26808345905883$ |
|
|
? |
$D_{10}:C_4$ (as 20T19) |
$[2]$ |
$4$ |
$9$ |
$161034127857.1763$ |
| 20.0.200...000.2 |
$x^{20} + 5$ |
$20$ |
[0,10] |
$2^{40}\cdot 5^{39}$ |
$2$ |
$92.2680834591$ |
$92.26808345905883$ |
|
|
✓ |
$D_{10}:C_4$ (as 20T19) |
$[2, 4]$ |
$2$ |
$9$ |
$196156005437$ |
| 20.20.343...072.1 |
$x^{20} - 10 x^{19} - 16 x^{18} + 413 x^{17} - 424 x^{16} - 6424 x^{15} + 12626 x^{14} + 46828 x^{13} - 123202 x^{12} - 154754 x^{11} + 567584 x^{10} + 126754 x^{9} - 1261035 x^{8} + 390998 x^{7} + 1205290 x^{6} - 745555 x^{5} - 347964 x^{4} + 334262 x^{3} - 34480 x^{2} - 11276 x - 152$ |
$20$ |
[20,0] |
$2^{16}\cdot 17^{10}\cdot 53^{13}$ |
$3$ |
$94.804242492$ |
$161.9799865445327$ |
|
|
|
$D_{10}:C_4$ (as 20T19) |
trivial |
$2$ |
$19$ |
$301584210044000$ |
| 20.20.382...152.1 |
$x^{20} - 4 x^{19} - 56 x^{18} + 192 x^{17} + 1265 x^{16} - 3644 x^{15} - 14718 x^{14} + 35964 x^{13} + 94810 x^{12} - 202968 x^{11} - 339336 x^{10} + 669932 x^{9} + 629427 x^{8} - 1245448 x^{7} - 463526 x^{6} + 1143416 x^{5} - 56571 x^{4} - 348424 x^{3} + 106752 x^{2} - 2960 x - 263$ |
$20$ |
[20,0] |
$2^{40}\cdot 17^{13}\cdot 37^{8}$ |
$3$ |
$106.938104002$ |
$203.7030559815344$ |
|
|
? |
$D_{10}:C_4$ (as 20T19) |
trivial |
$2$ |
$19$ |
$110095846393000$ |
| 20.0.550...152.1 |
$x^{20} - 4 x^{19} + 72 x^{18} - 128 x^{17} + 1787 x^{16} - 638 x^{15} + 25166 x^{14} + 13740 x^{13} + 237865 x^{12} + 356230 x^{11} + 1013178 x^{10} + 4710184 x^{9} + 487944 x^{8} + 22409014 x^{7} + 13861755 x^{6} + 11751366 x^{5} + 120949292 x^{4} - 96683974 x^{3} + 226406567 x^{2} - 104041302 x + 87491689$ |
$20$ |
[0,10] |
$2^{20}\cdot 17^{10}\cdot 53^{13}$ |
$3$ |
$108.901477397$ |
$161.9799865445327$ |
✓ |
|
? |
$D_{10}:C_4$ (as 20T19) |
$[2, 2, 2, 110]$ |
$2$ |
$9$ |
$4097659676.87$ |
| 20.20.757...000.1 |
$x^{20} - 5 x^{19} - 55 x^{18} + 265 x^{17} + 1180 x^{16} - 5515 x^{15} - 12525 x^{14} + 58945 x^{13} + 68500 x^{12} - 351335 x^{11} - 172391 x^{10} + 1179155 x^{9} + 59480 x^{8} - 2123335 x^{7} + 516825 x^{6} + 1796557 x^{5} - 777570 x^{4} - 492375 x^{3} + 296525 x^{2} - 46175 x + 2179$ |
$20$ |
[20,0] |
$2^{16}\cdot 5^{21}\cdot 7^{8}\cdot 29^{10}$ |
$4$ |
$110.6574647696177$ |
$157.90195986798437$ |
|
|
? |
$D_{10}:C_4$ (as 20T19) |
trivial |
$2$ |
$19$ |
$194531761644245.97$ |
| 20.0.717...128.1 |
$x^{20} - 10 x^{19} + 44 x^{18} - 95 x^{17} + 207 x^{16} - 1248 x^{15} + 5178 x^{14} - 8264 x^{13} - 4648 x^{12} + 14090 x^{11} + 57242 x^{10} - 544 x^{9} - 656527 x^{8} - 150134 x^{7} + 8910324 x^{6} - 20172635 x^{5} + 3027826 x^{4} + 33580578 x^{3} - 1780784 x^{2} - 78898617 x + 68569153$ |
$20$ |
[0,10] |
$2^{16}\cdot 29^{10}\cdot 53^{13}$ |
$3$ |
$123.8232819122793$ |
$211.56113915201115$ |
✓ |
|
? |
$D_{10}:C_4$ (as 20T19) |
$[2, 410]$ |
$2$ |
$9$ |
$7598989323.24136$ |
