| 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 |
| 20.2.119...576.1 |
$x^{20} - 7 x^{18} + 28 x^{16} - 70 x^{14} + 112 x^{12} - 118 x^{10} + 80 x^{8} - 29 x^{6} + 2 x^{4} + 3 x^{2} - 1$ |
$20$ |
[2,9] |
$-\,2^{10}\cdot 7^{8}\cdot 17^{10}$ |
$3$ |
$12.6992675926$ |
$21.817424229271428$ |
|
|
? |
$D_4\times D_5$ (as 20T21) |
trivial |
$2$ |
$10$ |
$611.93739859$ |
| 20.0.645...312.1 |
$x^{20} - 2 x^{19} + 8 x^{18} - 16 x^{17} + 29 x^{16} - 63 x^{15} + 88 x^{14} - 103 x^{13} + 160 x^{12} - 175 x^{11} + 125 x^{10} - 136 x^{9} + 143 x^{8} - 77 x^{7} + 58 x^{6} - 77 x^{5} + 48 x^{4} - 12 x^{3} + 5 x^{2} - 4 x + 1$ |
$20$ |
[0,10] |
$2^{15}\cdot 7^{10}\cdot 17^{8}$ |
$3$ |
$13.8197785947$ |
$30.854497241083024$ |
|
|
? |
$D_4\times D_5$ (as 20T21) |
trivial |
$2$ |
$9$ |
$1171.26308565$ |
| 20.0.380...432.1 |
$x^{20} - 4 x^{19} + 8 x^{18} - 16 x^{17} + 35 x^{16} - 58 x^{15} + 98 x^{14} - 194 x^{13} + 339 x^{12} - 506 x^{11} + 672 x^{10} - 748 x^{9} + 650 x^{8} - 454 x^{7} + 336 x^{6} - 318 x^{5} + 275 x^{4} - 164 x^{3} + 60 x^{2} - 12 x + 1$ |
$20$ |
[0,10] |
$2^{15}\cdot 7^{8}\cdot 17^{10}$ |
$3$ |
$15.1020593765$ |
$30.854497241083024$ |
|
|
? |
$D_4\times D_5$ (as 20T21) |
trivial |
$2$ |
$9$ |
$2862.69597498$ |
| 20.0.522...677.1 |
$x^{20} - 2 x^{19} + 2 x^{18} - x^{17} - 2 x^{15} - 9 x^{14} + 3 x^{12} + x^{11} + 22 x^{9} + 45 x^{8} + 41 x^{7} + 29 x^{6} + 18 x^{5} + 7 x^{4} - 2 x^{3} - 3 x^{2} + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 13^{5}\cdot 47^{8}$ |
$3$ |
$15.342128242$ |
$42.81354925721529$ |
|
|
? |
$D_4\times D_5$ (as 20T21) |
trivial |
$6$ |
$9$ |
$8452.6678373$ |
| 20.2.583...224.1 |
$x^{20} - 6 x^{19} + 17 x^{18} - 26 x^{17} + 3 x^{16} + 99 x^{15} - 278 x^{14} + 401 x^{13} - 222 x^{12} - 386 x^{11} + 1130 x^{10} - 1293 x^{9} + 290 x^{8} + 1647 x^{7} - 3426 x^{6} + 3993 x^{5} - 3230 x^{4} + 1866 x^{3} - 736 x^{2} + 176 x - 19$ |
$20$ |
[2,9] |
$-\,2^{10}\cdot 7^{10}\cdot 17^{10}$ |
$3$ |
$15.4272486205$ |
$21.817424229271428$ |
|
|
? |
$D_4\times D_5$ (as 20T21) |
trivial |
$2$ |
$10$ |
$5497.47001539$ |
| 20.4.186...168.1 |
$x^{20} - 7 x^{19} + 26 x^{18} - 74 x^{17} + 178 x^{16} - 348 x^{15} + 530 x^{14} - 614 x^{13} + 478 x^{12} + 34 x^{11} - 884 x^{10} + 1523 x^{9} - 1585 x^{8} + 1413 x^{7} - 1104 x^{6} + 634 x^{5} - 304 x^{4} + 151 x^{3} - 52 x^{2} + 4 x + 1$ |
$20$ |
[4,8] |
$2^{15}\cdot 7^{10}\cdot 17^{10}$ |
$3$ |
$18.3461938245$ |
$30.854497241083024$ |
|
|
? |
$D_4\times D_5$ (as 20T21) |
trivial |
$2$ |
$11$ |
$49924.022929$ |
| 20.4.389...368.1 |
$x^{20} + 8 x^{18} + 24 x^{16} + x^{14} - 170 x^{12} - 403 x^{10} - 340 x^{8} + 4 x^{6} + 192 x^{4} + 128 x^{2} + 32$ |
$20$ |
[4,8] |
$2^{25}\cdot 7^{8}\cdot 17^{10}$ |
$3$ |
$21.35753719$ |
$43.634848458542855$ |
|
|
? |
$D_4\times D_5$ (as 20T21) |
trivial |
$2$ |
$11$ |
$219934.649034$ |
| 20.0.734...928.1 |
$x^{20} - 4 x^{19} + 14 x^{18} - 14 x^{17} + 8 x^{16} + 12 x^{15} + 27 x^{14} - 42 x^{13} + 135 x^{12} + 10 x^{11} + 220 x^{10} + 160 x^{9} + 322 x^{8} + 668 x^{7} + 816 x^{6} + 644 x^{5} + 332 x^{4} + 128 x^{3} + 35 x^{2} + 6 x + 1$ |
$20$ |
[0,10] |
$2^{30}\cdot 7^{8}\cdot 17^{9}$ |
$3$ |
$22.0437879216$ |
$30.854497241083024$ |
|
|
? |
$D_4\times D_5$ (as 20T21) |
trivial |
$2$ |
$9$ |
$311018.518626$ |
| 20.0.146...757.1 |
$x^{20} - x^{19} - 16 x^{18} + 15 x^{17} + 140 x^{16} - 106 x^{15} - 609 x^{14} + 388 x^{13} + 1656 x^{12} - 814 x^{11} - 2628 x^{10} + 827 x^{9} + 2615 x^{8} - 246 x^{7} - 1201 x^{6} + 121 x^{5} + 310 x^{4} - 56 x^{3} - 21 x^{2} + 3 x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 13^{5}\cdot 401^{8}$ |
$3$ |
$36.1663111613$ |
$125.05598746161657$ |
|
|
|
$D_4\times D_5$ (as 20T21) |
$[2, 2]$ |
$6$ |
$9$ |
$19881261.2295$ |
| 20.10.163...375.1 |
$x^{20} - 9 x^{19} + 24 x^{18} + 54 x^{17} - 631 x^{16} + 2452 x^{15} - 5691 x^{14} + 8318 x^{13} - 6817 x^{12} - 504 x^{11} + 11216 x^{10} - 22964 x^{9} + 34562 x^{8} - 23706 x^{7} - 24944 x^{6} + 53552 x^{5} - 20774 x^{4} - 13526 x^{3} + 11231 x^{2} - 1890 x + 45$ |
$20$ |
[10,5] |
$-\,3^{8}\cdot 5^{10}\cdot 239^{9}$ |
$3$ |
$40.7955281017$ |
$59.87486951969081$ |
|
|
|
$D_4\times D_5$ (as 20T21) |
trivial |
$2$ |
$14$ |
$1393819795.17$ |
| 20.10.105...875.1 |
$x^{20} - x^{19} - 5 x^{18} + 12 x^{17} + 38 x^{16} - 63 x^{15} - 360 x^{14} + 471 x^{13} + 577 x^{12} - 1603 x^{11} - 191 x^{10} + 1926 x^{9} + 566 x^{8} - 1116 x^{7} - 765 x^{6} + 582 x^{5} + 79 x^{4} - 88 x^{3} + 16 x^{2} + 6 x - 1$ |
$20$ |
[10,5] |
$-\,5^{10}\cdot 11^{5}\cdot 401^{8}$ |
$3$ |
$44.7807045816$ |
$148.509258970611$ |
|
|
|
$D_4\times D_5$ (as 20T21) |
trivial |
$2$ |
$14$ |
$3242123709.9$ |
| 20.0.224...000.1 |
$x^{20} - 2 x^{19} - 20 x^{18} + 40 x^{17} + 247 x^{16} - 412 x^{15} - 1048 x^{14} + 1552 x^{13} + 3039 x^{12} - 2670 x^{11} - 4608 x^{10} + 2708 x^{9} + 4444 x^{8} - 1252 x^{7} - 1796 x^{6} + 478 x^{5} + 405 x^{4} - 136 x^{3} - 16 x^{2} + 6 x + 1$ |
$20$ |
[0,10] |
$2^{30}\cdot 5^{5}\cdot 401^{8}$ |
$3$ |
$46.5098826384$ |
$126.64912159190051$ |
|
|
? |
$D_4\times D_5$ (as 20T21) |
$[5]$ |
$4$ |
$9$ |
$85215123.6135$ |
| 20.20.133...125.1 |
$x^{20} - x^{19} - 38 x^{18} + 29 x^{17} + 484 x^{16} - 284 x^{15} - 2761 x^{14} + 1136 x^{13} + 7908 x^{12} - 2304 x^{11} - 11892 x^{10} + 2701 x^{9} + 9451 x^{8} - 1736 x^{7} - 3821 x^{6} + 509 x^{5} + 732 x^{4} - 62 x^{3} - 55 x^{2} + 3 x + 1$ |
$20$ |
[20,0] |
$5^{10}\cdot 29^{5}\cdot 401^{8}$ |
$3$ |
$57.0613773795$ |
$241.13274352522097$ |
|
|
? |
$D_4\times D_5$ (as 20T21) |
trivial |
$2$ |
$19$ |
$115786840574$ |
| 20.0.728...832.1 |
$x^{20} - 9 x^{19} + 61 x^{18} - 221 x^{17} + 822 x^{16} - 1892 x^{15} + 5219 x^{14} - 8472 x^{13} + 27597 x^{12} - 48534 x^{11} + 163342 x^{10} - 238292 x^{9} + 523033 x^{8} - 258674 x^{7} + 365450 x^{6} + 574249 x^{5} + 872126 x^{4} + 87755 x^{3} + 1041518 x^{2} + 1084745 x + 1823113$ |
$20$ |
[0,10] |
$2^{10}\cdot 3^{10}\cdot 7^{5}\cdot 19^{10}\cdot 43^{8}$ |
$5$ |
$78.1833576978$ |
$261.96946386936014$ |
✓ |
|
? |
$D_4\times D_5$ (as 20T21) |
$[2, 4, 404]$ |
$2$ |
$9$ |
$13701218.918$ |
| 20.0.170...000.1 |
$x^{20} + 55 x^{18} + 1286 x^{16} + 16755 x^{14} + 134201 x^{12} + 688496 x^{10} + 2284561 x^{8} + 4822473 x^{6} + 6162421 x^{4} + 4269541 x^{2} + 1204799$ |
$20$ |
[0,10] |
$2^{20}\cdot 3^{8}\cdot 5^{10}\cdot 239^{9}$ |
$4$ |
$81.5910562035$ |
$169.35170504013237$ |
✓ |
|
? |
$D_4\times D_5$ (as 20T21) |
$[37, 148]$ |
$2$ |
$9$ |
$10123076.9997$ |
| 20.20.170...000.1 |
$x^{20} - 55 x^{18} + 1286 x^{16} - 16755 x^{14} + 134201 x^{12} - 688496 x^{10} + 2284561 x^{8} - 4822473 x^{6} + 6162421 x^{4} - 4269541 x^{2} + 1204799$ |
$20$ |
[20,0] |
$2^{20}\cdot 3^{8}\cdot 5^{10}\cdot 239^{9}$ |
$4$ |
$81.5910562035$ |
$169.35170504013237$ |
|
|
? |
$D_4\times D_5$ (as 20T21) |
trivial |
$2$ |
$19$ |
$6330334603990$ |
