| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
| 20.4.230...189.1 |
$x^{20} - 2 x^{19} + 5 x^{18} - 10 x^{17} + 17 x^{16} - 34 x^{15} + 32 x^{14} - 30 x^{13} + 16 x^{12} - 9 x^{11} - 27 x^{10} + 89 x^{9} - 18 x^{8} - 74 x^{7} + 53 x^{6} + 24 x^{5} - 7 x^{4} + 19 x^{3} + 4 x^{2} - 7 x - 1$ |
$20$ |
[4,8] |
$29^{3}\cdot 79^{10}$ |
$2$ |
$14.7289994289$ |
$331.1454688754594$ |
|
|
? |
$C_4\wr D_5$ (as 20T418) |
trivial |
trivial |
$2$ |
$11$ |
$4134.35833823$ |
| 20.0.378...793.1 |
$x^{20} - x^{19} - 4 x^{18} + 4 x^{17} + 3 x^{16} - 6 x^{15} + 13 x^{14} + 36 x^{13} - 4 x^{12} - 82 x^{11} - 75 x^{10} + 71 x^{9} + 199 x^{8} + 28 x^{7} - 72 x^{6} - 113 x^{5} - 58 x^{4} + 96 x^{3} + 87 x^{2} + 57 x + 31$ |
$20$ |
[0,10] |
$47^{10}\cdot 193^{3}$ |
$2$ |
$15.0967173959$ |
$929.4828376842746$ |
|
|
? |
$C_4\wr D_5$ (as 20T418) |
trivial |
trivial |
$2$ |
$9$ |
$2098.65426229$ |
| 20.0.387...904.1 |
$x^{20} + 3 x^{18} - 4 x^{16} - 7 x^{14} + 32 x^{12} + 27 x^{10} - 100 x^{8} - 85 x^{6} + 95 x^{4} + 116 x^{2} + 29$ |
$20$ |
[0,10] |
$2^{20}\cdot 29^{3}\cdot 79^{8}$ |
$3$ |
$19.0300764006$ |
|
|
|
? |
$C_4\wr D_5$ (as 20T418) |
trivial |
trivial |
$2$ |
$9$ |
$23817.0125381$ |
| 20.4.387...904.1 |
$x^{20} - 7 x^{18} + 30 x^{16} - 76 x^{14} + 136 x^{12} - 188 x^{10} + 155 x^{8} - 158 x^{6} + 124 x^{4} - 87 x^{2} + 29$ |
$20$ |
[4,8] |
$2^{20}\cdot 29^{3}\cdot 79^{8}$ |
$3$ |
$19.0300764006$ |
|
|
|
? |
$C_4\wr D_5$ (as 20T418) |
trivial |
trivial |
$2$ |
$11$ |
$54780.1173245$ |
| 20.0.659...157.1 |
$x^{20} - 3 x^{19} + 43 x^{18} - 102 x^{17} + 794 x^{16} - 2060 x^{15} + 9343 x^{14} - 20615 x^{13} + 61749 x^{12} - 111807 x^{11} + 246498 x^{10} - 355752 x^{9} + 559168 x^{8} - 595790 x^{7} + 687028 x^{6} - 502104 x^{5} + 494386 x^{4} - 210983 x^{3} + 231277 x^{2} - 40869 x + 57087$ |
$20$ |
[0,10] |
$397^{5}\cdot 401^{8}$ |
$2$ |
$49.0857437391$ |
$1781.0047034117376$ |
✓ |
|
|
$C_4\wr D_5$ (as 20T418) |
$[466]$ |
$[466]$ |
$2$ |
$9$ |
$735584.085831$ |
| 20.8.659...157.1 |
$x^{20} - 2 x^{19} - 3 x^{18} + 33 x^{17} - 130 x^{16} + 437 x^{15} - 1067 x^{14} + 248 x^{13} + 5896 x^{12} - 14188 x^{11} + 21820 x^{10} - 43599 x^{9} - 7699 x^{8} + 97875 x^{7} - 91977 x^{6} + 302319 x^{5} - 49552 x^{4} - 292478 x^{3} - 70145 x^{2} + 111235 x + 28367$ |
$20$ |
[8,6] |
$397^{5}\cdot 401^{8}$ |
$2$ |
$49.0857437391$ |
$1781.0047034117376$ |
|
|
? |
$C_4\wr D_5$ (as 20T418) |
trivial |
$[2]$ |
$2$ |
$13$ |
$1587505433.56$ |
| 20.8.659...157.2 |
$x^{20} - 3 x^{19} - 19 x^{18} + 104 x^{17} + 46 x^{16} - 816 x^{15} - 377 x^{14} + 5750 x^{13} + 481 x^{12} - 23572 x^{11} - 5409 x^{10} + 29390 x^{9} + 61815 x^{8} + 58301 x^{7} - 79450 x^{6} - 129539 x^{5} - 98958 x^{4} + 12864 x^{3} + 90298 x^{2} + 75365 x + 16369$ |
$20$ |
[8,6] |
$397^{5}\cdot 401^{8}$ |
$2$ |
$49.0857437391$ |
$1781.0047034117376$ |
|
|
|
$C_4\wr D_5$ (as 20T418) |
trivial |
$[2, 2]$ |
$2$ |
$13$ |
$2188103870.28$ |
| 20.0.659...157.2 |
$x^{20} - 2 x^{19} + 16 x^{18} - 40 x^{17} + 153 x^{16} - 409 x^{15} + 531 x^{14} - 631 x^{13} + 1182 x^{12} - 2207 x^{11} + 9841 x^{10} - 31915 x^{9} + 59913 x^{8} - 71946 x^{7} + 315927 x^{6} - 188012 x^{5} - 202487 x^{4} - 100612 x^{3} + 686038 x^{2} + 650199 x + 329149$ |
$20$ |
[0,10] |
$397^{5}\cdot 401^{8}$ |
$2$ |
$49.0857437391$ |
$1781.0047034117376$ |
✓ |
|
? |
$C_4\wr D_5$ (as 20T418) |
$[2, 194]$ |
$[2, 194]$ |
$2$ |
$9$ |
$735584.085831$ |
| 20.20.226...873.1 |
$x^{20} - 10 x^{19} - 9 x^{18} + 360 x^{17} - 507 x^{16} - 5094 x^{15} + 11686 x^{14} + 36343 x^{13} - 105960 x^{12} - 139153 x^{11} + 502333 x^{10} + 274440 x^{9} - 1331717 x^{8} - 195165 x^{7} + 1954334 x^{6} - 179722 x^{5} - 1451928 x^{4} + 359345 x^{3} + 409455 x^{2} - 140766 x + 1777$ |
$20$ |
[20,0] |
$19^{8}\cdot 43^{8}\cdot 193^{2}\cdot 313^{3}$ |
$4$ |
$58.5836200053$ |
$29549.35026036373$ |
|
|
? |
$C_4\wr D_5$ (as 20T418) |
trivial |
$[2]$ |
$2$ |
$19$ |
$129217871434$ |
| 20.20.400...625.1 |
$x^{20} - x^{19} - 38 x^{18} + 32 x^{17} + 528 x^{16} - 350 x^{15} - 3494 x^{14} + 1700 x^{13} + 11599 x^{12} - 3821 x^{11} - 18216 x^{10} + 3821 x^{9} + 11599 x^{8} - 1700 x^{7} - 3494 x^{6} + 350 x^{5} + 528 x^{4} - 32 x^{3} - 38 x^{2} + x + 1$ |
$20$ |
[20,0] |
$3^{4}\cdot 5^{3}\cdot 13^{2}\cdot 37^{3}\cdot 2153^{8}$ |
$5$ |
$75.8773154981$ |
$14535.605069218584$ |
|
|
? |
$C_4\wr D_5$ (as 20T418) |
trivial |
$[2, 2, 2, 2]$ |
$2$ |
$19$ |
$3890518189520$ |
| 20.16.620...213.1 |
$x^{20} - 3 x^{19} - 39 x^{18} + 9 x^{17} + 1015 x^{16} + 2294 x^{15} - 23485 x^{14} - 33051 x^{13} + 332416 x^{12} - 18458 x^{11} - 2365731 x^{10} + 2808039 x^{9} + 6845411 x^{8} - 17537627 x^{7} + 1944729 x^{6} + 34047722 x^{5} - 36550142 x^{4} - 2338829 x^{3} + 19149302 x^{2} - 4012621 x - 2235791$ |
$20$ |
[16,2] |
$97^{2}\cdot 397^{5}\cdot 401^{8}$ |
$3$ |
$77.5590621944$ |
$17540.86206823225$ |
|
|
? |
$C_4\wr D_5$ (as 20T418) |
trivial |
$[2, 2]$ |
$2$ |
$17$ |
$1040133084100$ |
| 20.16.620...213.2 |
$x^{20} - x^{19} - 39 x^{18} + 24 x^{17} - 111 x^{16} + 1377 x^{15} + 24220 x^{14} - 57435 x^{13} - 444438 x^{12} + 883410 x^{11} + 3747451 x^{10} - 7378247 x^{9} - 17234947 x^{8} + 36901191 x^{7} + 47314304 x^{6} - 107472506 x^{5} - 84282926 x^{4} + 161726188 x^{3} + 98536502 x^{2} - 92415798 x - 56933073$ |
$20$ |
[16,2] |
$97^{2}\cdot 397^{5}\cdot 401^{8}$ |
$3$ |
$77.5590621944$ |
$17540.86206823225$ |
|
|
|
$C_4\wr D_5$ (as 20T418) |
trivial |
$[2, 2]$ |
$2$ |
$17$ |
$1548163427350$ |
| 20.12.258...392.1 |
$x^{20} - 13 x^{18} - 4 x^{16} + 500 x^{14} - 666 x^{12} - 5863 x^{10} + 8866 x^{8} + 21576 x^{6} - 25476 x^{4} - 7173 x^{2} + 7173$ |
$20$ |
[12,4] |
$2^{20}\cdot 3^{6}\cdot 401^{8}\cdot 797^{3}$ |
$4$ |
$83.2995910587$ |
|
|
|
? |
$C_4\wr D_5$ (as 20T418) |
$[2]$ |
$[2, 2, 2]$ |
$2$ |
$15$ |
$586016359007$ |
| 20.12.506...992.1 |
$x^{20} + 8 x^{18} - 82 x^{16} - 361 x^{14} + 2934 x^{12} + 701 x^{10} - 26750 x^{8} + 31719 x^{6} + 22482 x^{4} - 35892 x^{2} + 8973$ |
$20$ |
[12,4] |
$2^{20}\cdot 3^{6}\cdot 401^{8}\cdot 997^{3}$ |
$4$ |
$86.1446666706$ |
|
|
|
? |
$C_4\wr D_5$ (as 20T418) |
$[2]$ |
$[2, 2, 2, 2]$ |
$2$ |
$15$ |
$601358593098$ |
| 20.4.207...456.1 |
$x^{20} + 69 x^{18} + 1299 x^{16} + 7251 x^{14} - 1235 x^{12} - 115467 x^{10} - 282527 x^{8} - 50172 x^{6} + 489880 x^{4} + 490677 x^{2} + 133821$ |
$20$ |
[4,8] |
$2^{20}\cdot 3^{2}\cdot 401^{8}\cdot 14869^{3}$ |
$4$ |
$103.715134384$ |
|
|
|
? |
$C_4\wr D_5$ (as 20T418) |
$[2, 2]$ |
$[2, 2, 2]$ |
$2$ |
$11$ |
$753715998638$ |
| 20.4.159...864.1 |
$x^{20} + 113 x^{18} + 4679 x^{16} + 92642 x^{14} + 936165 x^{12} + 4697526 x^{10} + 10010207 x^{8} + 4906246 x^{6} - 2572937 x^{4} - 880230 x^{2} + 264069$ |
$20$ |
[4,8] |
$2^{20}\cdot 3^{2}\cdot 13^{3}\cdot 37^{3}\cdot 61^{3}\cdot 401^{8}$ |
$6$ |
$114.847383903$ |
|
|
|
? |
$C_4\wr D_5$ (as 20T418) |
$[2, 2, 2]$ |
$[2, 2, 2, 2, 2]$ |
$2$ |
$11$ |
$1162378179040$ |
