| 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 |
| 20.0.369...000.1 |
$x^{20} - 4 x^{19} + 2 x^{18} + 24 x^{17} - 61 x^{16} + 20 x^{15} + 184 x^{14} - 396 x^{13} + 203 x^{12} + 612 x^{11} - 1410 x^{10} + 968 x^{9} + 849 x^{8} - 2224 x^{7} + 1620 x^{6} - 56 x^{5} - 638 x^{4} + 368 x^{3} - 24 x^{2} - 56 x + 20$ |
$20$ |
[0,10] |
$2^{42}\cdot 3^{16}\cdot 5^{9}$ |
$3$ |
$21.3008285433$ |
$24.1776264427508$ |
|
|
? |
$S_5$ (as 20T35) |
trivial |
$2$ |
$9$ |
$383250.383654$ |
| 20.0.407...517.1 |
$x^{20} - 8 x^{19} + 40 x^{18} - 131 x^{17} + 333 x^{16} - 674 x^{15} + 1207 x^{14} - 1922 x^{13} + 2822 x^{12} - 3681 x^{11} + 4260 x^{10} - 4222 x^{9} + 3582 x^{8} - 2665 x^{7} + 1813 x^{6} - 1072 x^{5} + 587 x^{4} - 252 x^{3} + 74 x^{2} - 13 x + 1$ |
$20$ |
[0,10] |
$11^{12}\cdot 37^{9}$ |
$2$ |
$21.4055497896$ |
$30.08587537137172$ |
|
|
|
$S_5$ (as 20T35) |
trivial |
$2$ |
$9$ |
$172377.141044$ |
| 20.2.141...408.1 |
$x^{20} - 7 x^{19} + 19 x^{18} - 5 x^{17} - 108 x^{16} + 311 x^{15} - 333 x^{14} - 167 x^{13} + 992 x^{12} - 1203 x^{11} + 141 x^{10} + 1555 x^{9} - 2554 x^{8} + 2293 x^{7} - 1387 x^{6} + 609 x^{5} - 208 x^{4} + 77 x^{3} - 33 x^{2} + 9 x - 1$ |
$20$ |
[2,9] |
$-\,2^{16}\cdot 3^{16}\cdot 43^{9}$ |
$3$ |
$22.7814732171$ |
$27.49509522275834$ |
|
|
? |
$S_5$ (as 20T35) |
$[3]$ |
$2$ |
$10$ |
$121399.279846$ |
| 20.2.129...232.1 |
$x^{20} - 5 x^{19} + 5 x^{18} + 3 x^{17} + 42 x^{16} - 153 x^{15} + 131 x^{14} - 151 x^{13} + 700 x^{12} - 963 x^{11} + 273 x^{10} + 105 x^{9} + 106 x^{8} + x^{7} + 71 x^{6} - 651 x^{5} + 834 x^{4} - 453 x^{3} + 123 x^{2} - 21 x + 3$ |
$20$ |
[2,9] |
$-\,2^{16}\cdot 3^{27}\cdot 11^{10}$ |
$3$ |
$25.4468501861$ |
$30.005593487001327$ |
|
|
? |
$S_5$ (as 20T35) |
trivial |
$2$ |
$10$ |
$1605879.29863$ |
| 20.20.195...272.1 |
$x^{20} - 51 x^{18} + 1051 x^{16} - 11466 x^{14} + 73285 x^{12} - 288141 x^{10} + 708441 x^{8} - 1076170 x^{6} + 965263 x^{4} - 461747 x^{2} + 89557$ |
$20$ |
[20,0] |
$2^{16}\cdot 13^{15}\cdot 17^{12}$ |
$3$ |
$65.2455450632$ |
$97.59091824977558$ |
|
|
? |
$S_5$ (as 20T35) |
trivial |
$2$ |
$19$ |
$964006871003$ |
| 20.20.119...392.1 |
$x^{20} - 6 x^{19} - 42 x^{18} + 266 x^{17} + 601 x^{16} - 4412 x^{15} - 3160 x^{14} + 36624 x^{13} - 1906 x^{12} - 166956 x^{11} + 84220 x^{10} + 427696 x^{9} - 344106 x^{8} - 598132 x^{7} + 620232 x^{6} + 412832 x^{5} - 525839 x^{4} - 109710 x^{3} + 181022 x^{2} + 9590 x - 18511$ |
$20$ |
[20,0] |
$2^{16}\cdot 11^{12}\cdot 157^{9}$ |
$3$ |
$71.4191128525$ |
$107.90352012122878$ |
|
|
? |
$S_5$ (as 20T35) |
trivial |
$2$ |
$19$ |
$2864940973830$ |
