| 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 |
Unit signature rank |
| 20.0.218...424.1 |
$x^{20} - 5 x^{19} + 11 x^{18} - 15 x^{17} + 22 x^{16} - 47 x^{15} + 85 x^{14} - 115 x^{13} + 174 x^{12} - 321 x^{11} + 497 x^{10} - 625 x^{9} + 748 x^{8} - 825 x^{7} + 715 x^{6} - 469 x^{5} + 254 x^{4} - 119 x^{3} + 43 x^{2} - 9 x + 1$ |
$20$ |
(0, 10) |
$2^{16}\cdot 3^{15}\cdot 7^{5}\cdot 61^{4}$ |
$4$ |
$14.6894459163$ |
$281.4996282050667$ |
|
|
? |
$C_5\wr D_4$ (as 20T299) |
trivial |
trivial |
$6$ |
$9$ |
$5970.91953124$ |
$0$ |
| 20.0.510...912.1 |
$x^{20} - 8 x^{19} + 34 x^{18} - 104 x^{17} + 257 x^{16} - 536 x^{15} + 965 x^{14} - 1526 x^{13} + 2153 x^{12} - 2768 x^{11} + 3257 x^{10} - 3370 x^{9} + 2900 x^{8} - 1990 x^{7} + 1054 x^{6} - 416 x^{5} + 105 x^{4} + 10 x^{3} - 16 x^{2} - 2 x + 5$ |
$20$ |
(0, 10) |
$2^{20}\cdot 17^{5}\cdot 1361^{4}$ |
$3$ |
$17.1954620912$ |
$2650.5802431974057$ |
|
|
? |
$C_5\wr D_4$ (as 20T299) |
trivial |
trivial |
$4$ |
$9$ |
$45855.5542226$ |
$0$ |
| 20.10.160...000.1 |
$x^{20} - 2 x^{19} - 6 x^{18} + 22 x^{17} - 10 x^{16} - 88 x^{15} + 147 x^{14} + 84 x^{13} - 469 x^{12} + 240 x^{11} + 623 x^{10} - 708 x^{9} - 183 x^{8} + 732 x^{7} - 276 x^{6} - 262 x^{5} + 222 x^{4} - 10 x^{3} - 35 x^{2} + 6 x + 1$ |
$20$ |
(10, 5) |
$-\,2^{20}\cdot 5^{10}\cdot 11^{4}\cdot 181^{4}$ |
$4$ |
$20.4328642571$ |
$2756.0494380530954$ |
|
|
? |
$C_5\wr D_4$ (as 20T299) |
trivial |
trivial |
$2$ |
$14$ |
$458094.158162$ |
$10$ |
| 20.10.766...000.1 |
$x^{20} - 2 x^{19} - 13 x^{18} + 20 x^{17} + 75 x^{16} - 94 x^{15} - 239 x^{14} + 342 x^{13} + 336 x^{12} - 630 x^{11} - 339 x^{10} + 652 x^{9} + 504 x^{8} - 878 x^{7} - 205 x^{6} + 654 x^{5} - 200 x^{4} - 28 x^{3} + 24 x^{2} - 10 x + 1$ |
$20$ |
(10, 5) |
$-\,2^{20}\cdot 5^{10}\cdot 71^{4}\cdot 131^{4}$ |
$4$ |
$27.8112767469$ |
$9459.18482156389$ |
|
|
? |
$C_5\wr D_4$ (as 20T299) |
trivial |
trivial |
$2$ |
$14$ |
$10696061.9951$ |
$10$ |
| 20.20.405...125.1 |
$x^{20} - 8 x^{19} - 13 x^{18} + 254 x^{17} - 320 x^{16} - 2579 x^{15} + 6719 x^{14} + 7619 x^{13} - 39332 x^{12} + 13604 x^{11} + 77412 x^{10} - 67087 x^{9} - 57464 x^{8} + 71947 x^{7} + 14376 x^{6} - 25774 x^{5} - 3291 x^{4} + 3036 x^{3} + 850 x^{2} + 68 x + 1$ |
$20$ |
(20, 0) |
$5^{10}\cdot 29^{5}\cdot 331^{4}\cdot 641^{4}$ |
$4$ |
$60.3144964416$ |
$219802.59719342436$ |
|
|
? |
$C_5\wr D_4$ (as 20T299) |
trivial |
trivial |
$2$ |
$19$ |
$253215720131$ |
$20$ |
| 20.20.413...125.1 |
$x^{20} - 5 x^{19} - 55 x^{18} + 265 x^{17} + 1145 x^{16} - 5278 x^{15} - 11255 x^{14} + 49775 x^{13} + 56205 x^{12} - 233775 x^{11} - 163635 x^{10} + 558275 x^{9} + 306525 x^{8} - 639230 x^{7} - 338365 x^{6} + 285219 x^{5} + 142945 x^{4} - 35290 x^{3} - 13110 x^{2} + 475 x + 139$ |
$20$ |
(20, 0) |
$5^{26}\cdot 11^{4}\cdot 29^{5}\cdot 31^{4}$ |
$4$ |
$60.368638449$ |
|
|
|
? |
$C_5\wr D_4$ (as 20T299) |
trivial |
trivial |
$2$ |
$19$ |
$304766298548$ |
$20$ |
