| 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 |
| 20.0.267...376.1 |
$x^{20} - 2 x^{19} + 6 x^{16} - 18 x^{15} + 17 x^{14} + 4 x^{13} + 25 x^{12} - 92 x^{11} + 92 x^{10} - 34 x^{9} + 44 x^{8} - 140 x^{7} + 188 x^{6} - 144 x^{5} + 88 x^{4} - 54 x^{3} + 27 x^{2} - 8 x + 1$ |
$20$ |
[0,10] |
$2^{20}\cdot 761^{5}$ |
$2$ |
$10.5045187321$ |
$55.17245689653489$ |
|
|
? |
$D_5\wr C_2$ (as 20T48) |
trivial |
$4$ |
$9$ |
$99.9526828541$ |
| 20.0.287...032.1 |
$x^{20} - 4 x^{19} + 6 x^{18} - 4 x^{17} - 2 x^{16} + 10 x^{15} - 10 x^{14} - 12 x^{13} + 43 x^{12} - 38 x^{11} + 21 x^{10} - 38 x^{9} + 43 x^{8} - 12 x^{7} - 10 x^{6} + 10 x^{5} - 2 x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1$ |
$20$ |
[0,10] |
$2^{30}\cdot 193^{5}$ |
$2$ |
$10.5422745134$ |
$39.293765408777$ |
|
|
? |
$D_5\wr C_2$ (as 20T48) |
trivial |
$2$ |
$9$ |
$52.0455573525$ |
| 20.0.369...048.1 |
$x^{20} - 7 x^{19} + 26 x^{18} - 64 x^{17} + 116 x^{16} - 153 x^{15} + 128 x^{14} - 4 x^{13} - 199 x^{12} + 398 x^{11} - 478 x^{10} + 372 x^{9} - 118 x^{8} - 158 x^{7} + 328 x^{6} - 344 x^{5} + 249 x^{4} - 129 x^{3} + 46 x^{2} - 10 x + 1$ |
$20$ |
[0,10] |
$2^{16}\cdot 3^{10}\cdot 157^{5}$ |
$3$ |
$10.6747948392$ |
$37.7863071184893$ |
|
|
? |
$D_5\wr C_2$ (as 20T48) |
trivial |
$6$ |
$9$ |
$182.345344476$ |
| 20.0.540...000.1 |
$x^{20} - 3 x^{19} + 7 x^{18} - 5 x^{17} + 4 x^{16} + 11 x^{15} - 9 x^{14} + 21 x^{13} + 18 x^{12} - 9 x^{11} + 49 x^{10} - 9 x^{9} + 18 x^{8} + 21 x^{7} - 9 x^{6} + 11 x^{5} + 4 x^{4} - 5 x^{3} + 7 x^{2} - 3 x + 1$ |
$20$ |
[0,10] |
$2^{16}\cdot 5^{10}\cdot 61^{5}$ |
$3$ |
$10.8803147116$ |
$30.407023951240983$ |
|
|
? |
$D_5\wr C_2$ (as 20T48) |
trivial |
$2$ |
$9$ |
$75.025557452$ |
| 20.10.393...375.1 |
$x^{20} - x^{19} - x^{18} + 11 x^{17} - 53 x^{16} + 61 x^{15} - 54 x^{14} - 3 x^{13} + 266 x^{12} - 79 x^{11} - 167 x^{10} - 9 x^{9} - 215 x^{8} - 42 x^{7} + 305 x^{6} - 155 x^{5} + 17 x^{4} + 43 x^{3} - 30 x^{2} + 3 x + 1$ |
$20$ |
[10,5] |
$-\,5^{10}\cdot 3319^{5}$ |
$2$ |
$16.9721481969$ |
$128.82158204276178$ |
|
|
? |
$D_5\wr C_2$ (as 20T48) |
trivial |
$2$ |
$14$ |
$53457.8405658$ |
| 20.10.417...375.1 |
$x^{20} - 2 x^{19} - 11 x^{18} + 23 x^{17} + 31 x^{16} - 111 x^{15} + 48 x^{14} + 275 x^{13} - 467 x^{12} - 341 x^{11} + 1168 x^{10} + 107 x^{9} - 1480 x^{8} + 268 x^{7} + 1065 x^{6} - 330 x^{5} - 456 x^{4} + 70 x^{3} + 45 x^{2} - 13 x + 1$ |
$20$ |
[10,5] |
$-\,5^{10}\cdot 3359^{5}$ |
$2$ |
$17.0230550318$ |
$129.59552461408535$ |
|
|
? |
$D_5\wr C_2$ (as 20T48) |
trivial |
$2$ |
$14$ |
$55116.0718093$ |
| 20.20.321...000.1 |
$x^{20} - 8 x^{19} - 6 x^{18} + 175 x^{17} - 183 x^{16} - 1268 x^{15} + 1844 x^{14} + 4088 x^{13} - 5900 x^{12} - 6726 x^{11} + 9014 x^{10} + 5898 x^{9} - 7315 x^{8} - 2666 x^{7} + 3154 x^{6} + 539 x^{5} - 662 x^{4} - 30 x^{3} + 54 x^{2} - x - 1$ |
$20$ |
[20,0] |
$2^{16}\cdot 5^{10}\cdot 3469^{5}$ |
$3$ |
$29.8785882674$ |
$229.30374548237478$ |
|
|
? |
$D_5\wr C_2$ (as 20T48) |
trivial |
$2$ |
$19$ |
$160161061.462$ |
| 20.20.342...625.1 |
$x^{20} - 2 x^{19} - 31 x^{18} + 65 x^{17} + 310 x^{16} - 641 x^{15} - 1445 x^{14} + 2911 x^{13} + 3496 x^{12} - 6946 x^{11} - 4324 x^{10} + 9090 x^{9} + 2099 x^{8} - 6378 x^{7} + 470 x^{6} + 2072 x^{5} - 673 x^{4} - 143 x^{3} + 105 x^{2} - 18 x + 1$ |
$20$ |
[20,0] |
$5^{10}\cdot 19^{5}\cdot 1699^{5}$ |
$3$ |
$29.9724156823$ |
$401.75241131821474$ |
|
|
? |
$D_5\wr C_2$ (as 20T48) |
trivial |
$2$ |
$19$ |
$167949047.356$ |
