| 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 |
| 20.0.488...125.1 |
$x^{20} - 10 x^{19} + 40 x^{18} - 75 x^{17} + 45 x^{16} + 48 x^{15} - 5 x^{14} - 295 x^{13} + 535 x^{12} - 285 x^{11} - 261 x^{10} + 375 x^{9} + 50 x^{8} - 275 x^{7} + 65 x^{6} + 92 x^{5} - 35 x^{4} - 25 x^{3} + 10 x^{2} + 5 x + 1$ |
$20$ |
[0,10] |
$3^{8}\cdot 5^{27}$ |
$2$ |
$13.6288122183$ |
$15.211433151416195$ |
|
|
? |
$C_4\times D_5$ (as 20T6) |
trivial |
$10$ |
$9$ |
$6025.48578502$ |
| 20.4.439...125.1 |
$x^{20} - 3 x^{15} - 31 x^{10} + 3 x^{5} + 1$ |
$20$ |
[4,8] |
$3^{10}\cdot 5^{27}$ |
$2$ |
$15.2114331514$ |
$15.211433151416195$ |
|
|
? |
$C_4\times D_5$ (as 20T6) |
trivial |
$2$ |
$11$ |
$7296.61382034$ |
| 20.0.488...000.1 |
$x^{20} - 10 x^{19} + 50 x^{18} - 155 x^{17} + 325 x^{16} - 464 x^{15} + 420 x^{14} - 140 x^{13} - 205 x^{12} + 350 x^{11} - 194 x^{10} - 85 x^{9} + 220 x^{8} - 170 x^{7} + 45 x^{6} + 11 x^{5} - 5 x^{3} + 5 x^{2} + 5 x + 1$ |
$20$ |
[0,10] |
$2^{16}\cdot 5^{27}$ |
$2$ |
$15.2909159947$ |
$17.564650049460273$ |
|
|
? |
$C_4\times D_5$ (as 20T6) |
trivial |
$10$ |
$9$ |
$22883.422779$ |
| 20.4.781...000.1 |
$x^{20} - 22 x^{15} - 6 x^{10} + 22 x^{5} + 1$ |
$20$ |
[4,8] |
$2^{20}\cdot 5^{27}$ |
$2$ |
$17.5646500495$ |
$17.564650049460273$ |
|
|
? |
$C_4\times D_5$ (as 20T6) |
trivial |
$2$ |
$11$ |
$44054.0373872$ |
| 20.0.386...125.1 |
$x^{20} - 2 x^{19} + x^{18} + x^{17} - x^{15} - 4 x^{14} + 11 x^{13} - 6 x^{12} - 8 x^{11} + 22 x^{10} - 17 x^{9} + 9 x^{8} - 31 x^{7} + 56 x^{6} - 64 x^{5} + 27 x^{4} + 10 x^{3} + 4 x^{2} + x + 1$ |
$20$ |
[0,10] |
$5^{15}\cdot 103^{8}$ |
$2$ |
$21.348255561548747$ |
$33.93486420206204$ |
|
|
? |
$C_4\times D_5$ (as 20T6) |
trivial |
$10$ |
$9$ |
$661565.5195213907$ |
| 20.0.204...125.1 |
$x^{20} - x^{19} + 6 x^{18} - 7 x^{17} + 30 x^{16} - 18 x^{15} + 123 x^{14} - 78 x^{13} + 538 x^{12} - 412 x^{11} + 704 x^{10} - 501 x^{9} + 837 x^{8} + 172 x^{7} + 309 x^{6} + 49 x^{5} + 174 x^{4} - 46 x^{3} + 13 x^{2} - 3 x + 1$ |
$20$ |
[0,10] |
$5^{15}\cdot 401^{8}$ |
$2$ |
$36.7692907112$ |
$66.95757085563274$ |
✓ |
|
? |
$C_4\times D_5$ (as 20T6) |
$[29]$ |
$10$ |
$9$ |
$2526424.45141$ |
| 20.0.623...125.1 |
$x^{20} - 20 x^{18} + 170 x^{16} - 800 x^{14} + 2275 x^{12} - 3480 x^{10} - 950 x^{8} + 15700 x^{6} - 25375 x^{4} + 13000 x^{2} + 28880$ |
$20$ |
[0,10] |
$5^{35}\cdot 11^{8}$ |
$2$ |
$43.626922829798765$ |
$55.449016844865795$ |
|
|
|
$C_4\times D_5$ (as 20T6) |
$[5]$ |
$10$ |
$9$ |
$403949827.0826757$ |
| 20.0.213...125.1 |
$x^{20} - 5 x^{19} + 13 x^{18} - 17 x^{17} + 94 x^{16} - 151 x^{15} + 406 x^{14} - 633 x^{13} + 3653 x^{12} - 772 x^{11} + 13426 x^{10} + 5719 x^{9} + 24764 x^{8} + 15388 x^{7} + 21892 x^{6} + 15269 x^{5} + 9379 x^{4} + 3157 x^{3} + 732 x^{2} - 45 x + 1$ |
$20$ |
[0,10] |
$3^{8}\cdot 5^{15}\cdot 239^{8}$ |
$3$ |
$46.3911528894$ |
$89.53381316204927$ |
✓ |
|
? |
$C_4\times D_5$ (as 20T6) |
$[2, 58]$ |
$10$ |
$9$ |
$10123076.9997$ |
| 20.20.191...125.1 |
$x^{20} - 8 x^{19} - 20 x^{18} + 284 x^{17} - 21 x^{16} - 4198 x^{15} + 3737 x^{14} + 33772 x^{13} - 42360 x^{12} - 162403 x^{11} + 230822 x^{10} + 483926 x^{9} - 710001 x^{8} - 898678 x^{7} + 1266895 x^{6} + 1017051 x^{5} - 1261123 x^{4} - 651709 x^{3} + 616317 x^{2} + 185386 x - 101429$ |
$20$ |
[20,0] |
$3^{10}\cdot 5^{15}\cdot 239^{8}$ |
$3$ |
$51.77824081$ |
$89.53381316204927$ |
|
|
? |
$C_4\times D_5$ (as 20T6) |
trivial |
$2$ |
$19$ |
$62134578326.1$ |
| 20.4.754...125.1 |
$x^{20} - 18 x^{15} - 401 x^{10} + 1918 x^{5} + 1$ |
$20$ |
[4,8] |
$5^{35}\cdot 11^{10}$ |
$2$ |
$55.449016844865795$ |
$55.449016844865795$ |
|
|
|
$C_4\times D_5$ (as 20T6) |
$[5]$ |
$2$ |
$11$ |
$2222196566.3233886$ |
| 20.20.120...125.1 |
$x^{20} - 6 x^{19} - 49 x^{18} + 394 x^{17} + 431 x^{16} - 8836 x^{15} + 11137 x^{14} + 75642 x^{13} - 215641 x^{12} - 135520 x^{11} + 1183051 x^{10} - 1032083 x^{9} - 1892289 x^{8} + 4095435 x^{7} - 1533360 x^{6} - 2597056 x^{5} + 3317104 x^{4} - 1586360 x^{3} + 344740 x^{2} - 27105 x - 139$ |
$20$ |
[20,0] |
$5^{15}\cdot 7^{10}\cdot 139^{8}$ |
$3$ |
$63.6769778552$ |
$104.29990752889705$ |
|
|
? |
$C_4\times D_5$ (as 20T6) |
trivial |
$2$ |
$19$ |
$386511180224$ |
