| 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 |
| 20.0.680...129.1 |
$x^{20} - 8 x^{19} + 33 x^{18} - 96 x^{17} + 225 x^{16} - 428 x^{15} + 639 x^{14} - 722 x^{13} + 605 x^{12} - 426 x^{11} + 458 x^{10} - 746 x^{9} + 1001 x^{8} - 1010 x^{7} + 873 x^{6} - 694 x^{5} + 455 x^{4} - 214 x^{3} + 66 x^{2} - 12 x + 1$ |
$20$ |
[0,10] |
$11^{16}\cdot 23^{6}$ |
$2$ |
$17.4434545876$ |
$32.65713384043754$ |
|
|
? |
$C_2^4:C_5$ (as 20T17) |
$[2]$ |
$[2]$ |
$2$ |
$9$ |
$7947.13273942$ |
| 20.4.680...129.1 |
$x^{20} - 5 x^{19} + 6 x^{18} + 4 x^{17} - 17 x^{16} - 2 x^{15} + 41 x^{14} + 10 x^{13} - 52 x^{12} + 10 x^{11} + 99 x^{10} - 29 x^{9} - 260 x^{8} - 255 x^{7} - 53 x^{6} + 79 x^{5} + 42 x^{4} - 9 x^{3} - 12 x^{2} + 4 x + 1$ |
$20$ |
[4,8] |
$11^{16}\cdot 23^{6}$ |
$2$ |
$17.4434545876$ |
$32.65713384043754$ |
|
|
? |
$C_2^4:C_5$ (as 20T17) |
trivial |
$[2]$ |
$2$ |
$11$ |
$31805.2169747$ |
| 20.0.493...664.1 |
$x^{20} - 8 x^{19} + 34 x^{18} - 116 x^{17} + 338 x^{16} - 836 x^{15} + 1840 x^{14} - 3640 x^{13} + 6408 x^{12} - 10176 x^{11} + 14560 x^{10} - 18560 x^{9} + 21128 x^{8} - 21328 x^{7} + 18704 x^{6} - 14048 x^{5} + 8976 x^{4} - 4576 x^{3} + 1760 x^{2} - 704 x + 352$ |
$20$ |
[0,10] |
$2^{30}\cdot 11^{16}$ |
$2$ |
$19.2601267834$ |
$24.977294240287762$ |
|
|
? |
$C_2^4:C_5$ (as 20T17) |
trivial |
trivial |
$2$ |
$9$ |
$43044.7776734$ |
| 20.4.493...664.1 |
$x^{20} - 4 x^{19} - 2 x^{18} + 28 x^{17} + 5 x^{16} - 162 x^{15} + 88 x^{14} + 440 x^{13} - 328 x^{12} - 792 x^{11} + 562 x^{10} + 1012 x^{9} - 509 x^{8} - 880 x^{7} + 154 x^{6} + 410 x^{5} - 21 x^{4} - 108 x^{3} - 28 x^{2} + 2 x + 1$ |
$20$ |
[4,8] |
$2^{30}\cdot 11^{16}$ |
$2$ |
$19.2601267834$ |
$24.977294240287762$ |
|
|
? |
$C_2^4:C_5$ (as 20T17) |
trivial |
trivial |
$2$ |
$11$ |
$94333.9687476$ |
| 20.8.493...664.1 |
$x^{20} - 2 x^{19} - 6 x^{18} + 34 x^{17} - 23 x^{16} - 150 x^{15} + 350 x^{14} - 84 x^{13} - 824 x^{12} + 1584 x^{11} - 1154 x^{10} - 286 x^{9} + 1291 x^{8} - 978 x^{7} + 78 x^{6} + 356 x^{5} - 229 x^{4} + 26 x^{3} + 26 x^{2} - 10 x + 1$ |
$20$ |
[8,6] |
$2^{30}\cdot 11^{16}$ |
$2$ |
$19.2601267834$ |
$24.977294240287762$ |
|
|
? |
$C_2^4:C_5$ (as 20T17) |
trivial |
trivial |
$2$ |
$13$ |
$185091.7445$ |
| 20.8.493...664.2 |
$x^{20} - 6 x^{19} + 6 x^{18} + 40 x^{17} - 138 x^{16} + 134 x^{15} + 140 x^{14} - 428 x^{13} + 201 x^{12} + 320 x^{11} - 330 x^{10} - 70 x^{9} + 180 x^{8} + 68 x^{7} - 196 x^{6} - 68 x^{5} + 152 x^{4} + 20 x^{3} - 34 x^{2} - 4 x + 1$ |
$20$ |
[8,6] |
$2^{30}\cdot 11^{16}$ |
$2$ |
$19.2601267834$ |
$24.977294240287762$ |
|
|
? |
$C_2^4:C_5$ (as 20T17) |
trivial |
trivial |
$2$ |
$13$ |
$192042.173919$ |
| 20.20.730...296.1 |
$x^{20} - 4 x^{19} - 52 x^{18} + 138 x^{17} + 1252 x^{16} - 1396 x^{15} - 16494 x^{14} - 2978 x^{13} + 114593 x^{12} + 138432 x^{11} - 345938 x^{10} - 844624 x^{9} + 1044 x^{8} + 1741890 x^{7} + 1829836 x^{6} - 256700 x^{5} - 1985280 x^{4} - 1827912 x^{3} - 827226 x^{2} - 193988 x - 18877$ |
$20$ |
[20,0] |
$2^{30}\cdot 11^{16}\cdot 23^{6}$ |
$3$ |
$49.3375401049$ |
$119.78689508462926$ |
|
|
? |
$C_2^4:C_5$ (as 20T17) |
trivial |
$[2, 2, 2, 2]$ |
$2$ |
$19$ |
$41430036329.1$ |
| 20.20.730...296.2 |
$x^{20} - 8 x^{19} - 26 x^{18} + 398 x^{17} - 557 x^{16} - 5658 x^{15} + 21734 x^{14} + 2950 x^{13} - 161406 x^{12} + 328090 x^{11} - 83864 x^{10} - 525816 x^{9} + 641159 x^{8} + 15436 x^{7} - 485786 x^{6} + 263660 x^{5} + 54989 x^{4} - 87604 x^{3} + 22770 x^{2} + 22 x - 473$ |
$20$ |
[20,0] |
$2^{30}\cdot 11^{16}\cdot 23^{6}$ |
$3$ |
$49.3375401049$ |
$119.78689508462926$ |
|
|
? |
$C_2^4:C_5$ (as 20T17) |
trivial |
$[2, 2, 2, 2]$ |
$2$ |
$19$ |
$43619173869.6$ |
