| 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 |
| 20.2.120...008.1 |
$x^{20} - 2 x^{19} - x^{18} + 4 x^{17} + 12 x^{16} + 4 x^{15} - 20 x^{14} - 28 x^{13} - 68 x^{12} - 24 x^{11} + 70 x^{10} + 170 x^{9} + 249 x^{8} + 258 x^{7} + 271 x^{6} + 184 x^{5} + 126 x^{4} + 70 x^{3} + 34 x^{2} + 8 x + 1$ |
$20$ |
[2,9] |
$-\,2^{30}\cdot 47^{9}$ |
$2$ |
$15.9951762372$ |
$19.390719429665317$ |
|
|
? |
$C_5:D_4$ (as 20T7) |
trivial |
$2$ |
$10$ |
$6974.62635242$ |
| 20.2.128...856.1 |
$x^{20} - 4 x^{19} + 8 x^{17} + 15 x^{16} - 20 x^{15} + 22 x^{14} - 68 x^{13} - 99 x^{12} + 172 x^{11} - 154 x^{10} + 312 x^{9} + 88 x^{8} - 88 x^{7} + 424 x^{6} - 320 x^{5} + 309 x^{4} - 148 x^{3} + 58 x^{2} - 12 x + 1$ |
$20$ |
[2,9] |
$-\,2^{30}\cdot 79^{9}$ |
$2$ |
$20.2058527886$ |
$25.13961017995307$ |
|
|
? |
$C_5:D_4$ (as 20T7) |
trivial |
$2$ |
$10$ |
$107328.34068$ |
| 20.0.281...176.1 |
$x^{20} - 8 x^{19} + 31 x^{18} - 52 x^{17} - 19 x^{16} + 272 x^{15} - 387 x^{14} - 382 x^{13} + 2195 x^{12} - 2802 x^{11} - 399 x^{10} + 6486 x^{9} - 7787 x^{8} - 164 x^{7} + 13244 x^{6} - 15410 x^{5} + 6096 x^{4} + 4204 x^{3} - 499 x^{2} - 2000 x + 1261$ |
$20$ |
[0,10] |
$2^{20}\cdot 401^{9}$ |
$2$ |
$29.6787061152$ |
$40.049968789001575$ |
|
|
? |
$C_5:D_4$ (as 20T7) |
$[5]$ |
$4$ |
$9$ |
$951859.395024$ |
| 20.20.261...625.1 |
$x^{20} - 5 x^{19} - 17 x^{18} + 104 x^{17} + 108 x^{16} - 894 x^{15} - 253 x^{14} + 4107 x^{13} - 396 x^{12} - 10913 x^{11} + 3697 x^{10} + 16864 x^{9} - 8756 x^{8} - 14287 x^{7} + 9640 x^{6} + 5587 x^{5} - 4819 x^{4} - 514 x^{3} + 846 x^{2} - 100 x - 1$ |
$20$ |
[20,0] |
$5^{10}\cdot 401^{9}$ |
$2$ |
$33.1818021789$ |
$44.77722635447622$ |
|
|
? |
$C_5:D_4$ (as 20T7) |
trivial |
$2$ |
$19$ |
$481290724.965$ |
| 20.0.287...224.1 |
$x^{20} - 8 x^{19} + 42 x^{18} - 134 x^{17} + 290 x^{16} - 382 x^{15} + 449 x^{14} - 608 x^{13} + 1356 x^{12} - 2872 x^{11} + 3429 x^{10} - 4260 x^{9} + 5673 x^{8} - 6508 x^{7} + 10322 x^{6} - 8320 x^{5} + 2221 x^{4} + 1314 x^{3} + 523 x^{2} + 178 x + 191$ |
$20$ |
[0,10] |
$2^{30}\cdot 401^{9}$ |
$2$ |
$41.9720287018$ |
$56.639209034025185$ |
✓ |
|
? |
$C_5:D_4$ (as 20T7) |
$[7]$ |
$2$ |
$9$ |
$9087089.31038$ |
| 20.0.762...057.1 |
$x^{20} - 3 x^{19} - 18 x^{18} + 60 x^{17} + 193 x^{16} - 529 x^{15} - 906 x^{14} + 1894 x^{13} + 2040 x^{12} - 3325 x^{11} + 516 x^{10} - 3941 x^{9} + 21467 x^{8} - 56363 x^{7} + 81372 x^{6} - 111903 x^{5} + 175479 x^{4} - 114989 x^{3} + 56653 x^{2} - 53508 x + 20335$ |
$20$ |
[0,10] |
$19^{15}\cdot 43^{9}$ |
$2$ |
$49.4454126556$ |
$59.67596196855758$ |
|
|
? |
$C_5:D_4$ (as 20T7) |
$[2, 2]$ |
$2$ |
$9$ |
$281681007.343$ |
| 20.0.166...624.1 |
$x^{20} - 8 x^{19} + 53 x^{18} - 252 x^{17} + 1094 x^{16} - 4040 x^{15} + 13662 x^{14} - 40564 x^{13} + 109650 x^{12} - 261596 x^{11} + 564840 x^{10} - 1077446 x^{9} + 1869350 x^{8} - 2885718 x^{7} + 4091345 x^{6} - 5186800 x^{5} + 6013294 x^{4} - 5867098 x^{3} + 4235595 x^{2} - 1678698 x + 261817$ |
$20$ |
[0,10] |
$2^{20}\cdot 3^{10}\cdot 401^{9}$ |
$3$ |
$51.40502689444888$ |
$69.3685807840985$ |
|
|
|
$C_5:D_4$ (as 20T7) |
$[2, 2, 10]$ |
$4$ |
$9$ |
$45481396.835897334$ |
| 20.20.294...376.1 |
$x^{20} - 58 x^{18} - 40 x^{17} + 1207 x^{16} + 1424 x^{15} - 11068 x^{14} - 15868 x^{13} + 50037 x^{12} + 80696 x^{11} - 111270 x^{10} - 207804 x^{9} + 100886 x^{8} + 264656 x^{7} + 5488 x^{6} - 142076 x^{5} - 45525 x^{4} + 20760 x^{3} + 14322 x^{2} + 2848 x + 193$ |
$20$ |
[20,0] |
$2^{40}\cdot 401^{9}$ |
$2$ |
$59.3574122304$ |
$80.09993757800315$ |
|
|
? |
$C_5:D_4$ (as 20T7) |
trivial |
$2$ |
$19$ |
$194057079592$ |
| 20.0.274...000.1 |
$x^{20} + 35 x^{18} + 509 x^{16} + 4020 x^{14} + 18824 x^{12} + 53353 x^{10} + 89335 x^{8} + 82266 x^{6} + 36535 x^{4} + 6770 x^{2} + 401$ |
$20$ |
[0,10] |
$2^{20}\cdot 5^{10}\cdot 401^{9}$ |
$3$ |
$66.3636043578$ |
$89.55445270895244$ |
✓ |
|
? |
$C_5:D_4$ (as 20T7) |
$[2172]$ |
$2$ |
$9$ |
$2526424.45141$ |
| 20.0.729...776.1 |
$x^{20} - 2 x^{19} + 81 x^{18} - 188 x^{17} + 2734 x^{16} - 6654 x^{15} + 49469 x^{14} - 114622 x^{13} + 518862 x^{12} - 1038994 x^{11} + 3265803 x^{10} - 5320128 x^{9} + 12249774 x^{8} - 14230308 x^{7} + 23034434 x^{6} - 13145962 x^{5} + 14871717 x^{4} + 4774722 x^{3} + 3161709 x^{2} - 596504 x + 345613$ |
$20$ |
[0,10] |
$2^{20}\cdot 11^{10}\cdot 401^{9}$ |
$3$ |
$98.43313244737793$ |
$132.83071933856263$ |
✓ |
|
? |
$C_5:D_4$ (as 20T7) |
$[382]$ |
$2$ |
$9$ |
$682902769.402283$ |
