| 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 |
| 20.8.680...129.1 |
$x^{20} - x^{19} + 8 x^{17} - 23 x^{16} + 46 x^{15} - 74 x^{14} + 79 x^{13} - 60 x^{12} - 6 x^{11} + 81 x^{10} - 206 x^{9} + 260 x^{8} - 124 x^{7} + 71 x^{6} - 108 x^{5} - 214 x^{4} + 189 x^{3} + 77 x^{2} - 20 x + 1$ |
$20$ |
[8,6] |
$11^{16}\cdot 23^{6}$ |
$2$ |
$17.4434545876$ |
$32.65713384043754$ |
|
|
? |
$C_2\wr C_5$ (as 20T46) |
trivial |
$2$ |
$13$ |
$52598.7023471$ |
| 20.0.680...129.2 |
$x^{20} - 3 x^{19} + 14 x^{18} - 33 x^{17} + 85 x^{16} - 156 x^{15} + 281 x^{14} - 417 x^{13} + 590 x^{12} - 734 x^{11} + 869 x^{10} - 875 x^{9} + 908 x^{8} - 679 x^{7} + 668 x^{6} - 321 x^{5} + 303 x^{4} - 77 x^{3} + 42 x^{2} - 4 x + 1$ |
$20$ |
[0,10] |
$11^{16}\cdot 23^{6}$ |
$2$ |
$17.4434545876$ |
$32.65713384043754$ |
|
|
? |
$C_2\wr C_5$ (as 20T46) |
$[2]$ |
$2$ |
$9$ |
$6484.27631918$ |
| 20.0.493...664.2 |
$x^{20} - 2 x^{19} + 2 x^{18} + 6 x^{17} + x^{16} + 2 x^{15} + 20 x^{14} + 20 x^{13} + 81 x^{12} + 82 x^{11} + 56 x^{10} + 110 x^{9} + 140 x^{8} + 340 x^{7} + 676 x^{6} + 872 x^{5} + 1057 x^{4} + 988 x^{3} + 628 x^{2} + 332 x + 131$ |
$20$ |
[0,10] |
$2^{30}\cdot 11^{16}$ |
$2$ |
$19.2601267834$ |
$26.08313353110776$ |
|
|
? |
$C_2\wr C_5$ (as 20T46) |
trivial |
$2$ |
$9$ |
$36792.3507976$ |
| 20.8.493...664.5 |
$x^{20} - 2 x^{19} - 6 x^{18} + 4 x^{17} + 20 x^{16} - 6 x^{15} - 38 x^{14} + 102 x^{13} + 162 x^{12} - 306 x^{11} - 818 x^{10} - 648 x^{9} - 25 x^{8} + 368 x^{7} + 310 x^{6} + 76 x^{5} - 42 x^{4} - 24 x^{3} + 6 x^{2} + 6 x + 1$ |
$20$ |
[8,6] |
$2^{30}\cdot 11^{16}$ |
$2$ |
$19.2601267834$ |
$26.08313353110776$ |
|
|
? |
$C_2\wr C_5$ (as 20T46) |
trivial |
$2$ |
$13$ |
$162791.569572$ |
| 20.4.823...609.1 |
$x^{20} - 5 x^{19} + 9 x^{18} - 9 x^{17} + 11 x^{16} - 21 x^{15} - 16 x^{14} + 141 x^{13} - 361 x^{12} + 484 x^{11} - 461 x^{10} + 363 x^{9} - 445 x^{8} + 410 x^{7} - 133 x^{6} + 133 x^{5} - 143 x^{4} + 39 x^{3} - 8 x^{2} - x + 1$ |
$20$ |
[4,8] |
$11^{18}\cdot 23^{6}$ |
$2$ |
$22.1703100866$ |
$41.50661671665305$ |
|
|
? |
$C_2\wr C_5$ (as 20T46) |
$[2]$ |
$2$ |
$11$ |
$173434.395473$ |
| 20.4.823...609.2 |
$x^{20} - 3 x^{19} + 8 x^{18} - 21 x^{17} + 55 x^{16} - 89 x^{15} + 146 x^{14} - 272 x^{13} + 406 x^{12} - 385 x^{11} + 430 x^{10} - 627 x^{9} + 615 x^{8} - 349 x^{7} - 514 x^{6} + 890 x^{5} - 726 x^{4} + 287 x^{3} - 47 x^{2} - 3 x + 1$ |
$20$ |
[4,8] |
$11^{18}\cdot 23^{6}$ |
$2$ |
$22.1703100866$ |
$41.50661671665305$ |
|
|
? |
$C_2\wr C_5$ (as 20T46) |
$[2]$ |
$2$ |
$11$ |
$142451.10279$ |
| 20.4.596...344.4 |
$x^{20} - 4 x^{19} + 4 x^{18} - 12 x^{17} + 55 x^{16} - 98 x^{15} + 194 x^{14} - 348 x^{13} + 615 x^{12} - 1188 x^{11} + 1970 x^{10} - 3806 x^{9} + 3640 x^{8} - 4066 x^{7} + 7168 x^{6} - 12880 x^{5} + 11693 x^{4} - 4082 x^{3} + 70 x^{2} + 84 x + 1$ |
$20$ |
[4,8] |
$2^{30}\cdot 11^{18}$ |
$2$ |
$24.4792670483$ |
$33.15118318510912$ |
|
|
? |
$C_2\wr C_5$ (as 20T46) |
trivial |
$2$ |
$11$ |
$1092701.97171$ |
| 20.4.596...344.5 |
$x^{20} - 6 x^{19} + 6 x^{18} + 12 x^{17} - 32 x^{16} - 58 x^{15} + 208 x^{14} - 36 x^{13} - 480 x^{12} + 154 x^{11} + 1376 x^{10} - 44 x^{9} - 1295 x^{8} + 26 x^{7} + 1206 x^{6} + 168 x^{5} - 118 x^{4} - 86 x^{3} - 14 x^{2} + 2 x + 1$ |
$20$ |
[4,8] |
$2^{30}\cdot 11^{18}$ |
$2$ |
$24.4792670483$ |
$33.15118318510912$ |
|
|
? |
$C_2\wr C_5$ (as 20T46) |
trivial |
$2$ |
$11$ |
$928534.301244$ |
| 20.0.730...296.3 |
$x^{20} - 6 x^{19} + 24 x^{18} - 90 x^{17} + 351 x^{16} - 870 x^{15} + 806 x^{14} + 4518 x^{13} - 22332 x^{12} + 26478 x^{11} + 156658 x^{10} - 1013022 x^{9} + 3400561 x^{8} - 8011944 x^{7} + 14259924 x^{6} - 19938342 x^{5} + 22096203 x^{4} - 18640836 x^{3} + 10953478 x^{2} - 3882390 x + 612679$ |
$20$ |
[0,10] |
$2^{30}\cdot 11^{16}\cdot 23^{6}$ |
$3$ |
$49.3375401049$ |
$119.78689508462926$ |
✓ |
|
? |
$C_2\wr C_5$ (as 20T46) |
$[2, 4, 20]$ |
$2$ |
$9$ |
$2545371.69018$ |
| 20.0.730...296.4 |
$x^{20} - 4 x^{19} + 22 x^{18} + 125 x^{16} + 252 x^{15} + 544 x^{14} + 2908 x^{13} - 3650 x^{12} - 2204 x^{11} + 30356 x^{10} + 56748 x^{9} + 48918 x^{8} + 41876 x^{7} + 567360 x^{6} + 977364 x^{5} + 997121 x^{4} + 2976592 x^{3} + 3930518 x^{2} + 3465188 x + 2935789$ |
$20$ |
[0,10] |
$2^{30}\cdot 11^{16}\cdot 23^{6}$ |
$3$ |
$49.3375401049$ |
$119.78689508462926$ |
✓ |
|
? |
$C_2\wr C_5$ (as 20T46) |
$[2, 4, 20]$ |
$2$ |
$9$ |
$2417625.83378$ |
| 20.20.730...296.5 |
$x^{20} - 4 x^{19} - 54 x^{18} + 142 x^{17} + 1215 x^{16} - 1658 x^{15} - 14226 x^{14} + 5956 x^{13} + 91351 x^{12} + 20666 x^{11} - 319628 x^{10} - 208840 x^{9} + 584299 x^{8} + 561074 x^{7} - 505908 x^{6} - 639678 x^{5} + 156250 x^{4} + 296450 x^{3} - 2608 x^{2} - 43810 x - 263$ |
$20$ |
[20,0] |
$2^{30}\cdot 11^{16}\cdot 23^{6}$ |
$3$ |
$49.3375401049$ |
$125.0903140152616$ |
|
|
? |
$C_2\wr C_5$ (as 20T46) |
trivial |
$2$ |
$19$ |
$36744656987.7$ |
| 20.20.730...296.6 |
$x^{20} - 6 x^{19} - 40 x^{18} + 340 x^{17} + 74 x^{16} - 5752 x^{15} + 10688 x^{14} + 30864 x^{13} - 120232 x^{12} + 20384 x^{11} + 451848 x^{10} - 649264 x^{9} - 326024 x^{8} + 1665312 x^{7} - 1394144 x^{6} - 476416 x^{5} + 1818032 x^{4} - 1585536 x^{3} + 712224 x^{2} - 169280 x + 16928$ |
$20$ |
[20,0] |
$2^{30}\cdot 11^{16}\cdot 23^{6}$ |
$3$ |
$49.3375401049$ |
$125.0903140152616$ |
|
|
? |
$C_2\wr C_5$ (as 20T46) |
trivial |
$2$ |
$19$ |
$43517716745.6$ |
