| 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 |
| 20.4.128...401.1 |
$x^{20} - 2 x^{19} + 2 x^{18} + 2 x^{17} - 9 x^{16} + 24 x^{15} - 39 x^{14} + 48 x^{13} - 58 x^{12} + 60 x^{11} - 59 x^{10} + 60 x^{9} - 58 x^{8} + 48 x^{7} - 39 x^{6} + 24 x^{5} - 9 x^{4} + 2 x^{3} + 2 x^{2} - 2 x + 1$ |
$20$ |
[4,8] |
$11^{16}\cdot 23^{4}$ |
$2$ |
$12.7485184063$ |
$32.65713384043754$ |
|
|
? |
$C_2\wr C_5$ (as 20T41) |
trivial |
$2$ |
$11$ |
$845.372840783$ |
| 20.0.128...401.1 |
$x^{20} - 2 x^{19} + x^{18} - 3 x^{17} + 13 x^{16} - 20 x^{15} + 10 x^{14} + 17 x^{13} - 19 x^{12} + 8 x^{11} + 11 x^{10} + 8 x^{9} - 19 x^{8} + 17 x^{7} + 10 x^{6} - 20 x^{5} + 13 x^{4} - 3 x^{3} + x^{2} - 2 x + 1$ |
$20$ |
[0,10] |
$11^{16}\cdot 23^{4}$ |
$2$ |
$12.7485184063$ |
$32.65713384043754$ |
|
|
? |
$C_2\wr C_5$ (as 20T41) |
trivial |
$2$ |
$9$ |
$422.464665804$ |
| 20.0.157...961.1 |
$x^{20} - 2 x^{19} + 5 x^{18} - 10 x^{17} + 21 x^{16} - 29 x^{15} + 42 x^{14} - 62 x^{13} + 78 x^{12} - 77 x^{11} + 89 x^{10} - 77 x^{9} + 92 x^{8} - 54 x^{7} + 45 x^{6} - 18 x^{5} + 24 x^{4} - 7 x^{3} + 4 x^{2} + x + 1$ |
$20$ |
[0,10] |
$11^{16}\cdot 43^{4}$ |
$2$ |
$14.4480035355$ |
$44.65276699099921$ |
|
|
? |
$C_2\wr C_5$ (as 20T41) |
trivial |
$2$ |
$9$ |
$1838.7824$ |
| 20.4.157...961.1 |
$x^{20} - 2 x^{18} - 11 x^{15} - 39 x^{14} - 55 x^{13} - 67 x^{12} - 66 x^{11} - 51 x^{10} - 66 x^{9} - 67 x^{8} - 55 x^{7} - 39 x^{6} - 11 x^{5} - 2 x^{2} + 1$ |
$20$ |
[4,8] |
$11^{16}\cdot 43^{4}$ |
$2$ |
$14.4480035355$ |
$44.65276699099921$ |
|
|
? |
$C_2\wr C_5$ (as 20T41) |
trivial |
$2$ |
$11$ |
$3897.16327263$ |
| 20.4.155...521.1 |
$x^{20} - 7 x^{19} + 24 x^{18} - 59 x^{17} + 121 x^{16} - 208 x^{15} + 290 x^{14} - 328 x^{13} + 304 x^{12} - 209 x^{11} + 45 x^{10} + 110 x^{9} - 113 x^{8} - 23 x^{7} + 82 x^{6} + x^{5} - 33 x^{4} - 14 x^{3} - x^{2} + 5 x + 1$ |
$20$ |
[4,8] |
$11^{18}\cdot 23^{4}$ |
$2$ |
$16.2031325156$ |
$41.50661671665305$ |
|
|
? |
$C_2\wr C_5$ (as 20T41) |
trivial |
$2$ |
$11$ |
$12706.8234185$ |
| 20.8.155...521.1 |
$x^{20} - 5 x^{19} + 6 x^{18} + 10 x^{17} - 43 x^{16} + 58 x^{15} + 65 x^{14} - 261 x^{13} + 4 x^{12} + 418 x^{11} - 21 x^{10} - 308 x^{9} - 85 x^{8} + 73 x^{7} + 51 x^{6} + 63 x^{5} + 25 x^{4} - 24 x^{3} - 25 x^{2} - 2 x + 1$ |
$20$ |
[8,6] |
$11^{18}\cdot 23^{4}$ |
$2$ |
$16.2031325156$ |
$41.50661671665305$ |
|
|
? |
$C_2\wr C_5$ (as 20T41) |
trivial |
$2$ |
$13$ |
$25426.9866338$ |
| 20.0.288...801.1 |
$x^{20} - 4 x^{19} + 9 x^{18} - 16 x^{17} + 27 x^{16} - 30 x^{15} + 33 x^{14} - 33 x^{13} + 24 x^{12} - 11 x^{11} + 23 x^{10} + 8 x^{8} - 11 x^{7} + 22 x^{6} + 14 x^{5} + 12 x^{4} + 13 x^{3} + 5 x^{2} + 2 x + 1$ |
$20$ |
[0,10] |
$11^{16}\cdot 89^{4}$ |
$2$ |
$16.7106040704$ |
$64.24053534410318$ |
|
|
? |
$C_2\wr C_5$ (as 20T41) |
trivial |
$2$ |
$9$ |
$9528.73392243$ |
| 20.0.288...801.2 |
$x^{20} - 3 x^{19} + 3 x^{18} - 4 x^{17} + 14 x^{16} - 30 x^{15} + 44 x^{14} - 44 x^{13} + 50 x^{12} - 99 x^{11} + 144 x^{10} - 143 x^{9} + 109 x^{8} - 77 x^{7} + 77 x^{6} - 63 x^{5} + 42 x^{4} - 14 x^{3} + 4 x^{2} - x + 1$ |
$20$ |
[0,10] |
$11^{16}\cdot 89^{4}$ |
$2$ |
$16.7106040704$ |
$64.24053534410318$ |
|
|
? |
$C_2\wr C_5$ (as 20T41) |
trivial |
$2$ |
$9$ |
$10415.7103089$ |
| 20.4.648...921.1 |
$x^{20} - 3 x^{18} + 11 x^{16} - 45 x^{14} + 30 x^{12} - 103 x^{10} + 73 x^{8} - 124 x^{6} + 55 x^{4} - 27 x^{2} + 1$ |
$20$ |
[4,8] |
$11^{16}\cdot 109^{4}$ |
$2$ |
$17.4020113555$ |
$71.09309101858766$ |
|
|
? |
$C_2\wr C_5$ (as 20T41) |
trivial |
$2$ |
$11$ |
$19449.3777264$ |
| 20.8.648...921.1 |
$x^{20} - 7 x^{19} + 24 x^{18} - 57 x^{17} + 109 x^{16} - 169 x^{15} + 180 x^{14} - 117 x^{13} + 63 x^{12} - 44 x^{11} - 32 x^{10} + 154 x^{9} - 177 x^{8} + 78 x^{7} + 42 x^{6} - 81 x^{5} + 35 x^{4} + 14 x^{3} - 16 x^{2} - 2 x + 1$ |
$20$ |
[8,6] |
$11^{16}\cdot 109^{4}$ |
$2$ |
$17.4020113555$ |
$71.09309101858766$ |
|
|
? |
$C_2\wr C_5$ (as 20T41) |
trivial |
$2$ |
$13$ |
$51203.8375809$ |
| 20.12.493...664.1 |
$x^{20} - 8 x^{19} + 26 x^{18} - 40 x^{17} + 14 x^{16} + 76 x^{15} - 296 x^{14} + 658 x^{13} - 577 x^{12} - 362 x^{11} + 906 x^{10} - 866 x^{9} + 2214 x^{8} - 3458 x^{7} + 1784 x^{6} + 564 x^{5} - 1042 x^{4} + 542 x^{3} - 158 x^{2} + 22 x - 1$ |
$20$ |
[12,4] |
$2^{30}\cdot 11^{16}$ |
$2$ |
$19.2601267834$ |
$26.08313353110776$ |
|
|
? |
$C_2\wr C_5$ (as 20T41) |
trivial |
$2$ |
$15$ |
$311138.716179$ |
| 20.12.493...664.2 |
$x^{20} - 4 x^{19} - 4 x^{18} + 24 x^{17} + 18 x^{16} - 92 x^{15} - 52 x^{14} + 388 x^{13} - 411 x^{12} - 122 x^{11} + 92 x^{10} + 1352 x^{9} - 1651 x^{8} - 314 x^{7} + 986 x^{6} + 46 x^{5} - 275 x^{4} - 14 x^{3} + 32 x^{2} + 2 x - 1$ |
$20$ |
[12,4] |
$2^{30}\cdot 11^{16}$ |
$2$ |
$19.2601267834$ |
$26.08313353110776$ |
|
|
? |
$C_2\wr C_5$ (as 20T41) |
trivial |
$2$ |
$15$ |
$322822.36902$ |
| 20.0.203...961.1 |
$x^{20} - 2 x^{19} + 28 x^{18} - 49 x^{17} + 299 x^{16} - 440 x^{15} + 1587 x^{14} - 1735 x^{13} + 3660 x^{12} - 2792 x^{11} + 4305 x^{10} - 5140 x^{9} + 6147 x^{8} - 1757 x^{7} + 3498 x^{6} - 3970 x^{5} - 1705 x^{4} + 1606 x^{3} + 176 x^{2} - 121 x + 11$ |
$20$ |
[0,10] |
$11^{16}\cdot 1451^{4}$ |
$2$ |
$29.2043557835$ |
$259.3867898202987$ |
✓ |
|
? |
$C_2\wr C_5$ (as 20T41) |
trivial |
$2$ |
$9$ |
$2631079.35388$ |
| 20.0.203...961.2 |
$x^{20} - 8 x^{19} + 55 x^{18} - 247 x^{17} + 972 x^{16} - 3008 x^{15} + 8238 x^{14} - 18705 x^{13} + 37604 x^{12} - 63382 x^{11} + 93279 x^{10} - 111873 x^{9} + 112680 x^{8} - 83184 x^{7} + 45374 x^{6} - 11082 x^{5} - 5227 x^{4} + 8834 x^{3} - 3846 x^{2} + 1831 x + 2837$ |
$20$ |
[0,10] |
$11^{16}\cdot 1451^{4}$ |
$2$ |
$29.2043557835$ |
$259.3867898202987$ |
✓ |
|
? |
$C_2\wr C_5$ (as 20T41) |
trivial |
$2$ |
$9$ |
$2227699.13388$ |
| 20.20.316...281.1 |
$x^{20} - 7 x^{19} - 12 x^{18} + 158 x^{17} - 22 x^{16} - 1371 x^{15} + 815 x^{14} + 5755 x^{13} - 3754 x^{12} - 12200 x^{11} + 6629 x^{10} + 13087 x^{9} - 5692 x^{8} - 7261 x^{7} + 2391 x^{6} + 2072 x^{5} - 418 x^{4} - 294 x^{3} + 17 x^{2} + 16 x + 1$ |
$20$ |
[20,0] |
$11^{16}\cdot 43^{4}\cdot 67^{4}$ |
$3$ |
$33.4983024782$ |
$365.49865006155005$ |
|
|
? |
$C_2\wr C_5$ (as 20T41) |
trivial |
$2$ |
$19$ |
$506580279.946$ |
| 20.20.316...281.2 |
$x^{20} - 2 x^{19} - 33 x^{18} + 54 x^{17} + 399 x^{16} - 470 x^{15} - 2298 x^{14} + 1592 x^{13} + 6862 x^{12} - 2024 x^{11} - 10603 x^{10} + 385 x^{9} + 8089 x^{8} + 480 x^{7} - 3142 x^{6} - 173 x^{5} + 625 x^{4} + 2 x^{3} - 55 x^{2} + 3 x + 1$ |
$20$ |
[20,0] |
$11^{16}\cdot 43^{4}\cdot 67^{4}$ |
$3$ |
$33.4983024782$ |
$365.49865006155005$ |
|
|
? |
$C_2\wr C_5$ (as 20T41) |
trivial |
$2$ |
$19$ |
$500606346.877$ |
