| 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 |
| 20.6.319...779.2 |
$x^{20} - x^{19} + 6 x^{18} + 8 x^{17} + 10 x^{16} + 71 x^{15} - 90 x^{14} + 8 x^{13} + 342 x^{12} - 447 x^{11} + 100 x^{10} + 418 x^{9} - 475 x^{8} + 37 x^{7} + 280 x^{6} - 138 x^{5} - 69 x^{4} + 42 x^{3} + 11 x^{2} - 4 x - 1$ |
$20$ |
[6,7] |
$-\,11^{17}\cdot 43^{6}$ |
$2$ |
$23.725988691$ |
$145.3298275879478$ |
|
|
? |
$C_2\times C_4^4:C_{10}$ (as 20T326) |
trivial |
$[2]$ |
$2$ |
$12$ |
$1096939.79122$ |
| 20.2.319...779.2 |
$x^{20} - 3 x^{19} + 4 x^{18} + 11 x^{17} - 31 x^{16} + 51 x^{15} + 44 x^{14} - 70 x^{13} + 323 x^{12} + 55 x^{11} + 32 x^{10} + 444 x^{9} - 329 x^{8} + 5 x^{7} - 38 x^{6} - 316 x^{5} + 104 x^{4} - 257 x^{3} + 22 x^{2} - 52 x - 23$ |
$20$ |
[2,9] |
$-\,11^{17}\cdot 43^{6}$ |
$2$ |
$23.725988691$ |
$145.3298275879478$ |
|
|
? |
$C_2\times C_4^4:C_{10}$ (as 20T326) |
trivial |
$[2]$ |
$2$ |
$10$ |
$556828.06097$ |
| 20.2.696...096.2 |
$x^{20} - 4 x^{19} + 6 x^{18} - 9 x^{17} + 39 x^{16} - 121 x^{15} + 219 x^{14} - 244 x^{13} + 118 x^{12} + 140 x^{11} - 517 x^{10} + 833 x^{9} - 854 x^{8} + 492 x^{7} + 31 x^{6} - 307 x^{5} + 220 x^{4} - 110 x^{2} + 55 x - 11$ |
$20$ |
[2,9] |
$-\,2^{10}\cdot 11^{16}\cdot 23^{6}$ |
$3$ |
$24.6687700525$ |
$143.03424265864493$ |
|
|
? |
$C_2\times C_4^4:C_{10}$ (as 20T326) |
trivial |
$[2]$ |
$2$ |
$10$ |
$753525.823577$ |
| 20.6.696...096.2 |
$x^{20} - 7 x^{19} + 21 x^{18} - 52 x^{17} + 122 x^{16} - 182 x^{15} + 167 x^{14} - 130 x^{13} - 123 x^{12} + 693 x^{11} - 897 x^{10} + 1365 x^{9} - 2195 x^{8} + 3272 x^{7} - 5451 x^{6} + 5455 x^{5} - 2486 x^{4} + 652 x^{3} - 368 x^{2} + 176 x - 32$ |
$20$ |
[6,7] |
$-\,2^{10}\cdot 11^{16}\cdot 23^{6}$ |
$3$ |
$24.6687700525$ |
$143.03424265864493$ |
|
|
? |
$C_2\times C_4^4:C_{10}$ (as 20T326) |
trivial |
$[2]$ |
$2$ |
$12$ |
$1409730.32164$ |
| 20.10.471...971.3 |
$x^{20} - 10 x^{19} + 14 x^{18} + 124 x^{17} - 519 x^{16} - 24 x^{15} + 4374 x^{14} - 3205 x^{13} - 15774 x^{12} + 3289 x^{11} + 46166 x^{10} + 56516 x^{9} - 229286 x^{8} - 661698 x^{7} - 274432 x^{6} + 772487 x^{5} + 1089529 x^{4} + 549299 x^{3} + 80270 x^{2} - 15797 x - 2333$ |
$20$ |
[10,5] |
$-\,11^{17}\cdot 1451^{6}$ |
$2$ |
$68.1842403166$ |
$2034.7168236198834$ |
|
|
? |
$C_2\times C_4^4:C_{10}$ (as 20T326) |
trivial |
$[2, 2]$ |
$2$ |
$14$ |
$90982181599.0$ |
| 20.0.822...144.1 |
$x^{20} + 80 x^{18} + 2725 x^{16} + 52004 x^{14} + 616265 x^{12} + 4747128 x^{10} + 24125607 x^{8} + 80059320 x^{6} + 166415810 x^{4} + 196170128 x^{2} + 99859859$ |
$20$ |
[0,10] |
$2^{40}\cdot 11^{17}\cdot 23^{6}$ |
$3$ |
$78.6614820292$ |
|
✓ |
|
? |
$C_2\times C_4^4:C_{10}$ (as 20T326) |
$[2, 2, 3888]$ |
$[2, 2, 3888]$ |
$2$ |
$9$ |
$2417625.83378$ |
| 20.0.822...144.2 |
$x^{20} + 100 x^{18} + 3758 x^{16} + 74104 x^{14} + 870719 x^{12} + 6447376 x^{10} + 30638916 x^{8} + 92413816 x^{6} + 169077370 x^{4} + 168727724 x^{2} + 69135539$ |
$20$ |
[0,10] |
$2^{40}\cdot 11^{17}\cdot 23^{6}$ |
$3$ |
$78.6614820292$ |
|
✓ |
|
? |
$C_2\times C_4^4:C_{10}$ (as 20T326) |
$[2, 2, 3804]$ |
$[2, 2, 3804]$ |
$2$ |
$9$ |
$2545371.69018$ |
| 20.16.822...144.3 |
$x^{20} - 72 x^{18} + 1869 x^{16} - 19680 x^{14} + 45743 x^{12} + 384176 x^{10} - 1191806 x^{8} + 235796 x^{6} + 569503 x^{4} - 116380 x^{2} + 5819$ |
$20$ |
[16,2] |
$2^{40}\cdot 11^{17}\cdot 23^{6}$ |
$3$ |
$78.6614820292$ |
|
|
|
? |
$C_2\times C_4^4:C_{10}$ (as 20T326) |
trivial |
$[2, 2, 2]$ |
$2$ |
$17$ |
$1505181860400$ |
| 20.16.822...144.4 |
$x^{20} - 14 x^{18} - 179 x^{16} + 3106 x^{14} - 8942 x^{12} - 22232 x^{10} + 126599 x^{8} - 198858 x^{6} + 140921 x^{4} - 46552 x^{2} + 5819$ |
$20$ |
[16,2] |
$2^{40}\cdot 11^{17}\cdot 23^{6}$ |
$3$ |
$78.6614820292$ |
|
|
|
? |
$C_2\times C_4^4:C_{10}$ (as 20T326) |
trivial |
$[2, 2, 2]$ |
$2$ |
$17$ |
$1856039941760$ |
| 20.4.822...144.5 |
$x^{20} + 52 x^{18} + 327 x^{16} - 11744 x^{14} - 223794 x^{12} - 1672364 x^{10} - 6309985 x^{8} - 11830280 x^{6} - 8707501 x^{4} + 23276 x^{2} + 5819$ |
$20$ |
[4,8] |
$2^{40}\cdot 11^{17}\cdot 23^{6}$ |
$3$ |
$78.6614820292$ |
|
|
|
? |
$C_2\times C_4^4:C_{10}$ (as 20T326) |
$[2, 4]$ |
$[2, 2, 4]$ |
$2$ |
$11$ |
$13706090007.1$ |
| 20.8.822...144.5 |
$x^{20} + 36 x^{18} - 520 x^{16} - 9024 x^{14} + 74625 x^{12} + 346116 x^{10} - 360173 x^{8} - 1875236 x^{6} - 1468159 x^{4} - 186208 x^{2} + 5819$ |
$20$ |
[8,6] |
$2^{40}\cdot 11^{17}\cdot 23^{6}$ |
$3$ |
$78.6614820292$ |
|
|
|
? |
$C_2\times C_4^4:C_{10}$ (as 20T326) |
trivial |
$[2, 2, 2]$ |
$2$ |
$13$ |
$274841012368$ |
| 20.20.822...144.5 |
$x^{20} - 100 x^{18} + 3439 x^{16} - 56240 x^{14} + 502714 x^{12} - 2665928 x^{10} + 8710790 x^{8} - 17539984 x^{6} + 20849477 x^{4} - 13011284 x^{2} + 3078251$ |
$20$ |
[20,0] |
$2^{40}\cdot 11^{17}\cdot 23^{6}$ |
$3$ |
$78.6614820292$ |
|
|
|
? |
$C_2\times C_4^4:C_{10}$ (as 20T326) |
trivial |
$[2, 2, 2, 2]$ |
$2$ |
$19$ |
$4324986461860$ |
| 20.8.822...144.6 |
$x^{20} - 28 x^{18} - 639 x^{16} + 10856 x^{14} + 168140 x^{12} + 761608 x^{10} + 1378531 x^{8} + 722568 x^{6} - 273493 x^{4} - 23276 x^{2} + 5819$ |
$20$ |
[8,6] |
$2^{40}\cdot 11^{17}\cdot 23^{6}$ |
$3$ |
$78.6614820292$ |
|
|
|
? |
$C_2\times C_4^4:C_{10}$ (as 20T326) |
trivial |
$[2, 2, 2]$ |
$2$ |
$13$ |
$247452160280$ |
| 20.20.822...144.6 |
$x^{20} - 80 x^{18} + 2736 x^{16} - 52796 x^{14} + 635559 x^{12} - 4959032 x^{10} + 25114837 x^{8} - 79828584 x^{6} + 146183147 x^{4} - 125992988 x^{2} + 26121491$ |
$20$ |
[20,0] |
$2^{40}\cdot 11^{17}\cdot 23^{6}$ |
$3$ |
$78.6614820292$ |
|
|
|
? |
$C_2\times C_4^4:C_{10}$ (as 20T326) |
trivial |
$[2, 2, 2]$ |
$2$ |
$19$ |
$4569755840760$ |
| 20.4.822...144.6 |
$x^{20} + 28 x^{18} - 980 x^{16} - 38444 x^{14} - 374193 x^{12} - 1268004 x^{10} - 1825384 x^{8} - 1130404 x^{6} - 268686 x^{4} + 5819$ |
$20$ |
[4,8] |
$2^{40}\cdot 11^{17}\cdot 23^{6}$ |
$3$ |
$78.6614820292$ |
|
|
|
? |
$C_2\times C_4^4:C_{10}$ (as 20T326) |
$[2, 2]$ |
$[2, 2, 2]$ |
$2$ |
$11$ |
$28658728544.9$ |
| 20.12.822...144.7 |
$x^{20} + 8 x^{18} - 1059 x^{16} + 4272 x^{14} + 103137 x^{12} - 614296 x^{10} + 921283 x^{8} + 611248 x^{6} - 2470292 x^{4} + 1512940 x^{2} + 5819$ |
$20$ |
[12,4] |
$2^{40}\cdot 11^{17}\cdot 23^{6}$ |
$3$ |
$78.6614820292$ |
|
|
|
? |
$C_2\times C_4^4:C_{10}$ (as 20T326) |
trivial |
$[2, 2, 2]$ |
$2$ |
$15$ |
$771793510725$ |
| 20.12.822...144.8 |
$x^{20} - 60 x^{18} + 131 x^{16} + 23816 x^{14} - 2503 x^{12} - 506320 x^{10} + 1283953 x^{8} - 1009976 x^{6} + 105754 x^{4} + 93104 x^{2} + 5819$ |
$20$ |
[12,4] |
$2^{40}\cdot 11^{17}\cdot 23^{6}$ |
$3$ |
$78.6614820292$ |
|
|
|
? |
$C_2\times C_4^4:C_{10}$ (as 20T326) |
trivial |
$[2, 2, 2]$ |
$2$ |
$15$ |
$747432165015$ |
