| 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 |
| 22.6.144...125.1 |
$x^{22} - 2 x^{21} - x^{20} + 18 x^{19} - 17 x^{18} - 44 x^{17} + 110 x^{16} - 3 x^{15} - 254 x^{14} + 59 x^{13} + 240 x^{12} - 102 x^{11} - 552 x^{10} - 230 x^{9} + 307 x^{8} + 320 x^{7} - 3 x^{6} - 154 x^{5} - 62 x^{4} + 18 x^{3} + 19 x^{2} + 2 x - 1$ |
$22$ |
[6,8] |
$5^{11}\cdot 7^{4}\cdot 83^{4}\cdot 127^{4}$ |
$4$ |
$17.1621719232$ |
$2844.1679033165196$ |
|
|
? |
$C_2\times A_{11}$ (as 22T46) |
trivial |
$2$ |
$13$ |
$95631.3345105$ |
| 22.0.152...375.1 |
$x^{22} - 4 x^{21} + 18 x^{20} - 48 x^{19} + 125 x^{18} - 249 x^{17} + 478 x^{16} - 766 x^{15} + 1216 x^{14} - 1618 x^{13} + 2242 x^{12} - 2454 x^{11} + 2995 x^{10} - 2616 x^{9} + 2692 x^{8} - 1937 x^{7} + 1684 x^{6} - 1102 x^{5} + 757 x^{4} - 253 x^{3} + 163 x^{2} + 2 x + 1$ |
$22$ |
[0,11] |
$-\,5^{4}\cdot 7^{11}\cdot 83^{4}\cdot 127^{4}$ |
$4$ |
$19.1015026172$ |
$2844.1679033165196$ |
|
|
? |
$C_2\times A_{11}$ (as 22T46) |
trivial |
$2$ |
$10$ |
$69206.6233764$ |
| 22.0.458...896.1 |
$x^{22} + 2 x^{20} + 3 x^{18} - 2 x^{16} - 7 x^{14} - 5 x^{12} + 4 x^{10} + 11 x^{8} - 2 x^{6} - 6 x^{4} + x^{2} + 1$ |
$22$ |
[0,11] |
$-\,2^{28}\cdot 11^{4}\cdot 19^{4}\cdot 547^{4}$ |
$4$ |
$20.081203729$ |
|
|
|
? |
$C_2\times A_{11}$ (as 22T46) |
trivial |
$4$ |
$10$ |
$460879.840354$ |
| 22.6.323...608.1 |
$x^{22} - 10 x^{20} + 20 x^{18} + 38 x^{16} + 30 x^{14} - 676 x^{12} + 645 x^{10} + 720 x^{8} - 79 x^{6} - 2438 x^{4} + 2236 x^{2} - 648$ |
$22$ |
[6,8] |
$2^{43}\cdot 43793^{4}$ |
$2$ |
$27.0563104099$ |
|
|
|
? |
$C_2\times A_{11}$ (as 22T46) |
trivial |
$2$ |
$13$ |
$50121925.16$ |
| 22.0.119...368.1 |
$x^{22} - 3 x^{21} + 45 x^{20} - 12 x^{19} + 1263 x^{18} - 891 x^{17} + 11013 x^{16} + 12294 x^{15} + 42993 x^{14} + 18555 x^{13} + 42921 x^{12} + 71280 x^{11} + 36558 x^{10} + 25902 x^{9} + 32238 x^{8} + 31986 x^{7} + 15876 x^{6} + 6156 x^{5} + 13644 x^{4} + 11880 x^{3} + 972 x^{2} + 1944 x + 2916$ |
$22$ |
[0,11] |
$-\,2^{24}\cdot 3^{29}\cdot 7^{4}\cdot 23^{4}\cdot 137^{16}$ |
$5$ |
$817.614499526$ |
|
|
|
|
$C_2\times A_{11}$ (as 22T46) |
trivial |
$6$ |
$10$ |
$1462413343710000000000000$ |
| 22.0.101...736.1 |
$x^{22} + 81 x^{20} + 2082 x^{18} + 19218 x^{16} + 53361 x^{14} + 19161 x^{12} - 39240 x^{10} - 1188 x^{8} + 6588 x^{6} - 11628 x^{4} + 648 x^{2} + 2916$ |
$22$ |
[0,11] |
$-\,2^{32}\cdot 3^{28}\cdot 7^{4}\cdot 23^{4}\cdot 137^{16}$ |
$5$ |
$1000.75255558$ |
|
|
|
|
$C_2\times A_{11}$ (as 22T46) |
trivial |
$4$ |
$10$ |
$89738500243100000000000000$ |
| 22.14.305...208.1 |
$x^{22} - 6 x^{21} - 96 x^{20} + 516 x^{19} + 3315 x^{18} - 15678 x^{17} - 58926 x^{16} + 239076 x^{15} + 605475 x^{14} - 2137974 x^{13} - 3792132 x^{12} + 12206088 x^{11} + 14763681 x^{10} - 46019430 x^{9} - 34917642 x^{8} + 112918896 x^{7} + 44592120 x^{6} - 169280496 x^{5} - 19547856 x^{4} + 127652544 x^{3} + 2781648 x^{2} - 33869664 x - 3859488$ |
$22$ |
[14,4] |
$2^{32}\cdot 3^{29}\cdot 7^{4}\cdot 23^{4}\cdot 137^{16}$ |
$5$ |
$1051.99587664$ |
|
|
|
? |
$C_2\times A_{11}$ (as 22T46) |
trivial |
$2$ |
$17$ |
$852811169305000000000000000$ |
| 22.14.832...312.1 |
$x^{22} - 6 x^{21} - 85 x^{20} + 456 x^{19} + 2554 x^{18} - 11784 x^{17} - 38526 x^{16} + 144516 x^{15} + 323265 x^{14} - 990414 x^{13} - 1608525 x^{12} + 4228056 x^{11} + 4901112 x^{10} - 11919636 x^{9} - 9151008 x^{8} + 22004508 x^{7} + 9743124 x^{6} - 25064112 x^{5} - 3630980 x^{4} + 14132688 x^{3} + 1997240 x^{2} - 2436432 x - 530108$ |
$22$ |
[14,4] |
$2^{45}\cdot 3^{28}\cdot 7^{4}\cdot 23^{4}\cdot 137^{16}$ |
$5$ |
$1507.32904904$ |
|
|
|
|
$C_2\times A_{11}$ (as 22T46) |
trivial |
$2$ |
$17$ |
$18736455246300000000000000000$ |
