| 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 |
| 22.10.379...009.1 |
$x^{22} - 9 x^{21} + 30 x^{20} - 42 x^{19} - 6 x^{18} + 128 x^{17} - 208 x^{16} + 41 x^{15} + 302 x^{14} - 426 x^{13} + 86 x^{12} + 571 x^{11} - 569 x^{10} - 541 x^{9} + 986 x^{8} - 5 x^{7} - 712 x^{6} + 381 x^{5} + 144 x^{4} - 180 x^{3} + 16 x^{2} + 14 x - 1$ |
$22$ |
[10,6] |
$23^{20}\cdot 47^{2}$ |
$2$ |
$24.5438841614$ |
$118.57232216797493$ |
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$15$ |
$10146146.0999$ |
| 22.14.379...009.1 |
$x^{22} - x^{21} - 16 x^{20} + 27 x^{19} + 68 x^{18} - 193 x^{17} + 15 x^{16} + 436 x^{15} - 469 x^{14} - 26 x^{13} + 234 x^{12} - 345 x^{11} + 554 x^{10} - 110 x^{9} - 487 x^{8} + 401 x^{7} + 17 x^{6} - 196 x^{5} + 76 x^{4} + 32 x^{3} - 18 x^{2} - 2 x + 1$ |
$22$ |
[14,4] |
$23^{20}\cdot 47^{2}$ |
$2$ |
$24.5438841614$ |
$118.57232216797493$ |
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$17$ |
$24016183.4425$ |
| 22.6.379...009.1 |
$x^{22} - x^{21} + 5 x^{20} - 13 x^{19} + 3 x^{18} - 23 x^{17} - 63 x^{16} + 117 x^{15} + 79 x^{14} + 221 x^{13} + 156 x^{12} + 15 x^{11} - 1069 x^{10} - 1131 x^{9} - 164 x^{8} + 1812 x^{7} + 1646 x^{6} - 690 x^{5} - 1234 x^{4} - 363 x^{3} - 6 x^{2} + 10 x + 1$ |
$22$ |
[6,8] |
$23^{20}\cdot 47^{2}$ |
$2$ |
$24.5438841614$ |
$118.57232216797493$ |
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$13$ |
$4141006.01086$ |
| 22.10.379...009.2 |
$x^{22} - 2 x^{21} - 10 x^{20} + 30 x^{19} + 20 x^{18} - 150 x^{17} + 9 x^{16} + 368 x^{15} + 116 x^{14} - 520 x^{13} - 753 x^{12} + 353 x^{11} + 1135 x^{10} + 407 x^{9} - 467 x^{8} - 1035 x^{7} - 43 x^{6} + 309 x^{5} + 310 x^{4} + 160 x^{3} - 227 x^{2} - 59 x + 47$ |
$22$ |
[10,6] |
$23^{20}\cdot 47^{2}$ |
$2$ |
$24.5438841614$ |
$118.57232216797493$ |
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$15$ |
$10678633.8472$ |
| 22.14.379...009.2 |
$x^{22} - 3 x^{21} - 10 x^{20} + 29 x^{19} + 22 x^{18} - 50 x^{17} - 4 x^{16} - 40 x^{15} - 36 x^{14} + 30 x^{13} + 27 x^{12} + 115 x^{11} + 27 x^{10} + 30 x^{9} - 36 x^{8} - 40 x^{7} - 4 x^{6} - 50 x^{5} + 22 x^{4} + 29 x^{3} - 10 x^{2} - 3 x + 1$ |
$22$ |
[14,4] |
$23^{20}\cdot 47^{2}$ |
$2$ |
$24.5438841614$ |
$118.57232216797493$ |
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$17$ |
$24067678.7128$ |
| 22.10.719...104.1 |
$x^{22} + x^{20} - 33 x^{18} - 55 x^{16} + 243 x^{14} + 373 x^{12} - 608 x^{10} - 633 x^{8} + 334 x^{6} + 222 x^{4} + 17 x^{2} - 1$ |
$22$ |
[10,6] |
$2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$15$ |
$460738076.984$ |
| 22.14.719...104.1 |
$x^{22} - 7 x^{20} - 7 x^{18} + 74 x^{16} + 2 x^{14} - 223 x^{12} + 52 x^{10} + 221 x^{8} - 86 x^{6} - 41 x^{4} + 14 x^{2} - 1$ |
$22$ |
[14,4] |
$2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$17$ |
$1184851889.99$ |
| 22.18.719...104.1 |
$x^{22} - 14 x^{20} + 64 x^{18} - 52 x^{16} - 451 x^{14} + 1535 x^{12} - 2054 x^{10} + 1332 x^{8} - 396 x^{6} + 30 x^{4} + 7 x^{2} - 1$ |
$22$ |
[18,2] |
$2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$19$ |
$2743636898.8$ |
| 22.2.719...104.1 |
$x^{22} + 24 x^{20} + 220 x^{18} + 980 x^{16} + 2267 x^{14} + 2696 x^{12} + 1324 x^{10} - 265 x^{8} - 563 x^{6} - 215 x^{4} - 29 x^{2} - 1$ |
$22$ |
[2,10] |
$2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$11$ |
$82577277.7619$ |
| 22.6.719...104.1 |
$x^{22} + 13 x^{20} + 58 x^{18} + 76 x^{16} - 157 x^{14} - 555 x^{12} - 497 x^{10} - 62 x^{8} + 93 x^{6} + 22 x^{4} - 4 x^{2} - 1$ |
$22$ |
[6,8] |
$2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$13$ |
$183099783.783$ |
| 22.10.719...104.2 |
$x^{22} - 11 x^{20} + 9 x^{18} + 180 x^{16} - 153 x^{14} - 945 x^{12} - 550 x^{10} + 245 x^{8} + 165 x^{6} - 9 x^{4} - 12 x^{2} - 1$ |
$22$ |
[10,6] |
$2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$15$ |
$550392576.427$ |
| 22.14.719...104.2 |
$x^{22} - 14 x^{20} + 64 x^{18} - 75 x^{16} - 198 x^{14} + 523 x^{12} - 122 x^{10} - 531 x^{8} + 386 x^{6} - 16 x^{4} - 16 x^{2} - 1$ |
$22$ |
[14,4] |
$2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$17$ |
$1048235250.12$ |
| 22.18.719...104.2 |
$x^{22} - 10 x^{20} + 12 x^{18} + 145 x^{16} - 502 x^{14} + 434 x^{12} + 331 x^{10} - 775 x^{8} + 484 x^{6} - 139 x^{4} + 19 x^{2} - 1$ |
$22$ |
[18,2] |
$2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$19$ |
$2666560227.43$ |
| 22.6.719...104.2 |
$x^{22} + 16 x^{20} + 85 x^{18} + 166 x^{16} - 21 x^{14} - 476 x^{12} - 477 x^{10} + 83 x^{8} + 328 x^{6} + 143 x^{4} + 14 x^{2} - 1$ |
$22$ |
[6,8] |
$2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$13$ |
$181073374.443$ |
| 22.10.719...104.3 |
$x^{22} + 2 x^{20} - 17 x^{18} - 26 x^{16} + 93 x^{14} + 114 x^{12} - 157 x^{10} - 202 x^{8} + 13 x^{6} + 44 x^{4} - 3 x^{2} - 1$ |
$22$ |
[10,6] |
$2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$15$ |
$425939887.407$ |
| 22.14.719...104.3 |
$x^{22} - 5 x^{20} - 20 x^{18} + 90 x^{16} + 144 x^{14} - 445 x^{12} - 333 x^{10} + 572 x^{8} - 107 x^{6} - 50 x^{4} + 15 x^{2} - 1$ |
$22$ |
[14,4] |
$2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$17$ |
$1094333914.95$ |
| 22.6.719...104.3 |
$x^{22} + 9 x^{20} + 18 x^{18} - 52 x^{16} - 221 x^{14} - 121 x^{12} + 384 x^{10} + 550 x^{8} + 179 x^{6} - 39 x^{4} - 16 x^{2} - 1$ |
$22$ |
[6,8] |
$2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$13$ |
$157258272.203$ |
| 22.10.719...104.4 |
$x^{22} + 8 x^{20} - 19 x^{18} - 215 x^{16} - 66 x^{14} + 1115 x^{12} + 905 x^{10} - 282 x^{8} - 205 x^{6} + 43 x^{4} + 5 x^{2} - 1$ |
$22$ |
[10,6] |
$2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$15$ |
$470025358.505$ |
| 22.14.719...104.4 |
$x^{22} - 7 x^{20} - 7 x^{18} + 97 x^{16} - 21 x^{14} - 269 x^{12} + 29 x^{10} + 198 x^{8} - 40 x^{6} - 41 x^{4} + 14 x^{2} - 1$ |
$22$ |
[14,4] |
$2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$17$ |
$1258786005.7$ |
| 22.10.719...104.5 |
$x^{22} + 9 x^{20} + 18 x^{18} - 29 x^{16} - 83 x^{14} + 40 x^{12} + 108 x^{10} - 25 x^{8} - 51 x^{6} + 7 x^{4} + 7 x^{2} - 1$ |
$22$ |
[10,6] |
$2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$15$ |
$420318143.254$ |
| 22.14.719...104.5 |
$x^{22} - 14 x^{20} + 64 x^{18} - 75 x^{16} - 175 x^{14} + 339 x^{12} + 200 x^{10} - 370 x^{8} - 166 x^{6} + 53 x^{4} + 7 x^{2} - 1$ |
$22$ |
[14,4] |
$2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$17$ |
$1109277573.58$ |
| 22.10.719...104.6 |
$x^{22} + 2 x^{20} - 17 x^{18} - 26 x^{16} + 93 x^{14} + 91 x^{12} - 180 x^{10} - 87 x^{8} + 59 x^{6} + 21 x^{4} - 3 x^{2} - 1$ |
$22$ |
[10,6] |
$2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$15$ |
$472033930.885$ |
| 22.14.719...104.6 |
$x^{22} - 7 x^{20} - 7 x^{18} + 97 x^{16} - 67 x^{14} - 338 x^{12} + 512 x^{10} + 14 x^{8} - 362 x^{6} + 166 x^{4} - 9 x^{2} - 1$ |
$22$ |
[14,4] |
$2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$17$ |
$1121614550.16$ |
| 22.10.719...104.7 |
$x^{22} + 4 x^{20} - 22 x^{18} - 70 x^{16} + 108 x^{14} + 198 x^{12} - 250 x^{10} - 73 x^{8} + 108 x^{6} + 11 x^{4} - 13 x^{2} - 1$ |
$22$ |
[10,6] |
$2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$15$ |
$436952227.13$ |
| 22.10.719...104.8 |
$x^{22} + 8 x^{20} + 4 x^{18} - 54 x^{16} - 20 x^{14} + 103 x^{12} + 31 x^{10} - 75 x^{8} - 21 x^{6} + 20 x^{4} + 5 x^{2} - 1$ |
$22$ |
[10,6] |
$2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$15$ |
$471956139.939$ |
| 22.10.719...104.9 |
$x^{22} + 8 x^{20} + 4 x^{18} - 100 x^{16} - 181 x^{14} + 287 x^{12} + 767 x^{10} + 132 x^{8} - 274 x^{6} + 43 x^{4} + 5 x^{2} - 1$ |
$22$ |
[10,6] |
$2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$15$ |
$500318135.958$ |
| 22.10.719...104.10 |
$x^{22} + 3 x^{20} - 44 x^{18} - 59 x^{16} + 409 x^{14} + 318 x^{12} - 965 x^{10} - 415 x^{8} + 417 x^{6} + 109 x^{4} - 2 x^{2} - 1$ |
$22$ |
[10,6] |
$2^{22}\cdot 23^{20}$ |
$2$ |
$34.5911015298$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$15$ |
$459926060.533$ |
| 22.10.719...104.11 |
$x^{22} + 4 x^{20} - 22 x^{18} - 93 x^{16} + 131 x^{14} + 589 x^{12} - 411 x^{10} - 1384 x^{8} + 821 x^{6} + 885 x^{4} - 473 x^{2} - 1$ |
$22$ |
[10,6] |
$2^{22}\cdot 23^{20}$ |
$2$ |
$34.59110152983455$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$15$ |
$441972416.1599637$ |
| 22.22.159...736.1 |
$x^{22} - 34 x^{20} + 492 x^{18} - 3983 x^{16} + 19949 x^{14} - 64494 x^{12} + 136185 x^{10} - 185894 x^{8} + 158865 x^{6} - 79911 x^{4} + 21056 x^{2} - 2209$ |
$22$ |
[22,0] |
$2^{22}\cdot 23^{20}\cdot 47^{2}$ |
$3$ |
$49.0877683229$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$21$ |
$318070378232$ |
| 22.22.159...736.2 |
$x^{22} - 34 x^{20} + 492 x^{18} - 3983 x^{16} + 19926 x^{14} - 64218 x^{12} + 134943 x^{10} - 183272 x^{8} + 156243 x^{6} - 78922 x^{4} + 21056 x^{2} - 2209$ |
$22$ |
[22,0] |
$2^{22}\cdot 23^{20}\cdot 47^{2}$ |
$3$ |
$49.0877683229$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$21$ |
$329717697236$ |
| 22.22.159...736.3 |
$x^{22} - 30 x^{20} + 384 x^{18} - 2778 x^{16} + 12652 x^{14} - 38127 x^{12} + 77539 x^{10} - 106223 x^{8} + 95755 x^{6} - 53838 x^{4} + 16873 x^{2} - 2209$ |
$22$ |
[22,0] |
$2^{22}\cdot 23^{20}\cdot 47^{2}$ |
$3$ |
$49.08776832289523$ |
|
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
trivial |
$2$ |
$21$ |
$304772134710.70905$ |
| 22.2.184...129.1 |
$x^{22} - 2 x^{21} + 16 x^{20} + 12 x^{19} - 55 x^{18} + 482 x^{17} - 2477 x^{16} + 1764 x^{15} - 26905 x^{14} - 8523 x^{13} - 179279 x^{12} - 129306 x^{11} - 552925 x^{10} - 120476 x^{9} - 752931 x^{8} + 162572 x^{7} - 958963 x^{6} + 202039 x^{5} - 1129686 x^{4} + 1534908 x^{3} - 1835434 x^{2} + 973620 x - 247433$ |
$22$ |
[2,10] |
$23^{20}\cdot 47^{6}$ |
$2$ |
$49.4266396108$ |
$118.57232216797493$ |
|
|
? |
$C_2^{10}:C_{11}$ (as 22T23) |
$[2, 2, 2, 4]$ |
$2$ |
$11$ |
$113968730.636$ |
