| 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 |
| 22.0.581...643.1 |
$x^{22} - 3 x^{11} + 3$ |
$22$ |
[0,11] |
$-\,3^{21}\cdot 11^{18}$ |
$2$ |
$20.2993665386$ |
$24.69945335406008$ |
|
|
? |
$C_2\times F_{11}$ (as 22T6) |
trivial |
$6$ |
$10$ |
$1362288.49255$ |
| 22.2.639...073.1 |
$x^{22} - x^{21} + 14 x^{19} - 11 x^{18} - 42 x^{17} + 99 x^{16} + 27 x^{15} - 297 x^{14} + 205 x^{13} + 473 x^{12} - 780 x^{11} - 121 x^{10} + 1273 x^{9} - 891 x^{8} - 915 x^{7} + 1485 x^{6} - 27 x^{5} - 1166 x^{4} + 1016 x^{3} - 429 x^{2} + 98 x - 8$ |
$22$ |
[2,10] |
$3^{21}\cdot 11^{19}$ |
$2$ |
$22.6369815399$ |
$24.69945335406008$ |
|
|
? |
$C_2\times F_{11}$ (as 22T6) |
trivial |
$2$ |
$11$ |
$5215069.85605$ |
| 22.2.397...125.1 |
$x^{22} - x^{11} - 1$ |
$22$ |
[2,10] |
$5^{11}\cdot 11^{22}$ |
$2$ |
$24.5967477525$ |
$29.928334099511996$ |
|
|
✓ |
$C_2\times F_{11}$ (as 22T6) |
trivial |
$2$ |
$11$ |
$4376192.65488$ |
| 22.0.874...875.1 |
$x^{22} - 11 x^{21} + 55 x^{20} - 154 x^{19} + 220 x^{18} + 44 x^{17} - 913 x^{16} + 1991 x^{15} - 1958 x^{14} - 275 x^{13} + 3795 x^{12} - 5801 x^{11} + 4323 x^{10} - 517 x^{9} - 2475 x^{8} + 2772 x^{7} - 1188 x^{6} - 330 x^{5} + 803 x^{4} - 550 x^{3} + 209 x^{2} - 44 x + 4$ |
$22$ |
[0,11] |
$-\,5^{10}\cdot 11^{23}$ |
$2$ |
$25.4942567152$ |
$29.928334099511996$ |
|
|
? |
$C_2\times F_{11}$ (as 22T6) |
trivial |
$2$ |
$10$ |
$9094108.72092$ |
| 22.0.349...016.1 |
$x^{22} - 2 x^{11} + 2$ |
$22$ |
[0,11] |
$-\,2^{32}\cdot 11^{22}$ |
$2$ |
$30.1477216638$ |
$36.68253605613202$ |
|
|
✓ |
$C_2\times F_{11}$ (as 22T6) |
trivial |
$4$ |
$10$ |
$95678654.2598$ |
| 22.0.813...824.1 |
$x^{22} + 9$ |
$22$ |
[0,11] |
$-\,2^{22}\cdot 3^{20}\cdot 11^{18}$ |
$3$ |
$38.62114556$ |
$46.99265769833527$ |
|
|
? |
$C_2\times F_{11}$ (as 22T6) |
trivial |
$4$ |
$10$ |
$1426670983.37$ |
| 22.2.243...472.1 |
$x^{22} - 3$ |
$22$ |
[2,10] |
$2^{22}\cdot 3^{21}\cdot 11^{18}$ |
$3$ |
$40.5987330771$ |
$49.39890670812016$ |
|
|
? |
$C_2\times F_{11}$ (as 22T6) |
trivial |
$2$ |
$11$ |
$2212360251.73$ |
| 22.0.716...768.1 |
$x^{22} + 2$ |
$22$ |
[0,11] |
$-\,2^{43}\cdot 11^{22}$ |
$2$ |
$42.6353168517$ |
$51.87693999282197$ |
|
|
✓ |
$C_2\times F_{11}$ (as 22T6) |
trivial |
$2$ |
$10$ |
$3129917735.0$ |
| 22.2.716...768.1 |
$x^{22} - 2$ |
$22$ |
[2,10] |
$2^{43}\cdot 11^{22}$ |
$2$ |
$42.6353168517$ |
$51.87693999282197$ |
|
|
✓ |
$C_2\times F_{11}$ (as 22T6) |
trivial |
$2$ |
$11$ |
$2391349702.91$ |
| 22.2.388...125.1 |
$x^{22} - 5$ |
$22$ |
[2,10] |
$5^{21}\cdot 11^{22}$ |
$2$ |
$51.12005656$ |
$62.20083026054015$ |
|
|
? |
$C_2\times F_{11}$ (as 22T6) |
trivial |
$2$ |
$11$ |
$13513704873.9$ |
| 22.0.168...728.1 |
$x^{22} - 88 x^{11} + 2048$ |
$22$ |
[0,11] |
$-\,2^{20}\cdot 7^{11}\cdot 11^{22}$ |
$3$ |
$54.6519091334$ |
$66.49824652345667$ |
✓ |
|
? |
$C_2\times F_{11}$ (as 22T6) |
$[22]$ |
$2$ |
$10$ |
$2013788572.23$ |
| 22.0.265...144.1 |
$x^{22} - 11 x^{21} + 44 x^{20} - 33 x^{19} - 264 x^{18} + 495 x^{17} + 1331 x^{16} - 5698 x^{15} + 3619 x^{14} + 13915 x^{13} + 14498 x^{12} - 61939 x^{11} - 78386 x^{10} + 27313 x^{9} + 373593 x^{8} - 284306 x^{7} + 237369 x^{6} - 11385 x^{5} + 47520 x^{4} + 99 x^{3} + 4334 x^{2} - 913 x + 45$ |
$22$ |
[0,11] |
$-\,2^{20}\cdot 7^{10}\cdot 11^{23}$ |
$3$ |
$55.7863338432$ |
$66.49824652345667$ |
✓ |
|
? |
$C_2\times F_{11}$ (as 22T6) |
$[22]$ |
$2$ |
$10$ |
$2013788572.23$ |
| 22.0.454...247.1 |
$x^{22} + 7$ |
$22$ |
[0,11] |
$-\,7^{21}\cdot 11^{22}$ |
$2$ |
$70.481831017$ |
$85.75945925242507$ |
|
|
? |
$C_2\times F_{11}$ (as 22T6) |
trivial |
$2$ |
$10$ |
$751006737052$ |
| 22.22.691...888.1 |
$x^{22} - 44 x^{20} + 836 x^{18} - 8976 x^{16} + 59840 x^{14} - 256256 x^{12} - 124 x^{11} + 704704 x^{10} + 2728 x^{9} - 1208064 x^{8} - 21824 x^{7} + 1208064 x^{6} + 76384 x^{5} - 619520 x^{4} - 109120 x^{3} + 123904 x^{2} + 43648 x + 3592$ |
$22$ |
[22,0] |
$2^{32}\cdot 7^{11}\cdot 11^{22}$ |
$3$ |
$79.7633741177$ |
$97.0528678636854$ |
|
|
? |
$C_2\times F_{11}$ (as 22T6) |
trivial |
$2$ |
$21$ |
$398119325026000$ |
| 22.22.108...824.1 |
$x^{22} - 55 x^{20} + 1177 x^{18} - 12551 x^{16} + 72050 x^{14} - 230406 x^{12} - 776 x^{11} + 417890 x^{10} + 1144 x^{9} - 424182 x^{8} + 4048 x^{7} + 227469 x^{6} - 7920 x^{5} - 56419 x^{4} + 2904 x^{3} + 4389 x^{2} + 88 x - 35$ |
$22$ |
[22,0] |
$2^{32}\cdot 7^{10}\cdot 11^{23}$ |
$3$ |
$81.4190444131$ |
$97.0528678636854$ |
|
|
? |
$C_2\times F_{11}$ (as 22T6) |
trivial |
$2$ |
$21$ |
$430410424025000$ |
| 22.0.162...000.1 |
$x^{22} + 5$ |
$22$ |
[0,11] |
$-\,2^{22}\cdot 5^{21}\cdot 11^{22}$ |
$3$ |
$102.24011312$ |
$124.4016605210803$ |
|
|
✓ |
$C_2\times F_{11}$ (as 22T6) |
$[2]$ |
$2$ |
$10$ |
$26146397217800$ |
| 22.0.748...904.1 |
$x^{22} + 6$ |
$22$ |
[0,11] |
$-\,2^{43}\cdot 3^{21}\cdot 11^{22}$ |
$3$ |
$121.675578521$ |
$148.04995369173014$ |
|
|
✓ |
$C_2\times F_{11}$ (as 22T6) |
$[2]$ |
$2$ |
$10$ |
$185238267204000$ |
| 22.2.748...904.1 |
$x^{22} - 6$ |
$22$ |
[2,10] |
$2^{43}\cdot 3^{21}\cdot 11^{22}$ |
$3$ |
$121.675578521$ |
$148.04995369173014$ |
|
|
✓ |
$C_2\times F_{11}$ (as 22T6) |
trivial |
$2$ |
$11$ |
$377922606130000$ |
| 22.2.190...088.1 |
$x^{22} - 7$ |
$22$ |
[2,10] |
$2^{22}\cdot 7^{21}\cdot 11^{22}$ |
$3$ |
$140.963662034$ |
$171.51891850485015$ |
|
|
✓ |
$C_2\times F_{11}$ (as 22T6) |
trivial |
$2$ |
$11$ |
$2507352098510000$ |
