| 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 |
| 22.0.119...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 |
$6$ |
$10$ |
$1462413343710000000000000$ |
| 22.10.254...184.1 |
$x^{22} - 4 x^{21} - 92 x^{20} + 978 x^{19} - 23031 x^{18} + 208542 x^{17} + 3327324 x^{16} - 36397800 x^{15} - 19963545 x^{14} - 406653528 x^{13} - 16539946488 x^{12} + 256034067942 x^{11} + 682357346031 x^{10} - 13494358927986 x^{9} + 9822827363220 x^{8} + 261815058820176 x^{7} - 813912422758992 x^{6} - 647257611403968 x^{5} + 8751031478070272 x^{4} - 24165278101734848 x^{3} + 30990808995877088 x^{2} - 13115399746724928 x - 2634468582334464$ |
$22$ |
[10,6] |
$2^{30}\cdot 3^{28}\cdot 7^{4}\cdot 23^{4}\cdot 137^{16}$ |
$5$ |
$939.63750836$ |
$16209.655612939698$ |
|
|
|
$C_2^{10}.A_{11}$ (as 22T49) |
trivial |
$2$ |
$15$ |
$739930020231000000000000000$ |
| 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 |
$2$ |
$17$ |
$852811169305000000000000000$ |
| 22.6.624...984.1 |
$x^{22} + 3 x^{20} - 36 x^{18} - 60 x^{16} + 213 x^{14} + 9 x^{12} - 114 x^{10} + 180 x^{8} - 108 x^{6} - 6 x^{4} + 36 x^{2} - 54$ |
$22$ |
[6,8] |
$2^{43}\cdot 3^{29}\cdot 7^{4}\cdot 23^{4}\cdot 137^{16}$ |
$5$ |
$1487.74683631$ |
|
|
|
|
$C_2^{11}.A_{11}$ (as 22T52) |
trivial |
$2$ |
$13$ |
$18112506929300000000000000000$ |
| 22.8.249...936.1 |
$x^{22} - 3 x^{20} - 36 x^{18} + 60 x^{16} + 213 x^{14} - 9 x^{12} - 114 x^{10} - 180 x^{8} - 108 x^{6} + 6 x^{4} + 36 x^{2} + 54$ |
$22$ |
[8,7] |
$-\,2^{45}\cdot 3^{29}\cdot 7^{4}\cdot 23^{4}\cdot 137^{16}$ |
$5$ |
$1584.51151135$ |
|
|
|
|
$C_2^{11}.A_{11}$ (as 22T52) |
trivial |
$2$ |
$14$ |
$17750647107900000000000000000$ |
| 22.8.333...480.1 |
$x^{22} - 8 x^{20} - 11 x^{18} + 234 x^{16} - 633 x^{14} + 30 x^{12} + 2835 x^{10} - 5934 x^{8} + 5448 x^{6} - 2104 x^{4} + 8 x^{2} + 80$ |
$22$ |
[8,7] |
$-\,2^{48}\cdot 3^{28}\cdot 5\cdot 7^{4}\cdot 23^{4}\cdot 137^{16}$ |
$6$ |
$1782.49769773$ |
|
|
|
|
$C_2^{11}.A_{11}$ (as 22T52) |
trivial |
$2$ |
$14$ |
$140217818601000000000000000000$ |
| 22.12.257...080.1 |
$x^{22} - 25 x^{20} + 244 x^{18} - 1152 x^{16} + 2229 x^{14} + 3057 x^{12} - 27810 x^{10} + 70572 x^{8} - 95244 x^{6} + 70846 x^{4} - 25252 x^{2} + 2470$ |
$22$ |
[12,5] |
$-\,2^{43}\cdot 3^{28}\cdot 5\cdot 7^{4}\cdot 13\cdot 19\cdot 23^{4}\cdot 137^{16}$ |
$8$ |
$1956.01428383$ |
|
|
|
|
$C_2^{11}.A_{11}$ (as 22T52) |
trivial |
$2$ |
$16$ |
$642145413743000000000000000000$ |
| 22.12.149...600.1 |
$x^{22} - 36 x^{20} + 549 x^{18} - 4638 x^{16} + 23559 x^{14} - 71010 x^{12} + 102675 x^{10} + 60498 x^{8} - 550584 x^{6} + 1014936 x^{4} - 865080 x^{2} + 291600$ |
$22$ |
[12,5] |
$-\,2^{48}\cdot 3^{30}\cdot 5^{2}\cdot 7^{4}\cdot 23^{4}\cdot 137^{16}$ |
$6$ |
$2119.21491054$ |
|
|
|
|
$C_2^{11}.A_{11}$ (as 22T52) |
trivial |
$2$ |
$16$ |
$1693786329280000000000000000000$ |
| 22.0.233...016.1 |
$x^{22} + 58 x^{20} + 1489 x^{18} + 22320 x^{16} + 216663 x^{14} + 1424964 x^{12} + 6438231 x^{10} + 19757580 x^{8} + 39484992 x^{6} + 46601624 x^{4} + 25144376 x^{2} + 898976$ |
$22$ |
[0,11] |
$-\,2^{45}\cdot 3^{28}\cdot 7^{4}\cdot 13\cdot 23^{4}\cdot 137^{16}\cdot 2161$ |
$7$ |
$2401.13774258$ |
|
|
|
|
$C_2^{11}.A_{11}$ (as 22T52) |
not computed |
$2$ |
$10$ |
|
| 22.14.935...064.1 |
$x^{22} - 58 x^{20} + 1489 x^{18} - 22320 x^{16} + 216663 x^{14} - 1424964 x^{12} + 6438231 x^{10} - 19757580 x^{8} + 39484992 x^{6} - 46601624 x^{4} + 25144376 x^{2} - 898976$ |
$22$ |
[14,4] |
$2^{47}\cdot 3^{28}\cdot 7^{4}\cdot 13\cdot 23^{4}\cdot 137^{16}\cdot 2161$ |
$7$ |
$2557.31035725$ |
|
|
|
|
$C_2^{11}.A_{11}$ (as 22T52) |
trivial |
$2$ |
$17$ |
$10304301830700000000000000000000$ |
| 22.14.126...600.1 |
$x^{22} - 74 x^{20} + 2449 x^{18} - 47772 x^{16} + 608919 x^{14} - 5307720 x^{12} + 32127975 x^{10} - 134044248 x^{8} + 373194336 x^{6} - 645946216 x^{4} + 597000440 x^{2} - 195030400$ |
$22$ |
[14,4] |
$2^{45}\cdot 3^{28}\cdot 5^{2}\cdot 7^{4}\cdot 23^{4}\cdot 59\cdot 137^{16}\cdot 1033$ |
$8$ |
$2879.0461724$ |
|
|
|
|
$C_2^{11}.A_{11}$ (as 22T52) |
trivial |
$2$ |
$17$ |
$171825983862000000000000000000000$ |
| 22.14.127...344.1 |
$x^{22} - 242454 x^{20} - 66254755944 x^{18} + 9988149125214624 x^{16} + 2412251307077297217168 x^{14} - 97126283753436220637656848 x^{12} - 36043439335840553783024429840880 x^{10} - 968324930877205693808500678923025440 x^{8} + 411693823788000055227773052463075223008512 x^{6} - 14674638475171337576102371060253129696887988224 x^{4} + 164949721485379801300637463025582558350584505753600 x^{2} - 571411117069770362003780702945732790998630818613760000$ |
$22$ |
[14,4] |
$2^{44}\cdot 3^{28}\cdot 7^{4}\cdot 13^{10}\cdot 23^{4}\cdot 137^{16}\cdot 2161^{10}$ |
$7$ |
$153679.147054$ |
|
|
|
|
$C_2^{10}.A_{11}$ (as 22T49) |
not computed |
$2$ |
$17$ |
|
| 24.4.280...125.1 |
$x^{24} + 5 x^{22} - 820 x^{21} + 850 x^{20} - 64060 x^{19} + 125490 x^{18} - 1019390 x^{17} + 2075810 x^{16} + 34430400 x^{15} - 113294671 x^{14} + 1533144620 x^{13} - 5066301515 x^{12} - 4871260730 x^{11} + 65826141760 x^{10} - 558545063332 x^{9} + 614861168640 x^{8} + 6017457010880 x^{7} - 9349627539690 x^{6} - 13528780472670 x^{5} + 30394404884437 x^{4} - 48843120535250 x^{3} - 12986475171105 x^{2} + 99571242500180 x - 185396573831840$ |
$24$ |
[4,10] |
$5^{39}\cdot 137^{16}$ |
$2$ |
$363.33449783152196$ |
$1181.321102877966$ |
|
|
|
$\GL(2,5)$ (as 24T1353) |
trivial |
$2$ |
$13$ |
$964408150830427800000000$ |
| 24.4.280...125.2 |
$x^{24} - 6 x^{23} - 44 x^{22} + 609 x^{21} - 329 x^{20} - 17961 x^{19} + 70111 x^{18} - 91491 x^{17} + 1723311 x^{16} + 2038739 x^{15} - 97705442 x^{14} + 398197922 x^{13} - 7336432 x^{12} + 879041527 x^{11} - 25909276027 x^{10} + 99136888897 x^{9} - 756578058337 x^{8} + 4220558346612 x^{7} - 7989019339872 x^{6} + 2124415621142 x^{5} - 6211071879401 x^{4} + 34521567288386 x^{3} - 56725055828156 x^{2} + 145508882897631 x - 169815998917611$ |
$24$ |
[4,10] |
$5^{39}\cdot 137^{16}$ |
$2$ |
$363.33449783152196$ |
$1181.321102877966$ |
|
|
|
$\GL(2,5)$ (as 24T1353) |
trivial |
$2$ |
$13$ |
$11949243702977367000000$ |
| 24.4.280...125.3 |
$x^{24} - 1500 x^{20} + 28890 x^{18} - 1136590 x^{16} + 20443191 x^{14} + 184328435 x^{12} - 1617555390 x^{10} + 5518780545 x^{8} + 3347456430 x^{6} - 7889170286 x^{4} - 7948851420 x^{2} + 1063027805$ |
$24$ |
[4,10] |
$5^{39}\cdot 137^{16}$ |
$2$ |
$363.33449783152196$ |
$1181.321102877966$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
not computed |
$2$ |
$13$ |
|
| 24.4.700...125.5 |
$x^{24} - 5 x^{23} + 60 x^{22} - 175 x^{21} + 2865 x^{20} + 7711 x^{19} + 17420 x^{18} + 696980 x^{17} + 1921510 x^{16} + 10674435 x^{15} + 77227228 x^{14} + 64378000 x^{13} + 1516710965 x^{12} - 2401223005 x^{11} - 2426592535 x^{10} - 37834143328 x^{9} - 19369508140 x^{8} + 51646472785 x^{7} + 99491024115 x^{6} + 51302383350 x^{5} - 73669438246 x^{4} - 94017187265 x^{3} - 27884166535 x^{2} + 2435644055 x + 834721805$ |
$24$ |
[4,10] |
$5^{41}\cdot 137^{16}$ |
$2$ |
$415.4838387485505$ |
$1181.321102877966$ |
|
|
? |
$\GL(2,5)$ (as 24T1353) |
$[2]$ |
$2$ |
$13$ |
$8076097306100833000000$ |
