| 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 |
| 22.0.641...828.1 |
$x^{22} - x^{21} + 3 x^{20} - 7 x^{19} + 11 x^{18} - 18 x^{17} + 29 x^{16} - 40 x^{15} + 53 x^{14} - 67 x^{13} + 79 x^{12} - 87 x^{11} + 92 x^{10} - 90 x^{9} + 83 x^{8} - 73 x^{7} + 59 x^{6} - 43 x^{5} + 30 x^{4} - 18 x^{3} + 9 x^{2} - 4 x + 1$ |
$22$ |
[0,11] |
$-\,2^{2}\cdot 2029\cdot 7909899338257898069783$ |
$3$ |
$14.8959694347$ |
$6359356409154.484$ |
|
|
✓ |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$10$ |
$9202.86473748$ |
| 22.0.103...363.1 |
$x^{22} - 5 x^{21} + 15 x^{20} - 35 x^{19} + 68 x^{18} - 114 x^{17} + 170 x^{16} - 230 x^{15} + 285 x^{14} - 325 x^{13} + 343 x^{12} - 335 x^{11} + 306 x^{10} - 258 x^{9} + 202 x^{8} - 146 x^{7} + 97 x^{6} - 59 x^{5} + 32 x^{4} - 16 x^{3} + 7 x^{2} - 2 x + 1$ |
$22$ |
[0,11] |
$-\,79\cdot 22109\cdot 59513372976908430233$ |
$3$ |
$15.2258766495$ |
$10195426027811.246$ |
|
|
? |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$10$ |
$14889.9809115$ |
| 22.2.635...313.1 |
$x^{22} - x^{21} + 5 x^{20} - 8 x^{19} + 16 x^{18} - 27 x^{17} + 41 x^{16} - 61 x^{15} + 80 x^{14} - 104 x^{13} + 121 x^{12} - 138 x^{11} + 143 x^{10} - 142 x^{9} + 131 x^{8} - 112 x^{7} + 89 x^{6} - 64 x^{5} + 43 x^{4} - 24 x^{3} + 12 x^{2} - 4 x + 1$ |
$22$ |
[2,10] |
$60821\cdot 1487459\cdot 7024799976319967$ |
$3$ |
$16.5319546621$ |
$25209617799123.895$ |
|
|
✓ |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$11$ |
$66805.8364906$ |
| 22.2.890...989.1 |
$x^{22} - 2 x^{21} + 6 x^{20} - 10 x^{19} + 17 x^{18} - 21 x^{17} + 22 x^{16} - 15 x^{15} - 5 x^{14} + 38 x^{13} - 83 x^{12} + 135 x^{11} - 185 x^{10} + 221 x^{9} - 234 x^{8} + 222 x^{7} - 187 x^{6} + 138 x^{5} - 88 x^{4} + 47 x^{3} - 20 x^{2} + 6 x - 1$ |
$22$ |
[2,10] |
$34092855421\cdot 26129523845912209$ |
$2$ |
$16.7876797584$ |
$29846776688584.93$ |
|
|
? |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$11$ |
$58031.388562$ |
| 22.4.255...823.1 |
$x^{22} - x^{21} - 4 x^{20} + 5 x^{19} + 9 x^{18} - 14 x^{17} - 15 x^{16} + 28 x^{15} + 20 x^{14} - 44 x^{13} - 20 x^{12} + 55 x^{11} + 15 x^{10} - 55 x^{9} - 9 x^{8} + 45 x^{7} + x^{6} - 28 x^{5} + 2 x^{4} + 12 x^{3} - 2 x^{2} - 3 x + 1$ |
$22$ |
[4,9] |
$-\,13\cdot 769\cdot 941\cdot 27630898417\cdot 98112787247$ |
$5$ |
$19.5527649214$ |
$159694503199018.72$ |
|
|
? |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$12$ |
$336664.263278$ |
| 22.4.120...063.1 |
$x^{22} - 3 x^{21} + 2 x^{20} + 6 x^{19} - 15 x^{18} + 11 x^{17} + 10 x^{16} - 31 x^{15} + 28 x^{14} + 2 x^{13} - 32 x^{12} + 35 x^{11} - 11 x^{10} - 16 x^{9} + 25 x^{8} - 14 x^{7} - 4 x^{6} + 10 x^{5} - 8 x^{4} + 2 x^{3} + 2 x^{2} - 2 x + 1$ |
$22$ |
[4,9] |
$-\,13\cdot 9292748844744727822944291851$ |
$2$ |
$20.9851979667$ |
$347571194119537.9$ |
|
|
? |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$12$ |
$1008504.24777$ |
| 22.0.335...163.1 |
$x^{22} - x + 1$ |
$22$ |
[0,11] |
$-\,3697\cdot 90772326303985278570534379$ |
$2$ |
$21.9827464488$ |
$579297238337827.4$ |
|
|
✓ |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$10$ |
$685583.046278$ |
| 22.2.347...005.1 |
$x^{22} - x - 1$ |
$22$ |
[2,10] |
$5\cdot 69454092876521107983605569601$ |
$2$ |
$22.0169739943$ |
$589296584397538.8$ |
|
|
✓ |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$11$ |
$912353.207873$ |
| 22.6.199...337.1 |
$x^{22} - 3 x^{21} + 7 x^{20} - 13 x^{19} + 18 x^{18} - 21 x^{17} + 18 x^{16} - 9 x^{15} - 5 x^{14} + 16 x^{13} - 24 x^{12} + 25 x^{11} - 16 x^{10} + 6 x^{9} + 3 x^{8} - 12 x^{7} + 9 x^{6} - 6 x^{5} + 4 x^{4} + 2 x^{3} - x^{2} + x - 1$ |
$22$ |
[6,8] |
$3^{4}\cdot 7^{2}\cdot 59\cdot 5851\cdot 36319\cdot 400764924995207263$ |
$6$ |
$26.4677839917$ |
|
|
|
? |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$13$ |
$21280189.8381$ |
| 22.6.190...229.1 |
$x^{22} - x^{21} - 2 x^{20} + 6 x^{19} - 4 x^{18} - 5 x^{17} + 13 x^{16} - 11 x^{15} + 13 x^{13} - 18 x^{12} + 11 x^{11} + 3 x^{10} - 14 x^{9} + 15 x^{8} - 7 x^{7} - 3 x^{6} + 8 x^{5} - 8 x^{4} + 2 x^{3} + x^{2} - 2 x + 1$ |
$22$ |
[6,8] |
$1671032183\cdot 114013219157456550332963$ |
$2$ |
$29.3271594903$ |
$1.3802889498200804e+16$ |
|
|
✓ |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$13$ |
$34540709.9251$ |
| 22.0.133...736.1 |
$x^{22} - 4 x + 4$ |
$22$ |
[0,11] |
$-\,2^{22}\cdot 195359\cdot 16280669397912337149101$ |
$3$ |
$35.57491657$ |
|
|
|
? |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$10$ |
$410347496.209$ |
| 22.2.245...305.1 |
$x^{22} - 4 x - 1$ |
$22$ |
[2,10] |
$5\cdot 549569\cdot 7345029585473\cdot 1214169483036053$ |
$4$ |
$36.571974928$ |
$1.5654260155512237e+17$ |
|
|
? |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$11$ |
$364755463.699$ |
| 22.2.245...568.1 |
$x^{22} - 2 x - 1$ |
$22$ |
[2,10] |
$2^{23}\cdot 19\cdot 37\cdot 68639\cdot 132989\cdot 10028509\cdot 45394463$ |
$7$ |
$36.571998089$ |
|
|
|
✓ |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$11$ |
$316078749.505$ |
| 22.2.382...368.1 |
$x^{22} - 4 x - 4$ |
$22$ |
[2,10] |
$2^{22}\cdot 12799\cdot 7125522021989286027857083$ |
$3$ |
$41.4374766838$ |
|
|
|
? |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$11$ |
$1530252550.22$ |
| 22.0.618...832.1 |
$x^{22} - 8 x + 8$ |
$22$ |
[0,11] |
$-\,2^{24}\cdot 37811\cdot 73885382563\cdot 13185438208339$ |
$4$ |
$42.3509575626$ |
|
|
|
? |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$10$ |
$1203822911.13$ |
| 22.0.691...784.1 |
$x^{22} - 2 x + 2$ |
$22$ |
[0,11] |
$-\,2^{22}\cdot 2659\cdot 113083\cdot 3816585709\cdot 143666171927$ |
$5$ |
$42.5678827942$ |
|
|
|
✓ |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$10$ |
$2012694892.47$ |
| 22.0.716...347.1 |
$x^{22} - x + 2$ |
$22$ |
[0,11] |
$-\,149\cdot 10391\cdot 1813613257\cdot 255000239631570429569$ |
$4$ |
$42.6353168358$ |
$8.461832839447615e+17$ |
|
|
✓ |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$10$ |
$4834683950.41$ |
| 22.2.740...752.1 |
$x^{22} - 2 x - 2$ |
$22$ |
[2,10] |
$2^{22}\cdot 23\cdot 131\cdot 58598249485727102960406401$ |
$4$ |
$42.7005829017$ |
|
|
|
✓ |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$11$ |
$3462625066.22$ |
| 22.2.814...704.1 |
$x^{22} - 8 x - 8$ |
$22$ |
[2,10] |
$2^{24}\cdot 17\cdot 103\cdot 929\cdot 4760449\cdot 6265858854995939$ |
$6$ |
$42.8846910302$ |
|
|
|
? |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$11$ |
$6734832264.14$ |
| 22.2.156...320.1 |
$x^{22} - 8 x - 4$ |
$22$ |
[2,10] |
$2^{26}\cdot 5\cdot 1213\cdot 2791\cdot 144349\cdot 1885069\cdot 5073819587$ |
$7$ |
$44.1822238667$ |
|
|
|
? |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$11$ |
$5313442979.16$ |
| 22.8.197...632.1 |
$x^{22} - 3 x^{21} - 2 x^{20} + 17 x^{19} - 15 x^{18} - 29 x^{17} + 62 x^{16} - x^{15} - 98 x^{14} + 77 x^{13} + 66 x^{12} - 131 x^{11} + 24 x^{10} + 98 x^{9} - 81 x^{8} - 17 x^{7} + 57 x^{6} - 25 x^{5} - 12 x^{4} + 14 x^{3} - 3 x^{2} - 2 x + 1$ |
$22$ |
[8,7] |
$-\,2^{6}\cdot 673\cdot 683\cdot 4730027\cdot 141935338646968028959691$ |
$5$ |
$49.5739103748$ |
|
|
|
✓ |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$14$ |
$50370489046.5$ |
| 22.2.100...448.1 |
$x^{22} - 8 x + 4$ |
$22$ |
[2,10] |
$2^{32}\cdot 41\cdot 27310206881\cdot 20871555702578003$ |
$4$ |
$53.3760613821$ |
|
|
|
? |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$11$ |
$50190160566.4$ |
| 22.2.183...805.1 |
$x^{22} - 3 x + 1$ |
$22$ |
[2,10] |
$5\cdot 141073679\cdot 259930232844232011712508929559$ |
$3$ |
$54.8579623874$ |
$1.3540552837802164e+19$ |
|
|
✓ |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$11$ |
$27087582193.6$ |
| 22.2.183...973.1 |
$x^{22} - 3 x - 1$ |
$22$ |
[2,10] |
$199\cdot 5653\cdot 40609\cdot 77303058683\cdot 51918454852529597$ |
$5$ |
$54.8579623967$ |
$1.3540552863017374e+19$ |
|
|
✓ |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$11$ |
$33827975772.8$ |
| 22.2.184...157.1 |
$x^{22} - 3 x - 2$ |
$22$ |
[2,10] |
$23\cdot 29\cdot 38153\cdot 1179789290960933\cdot 6130650674847779$ |
$5$ |
$54.8676823616$ |
$1.3566967150052741e+19$ |
|
|
✓ |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$11$ |
$149072131930$ |
| 22.20.282...876.1 |
$x^{22} - 3 x^{21} - 17 x^{20} + 53 x^{19} + 120 x^{18} - 388 x^{17} - 461 x^{16} + 1529 x^{15} + 1071 x^{14} - 3536 x^{13} - 1601 x^{12} + 4931 x^{11} + 1610 x^{10} - 4134 x^{9} - 1099 x^{8} + 2031 x^{7} + 485 x^{6} - 555 x^{5} - 128 x^{4} + 76 x^{3} + 18 x^{2} - 4 x - 1$ |
$22$ |
[20,1] |
$-\,2^{2}\cdot 5647\cdot 36767\cdot 31618751\cdot 10757635112949841811531$ |
$5$ |
$55.9464601959$ |
|
|
|
✓ |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$20$ |
$2102811538580$ |
| 22.0.100...795.1 |
$x^{22} - 9 x + 9$ |
$22$ |
[0,11] |
$-\,3^{20}\cdot 5\cdot 17\cdot 5791\cdot 24023\cdot 24426683885548437839$ |
$6$ |
$59.2744724236$ |
$1459078698808233.8$ |
|
|
? |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$10$ |
$64985594632.5$ |
| 22.2.137...573.1 |
$x^{22} - 9 x - 9$ |
$22$ |
[2,10] |
$3^{20}\cdot 3347\cdot 9801413\cdot 12010583914412253043$ |
$4$ |
$60.1169560699$ |
$1704122682026273.2$ |
|
|
? |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$11$ |
$85925242131.2$ |
| 22.0.338...163.1 |
$x^{22} - 3 x + 3$ |
$22$ |
[0,11] |
$-\,3^{21}\cdot 19\cdot 17047374542582189991184386859$ |
$3$ |
$62.6348797341$ |
$1624199890743315.0$ |
|
|
✓ |
$S_{22}$ (as 22T59) |
$[2]$ |
$2$ |
$10$ |
$40479483158.9$ |
| 22.0.357...568.1 |
$x^{22} - 2 x + 3$ |
$22$ |
[0,11] |
$-\,2^{23}\cdot 3^{22}\cdot 389\cdot 2377\cdot 1298173\cdot 11302473251$ |
$6$ |
$62.7850826556$ |
|
|
|
✓ |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$10$ |
$200633546832$ |
| 22.0.357...131.1 |
$x^{22} - x + 3$ |
$22$ |
[0,11] |
$-\,3^{22}\cdot 3613717\cdot 31493692631313871703527$ |
$3$ |
$62.7851022375$ |
|
|
|
✓ |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$10$ |
$180245371053$ |
| 22.2.357...973.1 |
$x^{22} - x - 3$ |
$22$ |
[2,10] |
$3^{21}\cdot 5923\cdot 40639\cdot 119687\cdot 1802347\cdot 6575500927$ |
$6$ |
$62.7851022375$ |
|
|
|
✓ |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$11$ |
$163854024718$ |
| 22.2.375...941.1 |
$x^{22} - 3 x - 3$ |
$22$ |
[2,10] |
$3^{21}\cdot 29\cdot 947\cdot 13070518094140389067501369$ |
$4$ |
$62.9281362641$ |
$1709835440845365.2$ |
|
|
✓ |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$11$ |
$180041517788$ |
| 22.0.454...263.1 |
$x^{22} - 4 x + 7$ |
$22$ |
[0,11] |
$-\,7^{21}\cdot 13\cdot 59\cdot 1033\cdot 102740849884626719$ |
$5$ |
$70.4818292903$ |
|
|
|
? |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$10$ |
$503061097989$ |
| 22.2.102...368.1 |
$x^{22} - 4 x + 2$ |
$22$ |
[2,10] |
$2^{43}\cdot 17\cdot 53\cdot 2503\cdot 200867\cdot 25795142163554521$ |
$6$ |
$73.1439266948$ |
|
|
|
✓ |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$11$ |
$926250200951$ |
| 22.2.102...973.1 |
$x^{22} - 8 x + 3$ |
$22$ |
[2,10] |
$3^{22}\cdot 776186653056977\cdot 4219793712070861$ |
$3$ |
$73.1439498285$ |
|
|
|
? |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$11$ |
$1224952834120$ |
| 22.2.102...552.1 |
$x^{22} - 4 x + 1$ |
$22$ |
[2,10] |
$2^{22}\cdot 41\cdot 47\cdot 12239\cdot 18575205197\cdot 55937599419533243$ |
$6$ |
$73.143949856$ |
|
|
|
✓ |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$11$ |
$1792315744680$ |
| 22.2.102...457.1 |
$x^{22} - 8 x - 1$ |
$22$ |
[2,10] |
$1557197693053\cdot 13663933092517\cdot 4830649421245657$ |
$3$ |
$73.143949856$ |
$3.205992479843581e+20$ |
|
|
? |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$11$ |
$1504635922170$ |
| 22.2.102...904.1 |
$x^{22} - 4 x - 2$ |
$22$ |
[2,10] |
$2^{43}\cdot 13\cdot 23\cdot 157667\cdot 247871284868164353811$ |
$5$ |
$73.1439730171$ |
|
|
|
✓ |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$11$ |
$2312263802260$ |
| 22.2.102...261.1 |
$x^{22} - 8 x - 5$ |
$22$ |
[2,10] |
$163\cdot 10247\cdot 146563\cdot 31782379\cdot 13215813098629700022313$ |
$5$ |
$73.1452051968$ |
$3.206597786811179e+20$ |
|
|
? |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$11$ |
$1292489012420$ |
| 22.2.106...688.1 |
$x^{22} - 4 x - 3$ |
$22$ |
[2,10] |
$2^{22}\cdot 3^{21}\cdot 197\cdot 64577\cdot 263672609\cdot 722676469$ |
$6$ |
$73.257601309$ |
|
|
|
✓ |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$11$ |
$1802812519730$ |
| 22.0.187...096.1 |
$x^{22} - 4 x + 8$ |
$22$ |
[0,11] |
$-\,2^{20}\cdot 13\cdot 2003\cdot 2837839\cdot 6318427\cdot 264541421\cdot 1449286253$ |
$7$ |
$75.1738448693$ |
$8.187092076515809e+17$ |
|
|
? |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$10$ |
$2268922001860$ |
| 22.2.187...088.1 |
$x^{22} - 4 x - 8$ |
$22$ |
[2,10] |
$2^{20}\cdot 38527475164417\cdot 4646204923790201323589$ |
$3$ |
$75.1738450923$ |
$8.187092343733974e+17$ |
|
|
? |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$11$ |
$4603560574540$ |
| 22.20.245...088.1 |
$x^{22} - x^{21} - 22 x^{20} + 21 x^{19} + 204 x^{18} - 185 x^{17} - 1038 x^{16} + 888 x^{15} + 3162 x^{14} - 2526 x^{13} - 5908 x^{12} + 4344 x^{11} + 6683 x^{10} - 4429 x^{9} - 4388 x^{8} + 2536 x^{7} + 1577 x^{6} - 744 x^{5} - 294 x^{4} + 95 x^{3} + 28 x^{2} - 4 x - 1$ |
$22$ |
[20,1] |
$-\,2^{4}\cdot 3^{4}\cdot 19^{2}\cdot 31\cdot 65380800771598157\cdot 258573494153022619$ |
$6$ |
$76.092399426$ |
|
|
|
? |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$20$ |
$75826530958700$ |
| 22.0.375...688.1 |
$x^{22} - 2 x + 4$ |
$22$ |
[0,11] |
$-\,2^{20}\cdot 35\!\cdots\!63$ |
$2$ |
$77.5800303821$ |
$1.1578296745481853e+18$ |
|
|
? |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$10$ |
$4494072113760$ |
| 22.2.375...680.1 |
$x^{22} - 2 x - 4$ |
$22$ |
[2,10] |
$2^{20}\cdot 5\cdot 261563\cdot 273749027024197539409418576947$ |
$4$ |
$77.5800304972$ |
$1.1578296934433628e+18$ |
|
|
? |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$11$ |
$4719003322200$ |
| 22.0.150...347.1 |
$x^{22} - 3 x + 4$ |
$22$ |
[0,11] |
$-\,59\cdot 71693\cdot 246874073979902203\cdot 1437810054059874727$ |
$4$ |
$82.6254615394$ |
$1.2253294815125667e+21$ |
|
|
✓ |
$S_{22}$ (as 22T59) |
$[2]$ |
$2$ |
$10$ |
$4233746855930$ |
| 22.0.150...315.1 |
$x^{22} - x + 4$ |
$22$ |
[0,11] |
$-\,5\cdot 356579\cdot 84\!\cdots\!97$ |
$3$ |
$82.6259201382$ |
$1.225404294441367e+21$ |
|
|
✓ |
$S_{22}$ (as 22T59) |
$[2]$ |
$2$ |
$10$ |
$6589731323400$ |
| 22.2.150...157.1 |
$x^{22} - x - 4$ |
$22$ |
[2,10] |
$239\cdot 13411\cdot 21198679507\cdot 22099931293386408281220419$ |
$4$ |
$82.6259201382$ |
$1.2254042944413717e+21$ |
|
|
✓ |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$11$ |
$10705394162100$ |
| 22.2.154...397.1 |
$x^{22} - 5 x + 3$ |
$22$ |
[2,10] |
$3^{21}\cdot 3631\cdot 500891\cdot 4580831\cdot 17755434988447349$ |
$5$ |
$82.7387014563$ |
|
|
|
? |
$S_{22}$ (as 22T59) |
$[2]$ |
$2$ |
$11$ |
$1118742824550$ |
