| 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 |
| 22.18.276...125.1 |
$x^{22} - x^{21} - 19 x^{20} + 14 x^{19} + 121 x^{18} - 78 x^{17} - 261 x^{16} + 287 x^{15} - 160 x^{14} - 852 x^{13} + 1239 x^{12} + 1601 x^{11} - 1405 x^{10} - 1576 x^{9} + 348 x^{8} + 692 x^{7} + 274 x^{6} - 60 x^{5} - 159 x^{4} - 32 x^{3} + 22 x^{2} + 4 x - 1$ |
$22$ |
[18,2] |
$5^{11}\cdot 29^{2}\cdot 131^{2}\cdot 5399^{2}\cdot 367163^{2}$ |
$5$ |
$33.1212683614$ |
$6136288.465987807$ |
|
|
? |
$C_2\times S_{11}$ (as 22T47) |
trivial |
$2$ |
$19$ |
$1570808982.29$ |
| 22.18.367...125.1 |
$x^{22} - x^{21} - 22 x^{20} + 5 x^{19} + 191 x^{18} + 88 x^{17} - 819 x^{16} - 753 x^{15} + 1905 x^{14} + 2178 x^{13} - 2680 x^{12} - 3041 x^{11} + 2570 x^{10} + 2301 x^{9} - 1770 x^{8} - 1001 x^{7} + 811 x^{6} + 259 x^{5} - 211 x^{4} - 38 x^{3} + 25 x^{2} + 2 x - 1$ |
$22$ |
[18,2] |
$5^{11}\cdot 8674315276967^{2}$ |
$2$ |
$33.5496661146$ |
$6585710.013721755$ |
|
|
? |
$C_2\times S_{11}$ (as 22T47) |
trivial |
$2$ |
$19$ |
$2040269368.26$ |
| 22.18.409...729.1 |
$x^{22} - 3 x^{21} - 14 x^{20} + 42 x^{19} + 35 x^{18} - 82 x^{17} - 76 x^{16} - 508 x^{15} + 1938 x^{14} - 984 x^{13} - 5144 x^{12} + 9774 x^{11} + 1291 x^{10} - 17627 x^{9} + 8445 x^{8} + 12822 x^{7} - 10291 x^{6} - 3443 x^{5} + 4487 x^{4} - 121 x^{3} - 672 x^{2} + 130 x + 1$ |
$22$ |
[18,2] |
$23^{21}\cdot 47^{3}$ |
$2$ |
$33.7166533192$ |
$136.73511025656717$ |
|
|
? |
$C_{15}\times C_{420}$ (as 22T28) |
trivial |
$2$ |
$19$ |
$1999453068.78$ |
| 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 |
$2$ |
$19$ |
$2743636898.8$ |
| 22.18.719...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 |
$2$ |
$19$ |
$2666560227.43$ |
| 22.18.101...661.1 |
$x^{22} - 11 x^{21} + 40 x^{20} - 15 x^{19} - 254 x^{18} + 519 x^{17} + 310 x^{16} - 1970 x^{15} + 1107 x^{14} + 2977 x^{13} - 3993 x^{12} - 1171 x^{11} + 5121 x^{10} - 1997 x^{9} - 2876 x^{8} + 2700 x^{7} + 340 x^{6} - 1207 x^{5} + 283 x^{4} + 173 x^{3} - 80 x^{2} + 3 x + 1$ |
$22$ |
[18,2] |
$3363181\cdot 55029067682009^{2}$ |
$2$ |
$35.1410882696$ |
$13604143298.12233$ |
|
|
✓ |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$19$ |
$3109721457.4$ |
| 22.18.338...896.1 |
$x^{22} - 16 x^{20} + 105 x^{18} - 363 x^{16} + 700 x^{14} - 709 x^{12} + 248 x^{10} + 146 x^{8} - 135 x^{6} + 20 x^{4} + 5 x^{2} - 1$ |
$22$ |
[18,2] |
$2^{22}\cdot 2053^{2}\cdot 43747835269^{2}$ |
$3$ |
$37.112136067$ |
|
|
|
✓ |
$C_2^{10}.S_{11}$ (as 22T51) |
trivial |
$2$ |
$19$ |
$6802460318.29$ |
| 22.18.390...976.1 |
$x^{22} - 15 x^{20} + 91 x^{18} - 279 x^{16} + 417 x^{14} - 130 x^{12} - 453 x^{10} + 544 x^{8} - 66 x^{6} - 185 x^{4} + 75 x^{2} - 1$ |
$22$ |
[18,2] |
$2^{22}\cdot 137^{2}\cdot 293^{2}\cdot 11093^{2}\cdot 216649^{2}$ |
$5$ |
$37.3541218434$ |
|
|
|
✓ |
$C_2^{10}.S_{11}$ (as 22T51) |
trivial |
$2$ |
$19$ |
$7576192193.94$ |
| 22.18.165...392.1 |
$x^{22} - 23 x^{20} + 184 x^{18} - 598 x^{16} + 437 x^{14} + 1840 x^{12} - 4324 x^{10} + 2875 x^{8} + 253 x^{6} - 828 x^{4} + 253 x^{2} - 23$ |
$22$ |
[18,2] |
$2^{22}\cdot 23^{21}$ |
$2$ |
$39.8897313901$ |
|
|
|
? |
$C_{15}\times C_{420}$ (as 22T28) |
trivial |
$2$ |
$19$ |
$12568639506.3$ |
| 22.18.108...901.1 |
$x^{22} - 11 x^{21} + 40 x^{20} - 15 x^{19} - 254 x^{18} + 519 x^{17} + 309 x^{16} - 1962 x^{15} + 1086 x^{14} + 2984 x^{13} - 3923 x^{12} - 1318 x^{11} + 5184 x^{10} - 1751 x^{9} - 3296 x^{8} + 2717 x^{7} + 803 x^{6} - 1525 x^{5} + 161 x^{4} + 436 x^{3} - 110 x^{2} - 75 x - 1$ |
$22$ |
[18,2] |
$137^{2}\cdot 293^{2}\cdot 11093^{2}\cdot 216649^{2}\cdot 116499629$ |
$5$ |
$43.4469856952$ |
$106013022279.75117$ |
|
|
✓ |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$19$ |
$26299120217.5$ |
| 22.18.154...049.1 |
$x^{22} - 11 x^{21} + 39 x^{20} - 5 x^{19} - 289 x^{18} + 549 x^{17} + 438 x^{16} - 2382 x^{15} + 1432 x^{14} + 3832 x^{13} - 6324 x^{12} - 692 x^{11} + 9779 x^{10} - 5877 x^{9} - 7100 x^{8} + 8177 x^{7} + 1805 x^{6} - 4599 x^{5} + 512 x^{4} + 1102 x^{3} - 307 x^{2} - 80 x + 29$ |
$22$ |
[18,2] |
$1297^{10}\cdot 115001$ |
$2$ |
$44.1575132655$ |
$12212.956112260455$ |
|
|
? |
$C_2^{10}.D_{22}$ (as 22T32) |
trivial |
$2$ |
$19$ |
$71513086940.5$ |
| 22.18.228...581.1 |
$x^{22} - 11 x^{21} + 30 x^{20} + 85 x^{19} - 518 x^{18} + 45 x^{17} + 3394 x^{16} - 2978 x^{15} - 12837 x^{14} + 16021 x^{13} + 32642 x^{12} - 44805 x^{11} - 60933 x^{10} + 75322 x^{9} + 86609 x^{8} - 74536 x^{7} - 89913 x^{6} + 34489 x^{5} + 58999 x^{4} + 3076 x^{3} - 17033 x^{2} - 7149 x - 883$ |
$22$ |
[18,2] |
$131\cdot 2297\cdot 71647\cdot 10298992926983^{2}$ |
$4$ |
$44.946078922$ |
$471207864818.8128$ |
|
|
✓ |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$19$ |
$37601816880.6$ |
| 22.18.373...301.1 |
$x^{22} - 11 x^{21} + 30 x^{20} + 85 x^{19} - 516 x^{18} + 27 x^{17} + 3420 x^{16} - 2778 x^{15} - 13418 x^{14} + 15160 x^{13} + 36613 x^{12} - 43034 x^{11} - 75553 x^{10} + 73248 x^{9} + 119719 x^{8} - 70453 x^{7} - 136889 x^{6} + 22305 x^{5} + 97142 x^{4} + 21717 x^{3} - 29073 x^{2} - 17742 x - 2953$ |
$22$ |
[18,2] |
$29\cdot 151^{2}\cdot 2311^{2}\cdot 24910163^{2}\cdot 1702694681$ |
$5$ |
$45.9575047733$ |
$655155090331.9882$ |
|
|
✓ |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$19$ |
$74620353201.4$ |
| 22.18.565...896.1 |
$x^{22} - 16 x^{20} + 46 x^{18} + 155 x^{16} - 748 x^{14} + 688 x^{12} + 579 x^{10} - 1382 x^{8} + 904 x^{6} - 253 x^{4} + 28 x^{2} - 1$ |
$22$ |
[18,2] |
$2^{22}\cdot 1297^{10}$ |
$2$ |
$51.9999243795$ |
|
|
|
? |
$C_2^{10}.D_{11}$ (as 22T30) |
trivial |
$2$ |
$19$ |
$356788225608$ |
| 22.18.565...896.2 |
$x^{22} - 19 x^{20} + 110 x^{18} - 228 x^{16} - 81 x^{14} + 1073 x^{12} - 1656 x^{10} + 934 x^{8} - 71 x^{6} - 67 x^{4} + 16 x^{2} - 1$ |
$22$ |
[18,2] |
$2^{22}\cdot 1297^{10}$ |
$2$ |
$51.9999243795$ |
|
|
|
? |
$C_2^{10}.D_{11}$ (as 22T30) |
trivial |
$2$ |
$19$ |
$244248936396$ |
| 22.18.200...553.1 |
$x^{22} - 5 x^{21} - 19 x^{20} + 138 x^{19} - 234 x^{18} - 576 x^{17} + 8567 x^{16} - 17893 x^{15} - 75853 x^{14} + 255414 x^{13} + 209204 x^{12} - 1338618 x^{11} + 411447 x^{10} + 2870120 x^{9} - 2750667 x^{8} - 1555277 x^{7} + 2988765 x^{6} - 574462 x^{5} - 751638 x^{4} + 329506 x^{3} + 6664 x^{2} - 14874 x + 289$ |
$22$ |
[18,2] |
$1297^{11}\cdot 115001$ |
$2$ |
$61.1648450288$ |
$12212.956112260455$ |
|
|
? |
$C_2^{10}.D_{22}$ (as 22T32) |
$[2]$ |
$2$ |
$19$ |
$1094818736770$ |
| 22.18.285...232.1 |
$x^{22} - 22 x^{20} + 207 x^{18} - 2 x^{17} - 1092 x^{16} + 28 x^{15} + 3559 x^{14} - 156 x^{13} - 7445 x^{12} + 450 x^{11} + 10059 x^{10} - 736 x^{9} - 8611 x^{8} + 714 x^{7} + 4442 x^{6} - 426 x^{5} - 1238 x^{4} + 152 x^{3} + 140 x^{2} - 24 x - 1$ |
$22$ |
[18,2] |
$2^{33}\cdot 79\cdot 3767\cdot 449833\cdot 2443537\cdot 1016137678657$ |
$6$ |
$62.1495474636$ |
|
|
|
✓ |
$S_{11}\wr C_2$ (as 22T57) |
trivial |
$2$ |
$19$ |
$1871979355040$ |
| 22.18.429...609.1 |
$x^{22} - 5 x^{21} - 49 x^{20} + 149 x^{19} + 1117 x^{18} - 1000 x^{17} - 12006 x^{16} - 3533 x^{15} + 64273 x^{14} + 63958 x^{13} - 171145 x^{12} - 263217 x^{11} + 207316 x^{10} + 471355 x^{9} - 84325 x^{8} - 394692 x^{7} + 1221 x^{6} + 166543 x^{5} + 881 x^{4} - 34179 x^{3} + 1826 x^{2} + 2665 x - 347$ |
$22$ |
[18,2] |
$19^{11}\cdot 211^{11}$ |
$2$ |
$63.3166644731$ |
$503.8219009458458$ |
|
|
? |
$C_2^{10}.D_{11}$ (as 22T29) |
trivial |
$2$ |
$19$ |
$3627901913190$ |
| 22.18.732...112.1 |
$x^{22} - 48 x^{20} + 668 x^{18} - 3452 x^{16} + 1836 x^{14} + 41707 x^{12} - 117661 x^{10} + 18659 x^{8} + 239887 x^{6} - 220532 x^{4} + 55347 x^{2} - 1297$ |
$22$ |
[18,2] |
$2^{22}\cdot 1297^{11}$ |
$2$ |
$72.0277724215$ |
|
|
|
? |
$C_2^{10}.D_{11}$ (as 22T29) |
$[2]$ |
$2$ |
$19$ |
$7541989503400$ |
| 22.18.395...936.1 |
$x^{22} - 33 x^{20} + 429 x^{18} - 2673 x^{16} + 6578 x^{14} + 12122 x^{12} - 121726 x^{10} + 319682 x^{8} - 379335 x^{6} + 172667 x^{4} + 11253 x^{2} - 20449$ |
$22$ |
[18,2] |
$2^{34}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$77.7600145192$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$19$ |
$84012537963800$ |
| 22.18.158...744.1 |
$x^{22} - 11 x^{20} - 319 x^{18} + 7183 x^{16} - 57794 x^{14} + 234762 x^{12} - 526174 x^{10} + 651002 x^{8} - 398827 x^{6} + 67529 x^{4} + 26565 x^{2} - 3721$ |
$22$ |
[18,2] |
$2^{36}\cdot 7^{10}\cdot 11^{22}$ |
$3$ |
$82.8176105784$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$19$ |
$178623184551000$ |
| 22.18.276...552.1 |
$x^{22} - 22 x^{20} - 88 x^{18} + 3520 x^{16} - 4576 x^{14} - 99132 x^{12} + 468424 x^{10} - 870980 x^{8} + 806696 x^{6} - 380600 x^{4} + 81092 x^{2} - 4732$ |
$22$ |
[18,2] |
$2^{34}\cdot 7^{11}\cdot 11^{22}$ |
$3$ |
$84.9512708677$ |
|
|
|
? |
$C_2\times C_2^{10}.F_{11}$ (as 22T37) |
trivial |
$2$ |
$19$ |
$275497411266000$ |
| 22.18.434...296.1 |
$x^{22} - 44 x^{20} + 660 x^{18} - 2640 x^{16} - 27456 x^{14} + 312576 x^{12} - 1046848 x^{10} + 991232 x^{8} + 892672 x^{6} - 1402368 x^{4} + 259072 x^{2} - 11264$ |
$22$ |
[18,2] |
$2^{34}\cdot 7^{10}\cdot 11^{23}$ |
$3$ |
$86.7146277629$ |
|
|
|
? |
$C_2\times C_2^{10}.F_{11}$ (as 22T37) |
trivial |
$2$ |
$19$ |
$515955293802000$ |
| 22.18.113...984.1 |
$x^{22} - 33 x^{20} - 473 x^{18} - 1562 x^{17} + 23265 x^{16} + 76296 x^{15} - 108526 x^{14} - 1090342 x^{13} - 1720004 x^{12} + 3925524 x^{11} + 11886094 x^{10} - 3917782 x^{9} - 28429720 x^{8} - 3261940 x^{7} + 31213369 x^{6} + 8149526 x^{5} - 15186435 x^{4} - 4824908 x^{3} + 2175415 x^{2} + 1066868 x + 115123$ |
$22$ |
[18,2] |
$2^{22}\cdot 7^{16}\cdot 11^{22}$ |
$3$ |
$90.58148519459012$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T34) |
trivial |
$2$ |
$19$ |
$519373019408642.56$ |
| 22.18.156...000.1 |
$x^{22} - 36 x^{20} + 45 x^{18} + 7290 x^{16} - 90045 x^{14} + 482778 x^{12} - 1333233 x^{10} + 1837620 x^{8} - 984150 x^{6} - 46170 x^{4} + 102141 x^{2} - 1296$ |
$22$ |
[18,2] |
$2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16}$ |
$4$ |
$91.9141100158$ |
$292.8999259369444$ |
|
|
? |
$C_2^{10}:C_{11}:C_5$ (as 22T33) |
trivial |
$2$ |
$19$ |
$760178630770000$ |
| 22.18.178...832.1 |
$x^{22} - 88 x^{20} - 198 x^{19} + 2024 x^{18} + 6270 x^{17} - 19580 x^{16} - 78364 x^{15} + 78408 x^{14} + 496276 x^{13} + 7304 x^{12} - 1707542 x^{11} - 1055472 x^{10} + 3197810 x^{9} + 3138322 x^{8} - 3066712 x^{7} - 3678862 x^{6} + 1424742 x^{5} + 1891010 x^{4} - 280808 x^{3} - 376200 x^{2} + 13574 x + 18010$ |
$22$ |
[18,2] |
$2^{22}\cdot 7^{15}\cdot 11^{23}$ |
$3$ |
$92.4617099971$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T35) |
trivial |
$2$ |
$19$ |
$1417836653750000$ |
| 22.18.304...072.1 |
$x^{22} - 44 x^{20} + 660 x^{18} - 1408 x^{17} - 7304 x^{16} + 46200 x^{15} + 166496 x^{14} - 350240 x^{13} - 2140512 x^{12} - 1464576 x^{11} + 7791168 x^{10} + 16937536 x^{9} + 2342208 x^{8} - 31841920 x^{7} - 40416640 x^{6} - 4983616 x^{5} + 31308288 x^{4} + 32414976 x^{3} + 14386944 x^{2} + 2818816 x + 144512$ |
$22$ |
[18,2] |
$2^{34}\cdot 7^{11}\cdot 11^{23}$ |
$3$ |
$94.7340079194$ |
|
|
|
? |
$C_2^{10}.F_{11}$ (as 22T35) |
$[2]$ |
$2$ |
$19$ |
$777847954329000$ |
| 22.18.625...000.1 |
$x^{22} - 29 x^{20} - 35 x^{18} + 7965 x^{16} - 79140 x^{14} + 140187 x^{12} + 1374597 x^{10} - 6587220 x^{8} + 8430720 x^{6} - 2011840 x^{4} + 141056 x^{2} - 1024$ |
$22$ |
[18,2] |
$2^{12}\cdot 3^{20}\cdot 5^{20}\cdot 11^{16}$ |
$4$ |
$97.8923038661$ |
$305.86771353088227$ |
|
|
? |
$C_2^{10}:C_{11}:C_5$ (as 22T33) |
trivial |
$2$ |
$19$ |
$3681360209630000$ |
| 22.18.782...000.1 |
$x^{22} - 30 x^{20} - 30 x^{18} + 7440 x^{16} - 53325 x^{14} - 224685 x^{12} + 3618405 x^{10} - 14109120 x^{8} + 24309270 x^{6} - 19294740 x^{4} + 6187365 x^{2} - 669780$ |
$22$ |
[18,2] |
$2^{10}\cdot 3^{20}\cdot 5^{21}\cdot 11^{16}$ |
$4$ |
$98.8902671681$ |
$315.130635812495$ |
|
|
? |
$C_2^{10}.C_{11}:C_{10}$ (as 22T36) |
$[2]$ |
$2$ |
$19$ |
$1660027782690000$ |
| 22.18.172...000.1 |
$x^{22} - 19 x^{20} - 35 x^{18} + 2820 x^{16} - 19335 x^{14} + 18417 x^{12} + 263922 x^{10} - 1087185 x^{8} + 1651980 x^{6} - 1077890 x^{4} + 270611 x^{2} - 11264$ |
$22$ |
[18,2] |
$2^{10}\cdot 3^{20}\cdot 5^{20}\cdot 11^{17}$ |
$4$ |
$102.498667026$ |
$388.75224058411334$ |
|
|
? |
$C_2^{10}.C_{11}:C_{10}$ (as 22T36) |
trivial |
$2$ |
$19$ |
$4215018604390000$ |
| 22.18.924...581.1 |
$x^{22} - 11 x^{21} + 44 x^{20} - 55 x^{19} - 149 x^{18} + 714 x^{17} - 1042 x^{16} - 742 x^{15} + 5168 x^{14} - 5630 x^{13} - 5248 x^{12} + 15888 x^{11} - 6710 x^{10} - 12738 x^{9} + 15541 x^{8} - 1265 x^{7} - 8234 x^{6} + 5083 x^{5} + 294 x^{4} - 1334 x^{3} + 492 x^{2} - 67 x + 3$ |
$22$ |
[18,2] |
$74843^{8}\cdot 939181$ |
$2$ |
$110.638739198$ |
$265124.73212244833$ |
|
|
? |
$C_2^{11}.\PSL(2,11)$ (as 22T42) |
trivial |
$2$ |
$19$ |
$3410489314190000$ |
| 22.18.412...904.1 |
$x^{22} - 62 x^{20} + 1332 x^{18} - 12445 x^{16} + 46846 x^{14} - 17000 x^{12} - 234649 x^{10} + 219644 x^{8} + 210856 x^{6} - 218489 x^{4} + 42680 x^{2} - 81$ |
$22$ |
[18,2] |
$2^{22}\cdot 74843^{8}$ |
$2$ |
$118.426422289$ |
|
|
|
? |
$C_2^{10}.\PSL(2,11)$ (as 22T39) |
trivial |
$2$ |
$19$ |
$4003271696600000$ |
| 22.18.412...904.2 |
$x^{22} - 50 x^{20} + 967 x^{18} - 9172 x^{16} + 44799 x^{14} - 106893 x^{12} + 101941 x^{10} - 12539 x^{8} - 4786 x^{6} + 708 x^{4} + 4 x^{2} - 1$ |
$22$ |
[18,2] |
$2^{22}\cdot 74843^{8}$ |
$2$ |
$118.426422289$ |
|
|
|
? |
$C_2^{10}.\PSL(2,11)$ (as 22T39) |
trivial |
$2$ |
$19$ |
$6265992865560000$ |
| 22.18.412...904.3 |
$x^{22} - 37 x^{20} + 368 x^{18} + 466 x^{16} - 26158 x^{14} + 120420 x^{12} + 98802 x^{10} - 2086099 x^{8} + 5731387 x^{6} - 6492408 x^{4} + 3090478 x^{2} - 514089$ |
$22$ |
[18,2] |
$2^{22}\cdot 74843^{8}$ |
$2$ |
$118.42642228905491$ |
|
|
|
|
$C_2^{10}.\PSL(2,11)$ (as 22T39) |
trivial |
$2$ |
$19$ |
$14238434942850328$ |
| 22.18.661...732.1 |
$x^{22} - 2 x^{21} - 22 x^{20} + 36 x^{19} + 205 x^{18} - 257 x^{17} - 1042 x^{16} + 939 x^{15} + 3122 x^{14} - 1916 x^{13} - 5652 x^{12} + 2249 x^{11} + 6166 x^{10} - 1525 x^{9} - 3959 x^{8} + 601 x^{7} + 1438 x^{6} - 143 x^{5} - 281 x^{4} + 19 x^{3} + 27 x^{2} - x - 1$ |
$22$ |
[18,2] |
$2^{2}\cdot 23\cdot 43\cdot 2083\cdot 1669897\cdot 13592816541193\cdot 35388744506094820229$ |
$7$ |
$120.994069506$ |
|
|
|
? |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$19$ |
$10819783392900000$ |
| 22.18.106...721.1 |
$x^{22} - 2 x^{21} - 22 x^{20} + 36 x^{19} + 205 x^{18} - 257 x^{17} - 1042 x^{16} + 939 x^{15} + 3122 x^{14} - 1916 x^{13} - 5652 x^{12} + 2249 x^{11} + 6168 x^{10} - 1525 x^{9} - 3960 x^{8} + 601 x^{7} + 1438 x^{6} - 143 x^{5} - 281 x^{4} + 19 x^{3} + 27 x^{2} - x - 1$ |
$22$ |
[18,2] |
$3^{4}\cdot 29\cdot 1051\cdot 7796988506731\cdot 55511479826982340639646618909$ |
$5$ |
$152.449872359$ |
$4.138058921760083e+23$ |
|
|
✓ |
$S_{22}$ (as 22T59) |
trivial |
$2$ |
$19$ |
$172338502843000000$ |
| 22.18.309...072.1 |
$x^{22} - 152 x^{20} + 8733 x^{18} - 236350 x^{16} + 3051787 x^{14} - 17399125 x^{12} + 47374033 x^{10} - 62687488 x^{8} + 35737999 x^{6} - 4125223 x^{4} - 1571703 x^{2} - 74843$ |
$22$ |
[18,2] |
$2^{22}\cdot 74843^{9}$ |
$2$ |
$197.242698696$ |
|
|
|
? |
$C_2^{11}.\PSL(2,11)$ (as 22T42) |
trivial |
$2$ |
$19$ |
$1132407889300000000$ |
| 22.18.202...496.1 |
$x^{22} - 59199 x^{20} + 355785867 x^{18} + 15574863457179 x^{16} - 243890588632340310 x^{14} + 980617589843794278834 x^{12} + 3104638990661417055111462 x^{10} - 34961363048645624190273856458 x^{8} + 91888023235228572081111273993546 x^{6} - 75419055111706596835859501211384870 x^{4} + 5713137723447682436765249279773097994 x^{2} - 21260787460376367360486668899081431150$ |
$22$ |
[18,2] |
$2^{69}\cdot 3^{22}\cdot 31\cdot 337^{8}\cdot 991\cdot 310501^{8}\cdot 2473607$ |
$7$ |
$67934.91348618311$ |
|
|
|
|
$C_2^{11}.M_{11}$ (as 22T44) |
not computed |
$2$ |
$19$ |
|
| 22.18.359...104.1 |
$x^{22} - 257 x^{20} + 24474 x^{18} - 973488 x^{16} + 4911342 x^{14} + 833458818 x^{12} - 24773125392 x^{10} + 177479869188 x^{8} + 2609466379182 x^{6} - 46742377664590 x^{4} + 197759461441604 x^{2} - 49242609059256$ |
$22$ |
[18,2] |
$2^{73}\cdot 3^{20}\cdot 31\cdot 337^{8}\cdot 991\cdot 310501^{8}\cdot 2473607$ |
$7$ |
$69735.0463084$ |
|
|
|
? |
$C_2^{11}.M_{11}$ (as 22T44) |
not computed |
$2$ |
$19$ |
|
| 22.18.230...089.1 |
$x^{22} - 11 x^{21} - 8375382071 x^{20} + 83753821095 x^{19} + 30239391842106235938 x^{18} - 272154528965940026844 x^{17} - 62299005944745132263794581393 x^{16} + 498392053726797058825990959294 x^{15} + 81735614144568549821065357941455889481 x^{14} - 572149307733840810557332053781243645619 x^{13} - 72054944016577680888382418513797041923435706453 x^{12} + 432329671537407108547063573092233206919075350347 x^{11} + 43757681734213856060620813669474737589565734087455676069 x^{10} - 218788412634091283032227790410382382555583750616259162451 x^{9} - 18383728547378112693986359299316156439853557115655196996194040079 x^{8} + 73534915502242931336119545678495670841428298811136294653478844046 x^{7} + 5255787908282428375256316952646409006236043296299117696458810525050810930 x^{6} - 15767363982219490302530548353167437085483306741165131698814519612745966636 x^{5} - 976871499505339856726687787443673148702119347232311492713368377627444025708264939 x^{4} + 1953743025289619769609927935965174424151875711944819663352020838970899069862489543 x^{3} + 106511320841640709718273593909091112261150331893177419007223913489960065681716929693177288 x^{2} - 106511321818512224990977488006456113342508309352392142460740805431636636438802684226477536 x - 5171816474167505628125246930786194146064674226046415678576793740063088827110117886469640427968531$ |
$22$ |
[18,2] |
$131^{10}\cdot 2297^{10}\cdot 71647^{10}\cdot 10298992926983^{2}$ |
$4$ |
$758727.847426$ |
$471207864818.8128$ |
|
|
? |
$C_2^{10}.S_{11}$ (as 22T51) |
not computed |
$2$ |
$19$ |
|
| 22.18.651...449.1 |
$x^{22} - 11 x^{21} - 15789084607 x^{20} + 157890846455 x^{19} + 110746971971048806316 x^{18} - 996722752239328383006 x^{17} - 456686908335859663186856128341 x^{16} + 3653495289279259709985789751062 x^{15} + 1233340365680532560255064426238448307608 x^{14} - 8633382623699895563245834354737997399860 x^{13} - 2295306548915827818503229932405383312648591807203 x^{12} + 13771839405728941185352057872535434682817913093144 x^{11} + 3008235976397770175167222399027423306040909666725371574201 x^{10} - 15041180008230712300780359161086680732594538490261818878188 x^{9} - 2778656157484847280982897747877969488922506517585296579872733446640 x^{8} + 11114624720186469324806098611947733941638935381034067180114602303069 x^{7} + 1772974228559093358263195450183082391905157516634653024580978835244385317895 x^{6} - 5318922724578466658615185173429817814200518248972628117560517528924164100228 x^{5} - 744044115416507765021021196646690610169866572713152856848171728626532956098421434479 x^{4} + 1488088239697886750639882361285264147203086069826044503097773504915513387520157567545 x^{3} + 184729416370582242638251447645440388704667291009348175277482602807244002974054527942977543281 x^{2} - 184729417114626363373681945580896803659929128262623837964712319402315440375343750732884448014 x - 20544135315942859966369326009302529501882658344474338458010659738621792061984845009538823872127218171$ |
$22$ |
[18,2] |
$29^{10}\cdot 151^{2}\cdot 2311^{2}\cdot 24910163^{2}\cdot 1702694681^{10}$ |
$5$ |
$1088890.73961$ |
$655155090331.9882$ |
|
|
? |
$C_2^{10}.S_{11}$ (as 22T51) |
not computed |
$2$ |
$19$ |
|
| 22.18.128...872.1 |
$x^{22} - 2009490103931 x^{20} + 526602267859802799159645 x^{18} + 988279053415334178289363750353926452 x^{16} - 819326766692863869410148111965076126722979154585 x^{14} + 239340319600230472272040281251389649659121708277147285168591 x^{12} - 15554200560942019119825716560851668014618940061378455374898484976833395 x^{10} - 7991188767641513479716190781904721819893446459663483928557539251294687714589627909 x^{8} + 2318861889789028396727262122923174321768844612998237261756831922244114849453126624171424815864 x^{6} - 277449427902016927470154659418784562178478494616903571510460163437800259514140959819255187868889220394422 x^{4} + 16229418495452037087138926874836924479143094781831319180474914320307535395119039795914711221483780633091415368834233 x^{2} - 380285404598090805687120338784714075823625149397058132983127896500288700037572932949395339463602625320870799724926165797568857$ |
$22$ |
[18,2] |
$2^{22}\cdot 2053^{11}\cdot 43747835269^{11}$ |
$3$ |
$18954081.967455667$ |
|
|
|
? |
$C_2^{10}.S_{11}$ (as 22T50) |
not computed |
$2$ |
$19$ |
|
| 22.18.282...352.1 |
$x^{22} - 4587739888493 x^{20} + 8910413975349265360781418 x^{18} - 9510356791749240105237437355904115003 x^{16} + 6038070825307213388006289286451675516316045796212 x^{14} - 2286021538302049806179499386460024633775599100741820879602929 x^{12} + 475739171441172431091873461786474909214933211890777828362875297232644172 x^{10} - 37715628363923447820531741194217270740575417334200654321009309175420848049572409138 x^{8} - 2773582672938460382655907316060176298782142316511125307808074224701683226495640987793403832492 x^{6} + 485845024180794958816717103902375992678107808531478199308163016648478866625210760444608867714154388244769 x^{4} + 3053131594406122807803920908749708866333677357150375151814001872032143652389691884232613144062413779477970896076247 x^{2} - 723677388979637976274401418360697109584869174749406625301313588735946005557274699158139112896738462003076023753592942690234777$ |
$22$ |
[18,2] |
$2^{22}\cdot 137^{11}\cdot 293^{11}\cdot 11093^{11}\cdot 216649^{11}$ |
$5$ |
$19643864.975848008$ |
|
|
|
? |
$C_2^{10}.S_{11}$ (as 22T50) |
not computed |
$2$ |
$19$ |
|
