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 |
22.0.178...627.1 |
$x^{22} + 2 x^{20} + 5 x^{18} - x^{17} + 6 x^{16} - 3 x^{15} + 9 x^{14} - x^{13} + 7 x^{12} - 3 x^{11} + 13 x^{10} + 5 x^{8} + 3 x^{7} + 10 x^{6} + x^{4} + 4 x^{2} + 2 x + 1$ |
$22$ |
[0,11] |
$-\,3^{11}\cdot 1003532779^{2}$ |
$2$ |
$11.3993917419$ |
$54868.91959023797$ |
|
|
? |
$C_2\times S_{11}$ (as 22T47) |
trivial |
$6$ |
$10$ |
$622.138184002$ |
22.0.116...067.1 |
$x^{22} - 2 x^{21} + 6 x^{20} - 12 x^{19} + 22 x^{18} - 40 x^{17} + 62 x^{16} - 97 x^{15} + 138 x^{14} - 177 x^{13} + 216 x^{12} - 233 x^{11} + 238 x^{10} - 226 x^{9} + 195 x^{8} - 164 x^{7} + 124 x^{6} - 85 x^{5} + 55 x^{4} - 29 x^{3} + 13 x^{2} - 5 x + 1$ |
$22$ |
[0,11] |
$-\,971^{2}\cdot 1867\cdot 25709231^{2}$ |
$3$ |
$12.4136136602$ |
$6826943.634084509$ |
|
|
? |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$10$ |
$584.201894616$ |
22.0.281...983.1 |
$x^{22} - 4 x^{21} + 6 x^{20} - 8 x^{19} + 15 x^{18} - 9 x^{17} - 28 x^{16} + 46 x^{15} - 14 x^{14} + 23 x^{13} + 13 x^{12} - 297 x^{11} + 488 x^{10} - 240 x^{9} + 28 x^{8} - 134 x^{7} + 194 x^{6} - 130 x^{5} + 72 x^{4} - 28 x^{3} + 8 x^{2} - 2 x + 1$ |
$22$ |
[0,11] |
$-\,167^{11}$ |
$1$ |
$12.9228479833$ |
$12.922847983320086$ |
|
✓ |
|
$D_{11}$ (as 22T2) |
trivial |
$2$ |
$10$ |
$1029.39037079$ |
22.0.327...619.1 |
$x^{22} - x^{21} - 7 x^{19} + 8 x^{18} + 7 x^{17} + 17 x^{16} - 26 x^{15} - 35 x^{14} - 4 x^{13} + 68 x^{12} + 92 x^{11} + 10 x^{10} - 49 x^{9} - 27 x^{8} + 32 x^{7} + 57 x^{6} + 24 x^{5} - 13 x^{4} - 17 x^{3} - 3 x^{2} + 2 x + 1$ |
$22$ |
[0,11] |
$-\,61\cdot 1279\cdot 1609^{2}\cdot 4025911^{2}$ |
$4$ |
$13.0112804134$ |
$22480724.15308682$ |
|
|
? |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$10$ |
$1054.33143917$ |
22.0.451...371.1 |
$x^{22} + 2 x^{20} - 5 x^{19} - 4 x^{18} - 9 x^{17} + 8 x^{16} + 16 x^{15} + 29 x^{14} - 7 x^{13} - 29 x^{12} - 55 x^{11} + 4 x^{10} + 37 x^{9} + 57 x^{8} - 3 x^{7} - 30 x^{6} - 33 x^{5} + 7 x^{4} + 12 x^{3} + 5 x^{2} - 3 x + 1$ |
$22$ |
[0,11] |
$-\,11^{4}\cdot 181^{2}\cdot 101771\cdot 304099^{2}$ |
$4$ |
$13.2027018025$ |
$7849737.736003605$ |
|
|
? |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$10$ |
$1214.51296657$ |
22.0.625...347.1 |
$x^{22} - x^{20} - 4 x^{19} + 3 x^{18} + 3 x^{17} + 6 x^{16} - 9 x^{15} + x^{14} - 3 x^{13} + 9 x^{12} - 10 x^{11} + x^{10} - 2 x^{9} + 8 x^{8} - 5 x^{7} - x^{5} + 4 x^{4} - 2 x^{3} + x^{2} + 1$ |
$22$ |
[0,11] |
$-\,3^{11}\cdot 12917^{2}\cdot 459847^{2}$ |
$3$ |
$13.3994085466$ |
$133489.8164542899$ |
|
|
? |
$C_2\times S_{11}$ (as 22T47) |
trivial |
$6$ |
$10$ |
$4357.91042138$ |
22.0.629...867.1 |
$x^{22} - x^{21} - x^{19} + 3 x^{18} - 3 x^{17} - x^{16} + 5 x^{14} - 3 x^{13} - 2 x^{12} + x^{11} + 6 x^{10} - 4 x^{9} - 2 x^{8} - x^{7} + 5 x^{6} - 2 x^{5} - x^{4} - 2 x^{3} + x^{2} + x + 1$ |
$22$ |
[0,11] |
$-\,3^{11}\cdot 64661^{2}\cdot 92179^{2}$ |
$3$ |
$13.4036147668$ |
$133720.45078072388$ |
|
|
? |
$C_2\times S_{11}$ (as 22T47) |
trivial |
$6$ |
$10$ |
$4402.38521796$ |
22.2.412...237.1 |
$x^{22} - 7 x^{20} - 3 x^{19} + 17 x^{18} + 12 x^{17} - 15 x^{16} - 16 x^{15} - x^{14} - x^{13} - 28 x^{12} - 42 x^{11} + 3 x^{10} + 25 x^{9} - 16 x^{8} - 47 x^{7} - 35 x^{6} + 7 x^{5} + 16 x^{4} - 7 x^{3} - 5 x^{2} + 2 x + 1$ |
$22$ |
[2,10] |
$1070197\cdot 6205948139^{2}$ |
$2$ |
$14.5989566434$ |
$81495932.90780456$ |
|
|
? |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$11$ |
$5727.32762159$ |
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 |
$2$ |
$10$ |
$9202.86473748$ |
22.0.753...875.1 |
$x^{22} - 4 x^{21} + 10 x^{20} - 22 x^{19} + 47 x^{18} - 79 x^{17} + 124 x^{16} - 169 x^{15} + 213 x^{14} - 229 x^{13} + 259 x^{12} - 192 x^{11} + 188 x^{10} - 90 x^{9} + 134 x^{8} - 14 x^{7} + 62 x^{6} - 19 x^{5} + 22 x^{4} - 12 x^{3} + 3 x^{2} - x + 1$ |
$22$ |
[0,11] |
$-\,5^{4}\cdot 7^{6}\cdot 83^{5}\cdot 127^{4}$ |
$4$ |
$15.004814071$ |
$9662.20149052205$ |
|
|
? |
$C_2^{11}.A_{11}$ (as 22T52) |
trivial |
$2$ |
$10$ |
$7059.77912901$ |
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 |
$2$ |
$10$ |
$14889.9809115$ |
22.0.110...347.1 |
$x^{22} - 4 x^{19} + 4 x^{16} - 4 x^{15} + x^{14} - 6 x^{13} + 7 x^{12} - 3 x^{11} + 12 x^{10} + 2 x^{9} + 18 x^{8} + 4 x^{7} + 13 x^{6} + 5 x^{5} + 6 x^{4} + x^{3} + 4 x^{2} - x + 1$ |
$22$ |
[0,11] |
$-\,3^{11}\cdot 971^{2}\cdot 25709231^{2}$ |
$3$ |
$15.2675894913$ |
$273662.18208404316$ |
|
|
? |
$C_2\times S_{11}$ (as 22T47) |
trivial |
$6$ |
$10$ |
$18267.9467933$ |
22.2.147...704.1 |
$x^{22} - 2 x^{20} + 6 x^{18} - 14 x^{16} + 22 x^{14} - 31 x^{12} + 38 x^{10} - 34 x^{8} + 27 x^{6} - 17 x^{4} + 6 x^{2} - 1$ |
$22$ |
[2,10] |
$2^{22}\cdot 12917^{2}\cdot 459847^{2}$ |
$3$ |
$15.4723042627$ |
|
|
|
? |
$C_2^{10}.S_{11}$ (as 22T51) |
trivial |
$2$ |
$11$ |
$11319.5749854$ |
22.2.147...704.2 |
$x^{22} + x^{18} - 2 x^{16} - 2 x^{14} - x^{12} + 3 x^{8} + x^{6} + x^{4} - 1$ |
$22$ |
[2,10] |
$2^{22}\cdot 12917^{2}\cdot 459847^{2}$ |
$3$ |
$15.4723042627$ |
|
|
|
✓ |
$C_2^{10}.S_{11}$ (as 22T51) |
trivial |
$2$ |
$11$ |
$10254.8559154$ |
22.2.178...033.1 |
$x^{22} - 11 x^{21} + 65 x^{20} - 265 x^{19} + 825 x^{18} - 2067 x^{17} + 4301 x^{16} - 7582 x^{15} + 11469 x^{14} - 15003 x^{13} + 17039 x^{12} - 16811 x^{11} + 14374 x^{10} - 10594 x^{9} + 6680 x^{8} - 3576 x^{7} + 1630 x^{6} - 656 x^{5} + 261 x^{4} - 113 x^{3} + 48 x^{2} - 15 x + 1$ |
$22$ |
[2,10] |
$149\cdot 33797\cdot 64661^{2}\cdot 92179^{2}$ |
$4$ |
$15.6063233809$ |
$173248472.68320495$ |
|
|
✓ |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$11$ |
$11377.8928745$ |
22.2.289...513.1 |
$x^{22} - x^{21} + x^{20} - 3 x^{19} + 3 x^{18} + x^{17} + 5 x^{16} - 4 x^{15} - 18 x^{14} + 11 x^{13} + 16 x^{12} + 32 x^{11} - 45 x^{10} - 81 x^{9} + 100 x^{8} + 75 x^{7} - 101 x^{6} - 41 x^{5} + 53 x^{4} + 15 x^{3} - 15 x^{2} - 4 x + 1$ |
$22$ |
[2,10] |
$359753\cdot 28385393161^{2}$ |
$2$ |
$15.9524360191$ |
$101053106.56209058$ |
|
|
? |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$11$ |
$15832.2441917$ |
22.6.440...573.1 |
$x^{22} - 11 x^{21} + 64 x^{20} - 255 x^{19} + 770 x^{18} - 1857 x^{17} + 3688 x^{16} - 6146 x^{15} + 8690 x^{14} - 10480 x^{13} + 10777 x^{12} - 9386 x^{11} + 6807 x^{10} - 3960 x^{9} + 1680 x^{8} - 341 x^{7} - 170 x^{6} + 212 x^{5} - 109 x^{4} + 28 x^{3} + 3 x^{2} - 5 x + 1$ |
$22$ |
[6,8] |
$37\cdot 163^{2}\cdot 14281\cdot 177106931^{2}$ |
$4$ |
$16.2585616162$ |
$123507051.11934274$ |
|
|
✓ |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$13$ |
$42752.2517797$ |
22.0.492...744.1 |
$x^{22} + 2 x^{20} - 5 x^{18} - 22 x^{16} + 29 x^{14} + 153 x^{12} + 72 x^{10} - 195 x^{8} - 158 x^{6} + 66 x^{4} + 77 x^{2} + 11$ |
$22$ |
[0,11] |
$-\,2^{18}\cdot 11^{5}\cdot 19^{4}\cdot 547^{4}$ |
$4$ |
$16.3415767174$ |
|
|
|
? |
$C_2^{11}.A_{11}$ (as 22T52) |
trivial |
$2$ |
$10$ |
$19198.3237336$ |
22.0.577...104.1 |
$x^{22} - 2 x^{20} - 2 x^{19} + 5 x^{18} + 6 x^{17} - 5 x^{16} - 12 x^{15} + 2 x^{14} + 18 x^{13} + 4 x^{12} - 18 x^{11} - 11 x^{10} + 14 x^{9} + 14 x^{8} - 8 x^{7} - 11 x^{6} + 2 x^{5} + 8 x^{4} - 4 x^{2} + 1$ |
$22$ |
[0,11] |
$-\,2^{30}\cdot 73^{2}\cdot 577\cdot 53149\cdot 3293113$ |
$5$ |
$16.4606320126$ |
|
|
|
✓ |
$S_{11}\wr C_2$ (as 22T57) |
trivial |
$4$ |
$10$ |
$65028.759848$ |
22.0.578...471.1 |
$x^{22} - 11 x^{21} + 67 x^{20} - 285 x^{19} + 929 x^{18} - 2433 x^{17} + 5271 x^{16} - 9630 x^{15} + 15091 x^{14} - 20633 x^{13} + 25057 x^{12} - 27453 x^{11} + 27302 x^{10} - 24426 x^{9} + 19254 x^{8} - 13050 x^{7} + 7570 x^{6} - 3890 x^{5} + 1921 x^{4} - 927 x^{3} + 362 x^{2} - 87 x + 9$ |
$22$ |
[0,11] |
$-\,271^{11}$ |
$1$ |
$16.4620776332$ |
$16.46207763315433$ |
|
✓ |
|
$D_{11}$ (as 22T2) |
trivial |
$2$ |
$10$ |
$33482.7947011$ |
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 |
$2$ |
$11$ |
$66805.8364906$ |
22.2.716...264.1 |
$x^{22} + 4 x^{20} + x^{18} - 20 x^{16} - 7 x^{14} + 93 x^{12} + 46 x^{10} - 121 x^{8} - 80 x^{6} - 34 x^{4} - 9 x^{2} - 1$ |
$22$ |
[2,10] |
$2^{22}\cdot 11^{4}\cdot 19^{4}\cdot 547^{4}$ |
$4$ |
$16.6222822507$ |
|
|
|
? |
$C_2^{10}.A_{11}$ (as 22T49) |
trivial |
$2$ |
$11$ |
$38833.928533$ |
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 |
$2$ |
$11$ |
$58031.388562$ |
22.4.931...016.1 |
$x^{22} - 4 x^{21} + 5 x^{20} + 4 x^{19} - 26 x^{18} + 31 x^{17} + 15 x^{16} - 79 x^{15} + 76 x^{14} + 60 x^{13} - 153 x^{12} + 84 x^{11} + 83 x^{10} - 192 x^{9} + 24 x^{8} + 58 x^{7} - 150 x^{6} + 30 x^{5} + 19 x^{4} - 23 x^{3} + 6 x^{2} + 29 x + 1$ |
$22$ |
[4,9] |
$-\,2^{12}\cdot 11^{7}\cdot 19^{4}\cdot 547^{4}$ |
$4$ |
$16.8215855911$ |
$1193.6702363351474$ |
|
|
? |
$C_2^{11}.A_{11}$ (as 22T52) |
trivial |
$2$ |
$12$ |
$56735.8548792$ |
22.4.951...707.1 |
$x^{22} - 11 x^{21} + 66 x^{20} - 275 x^{19} + 879 x^{18} - 2268 x^{17} + 4871 x^{16} - 8878 x^{15} + 13903 x^{14} - 18847 x^{13} + 22192 x^{12} - 22691 x^{11} + 20056 x^{10} - 15173 x^{9} + 9644 x^{8} - 4974 x^{7} + 1932 x^{6} - 448 x^{5} - 27 x^{4} + 71 x^{3} - 24 x^{2} + x + 1$ |
$22$ |
[4,9] |
$-\,139\cdot 1583^{2}\cdot 2731^{2}\cdot 6217^{2}\cdot 9473$ |
$5$ |
$16.8377853307$ |
$188123439.29282743$ |
|
|
✓ |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$12$ |
$43108.9874663$ |
22.4.969...159.1 |
$x^{22} - x^{21} + 3 x^{20} + 3 x^{18} + 5 x^{17} + 7 x^{16} + 4 x^{15} + 12 x^{14} - 17 x^{13} - 35 x^{11} - 28 x^{10} - 29 x^{9} - 20 x^{8} - 6 x^{7} - 11 x^{6} - 26 x^{5} - 22 x^{4} - 11 x^{3} - 4 x^{2} + 9 x - 1$ |
$22$ |
[4,9] |
$-\,173\cdot 7043\cdot 28208540809^{2}$ |
$3$ |
$16.8524111845$ |
$185392519.41428798$ |
|
|
? |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$12$ |
$42357.726741$ |
22.0.144...128.1 |
$x^{22} - 2 x^{20} - 2 x^{19} + 5 x^{18} + 6 x^{17} - 5 x^{16} - 12 x^{15} + 2 x^{14} + 18 x^{13} + 4 x^{12} - 18 x^{11} - 11 x^{10} + 14 x^{9} + 15 x^{8} - 8 x^{7} - 12 x^{6} + 2 x^{5} + 8 x^{4} - 4 x^{2} + 1$ |
$22$ |
[0,11] |
$-\,2^{22}\cdot 10177\cdot 33765428299628041$ |
$3$ |
$17.1588716086$ |
|
|
|
✓ |
$S_{11}\wr C_2$ (as 22T57) |
trivial |
$4$ |
$10$ |
$148004.116661$ |
22.6.144...125.1 |
$x^{22} - 2 x^{21} - x^{20} + 18 x^{19} - 17 x^{18} - 44 x^{17} + 110 x^{16} - 3 x^{15} - 254 x^{14} + 59 x^{13} + 240 x^{12} - 102 x^{11} - 552 x^{10} - 230 x^{9} + 307 x^{8} + 320 x^{7} - 3 x^{6} - 154 x^{5} - 62 x^{4} + 18 x^{3} + 19 x^{2} + 2 x - 1$ |
$22$ |
[6,8] |
$5^{11}\cdot 7^{4}\cdot 83^{4}\cdot 127^{4}$ |
$4$ |
$17.1621719232$ |
$2844.1679033165196$ |
|
|
? |
$C_2\times A_{11}$ (as 22T46) |
trivial |
$2$ |
$13$ |
$95631.3345105$ |
22.4.153...375.1 |
$x^{22} - 2 x^{21} + 7 x^{20} - 20 x^{19} + 38 x^{18} - 74 x^{17} + 107 x^{16} - 167 x^{15} + 185 x^{14} - 284 x^{13} + 308 x^{12} - 417 x^{11} + 466 x^{10} - 462 x^{9} + 446 x^{8} - 292 x^{7} + 170 x^{6} - 55 x^{5} - 7 x^{4} + 11 x^{3} - 8 x^{2} + x + 1$ |
$22$ |
[4,9] |
$-\,5^{4}\cdot 7^{4}\cdot 83^{5}\cdot 127^{4}\cdot 997$ |
$5$ |
$17.2071065975$ |
$187563.85877253$ |
|
|
? |
$C_2^{11}.A_{11}$ (as 22T52) |
trivial |
$2$ |
$12$ |
$56909.7191275$ |
22.10.162...109.1 |
$x^{22} - 5 x^{21} + 4 x^{20} + 19 x^{19} - 39 x^{18} + 11 x^{17} - 8 x^{16} + 47 x^{15} + 183 x^{14} - 603 x^{13} + 274 x^{12} + 853 x^{11} - 1093 x^{10} - 146 x^{9} + 897 x^{8} - 256 x^{7} - 277 x^{6} + 109 x^{5} + 47 x^{4} - 10 x^{3} - 11 x^{2} + x + 1$ |
$22$ |
[10,6] |
$29101\cdot 372881^{2}\cdot 633263^{2}$ |
$3$ |
$17.2515463588$ |
$82895535.3815753$ |
|
|
? |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$15$ |
$172549.025737$ |
22.2.172...125.1 |
$x^{22} + 3 x^{20} - 8 x^{19} - 13 x^{18} - 13 x^{17} - 10 x^{16} + 79 x^{15} + 45 x^{14} + 111 x^{13} + 59 x^{12} - 172 x^{11} + 31 x^{10} - 94 x^{9} - 96 x^{8} + 55 x^{7} - 26 x^{6} + x^{5} + 20 x^{4} - 4 x^{3} + 3 x^{2} - 1$ |
$22$ |
[2,10] |
$5^{11}\cdot 12917^{2}\cdot 459847^{2}$ |
$3$ |
$17.29856205$ |
$172334.61200524983$ |
|
|
? |
$C_2\times S_{11}$ (as 22T47) |
trivial |
$2$ |
$11$ |
$42078.318318$ |
22.2.173...125.1 |
$x^{22} - x^{21} + 2 x^{20} + x^{19} - 13 x^{18} + 3 x^{17} - 35 x^{16} - 18 x^{15} + 37 x^{14} + 27 x^{13} + 152 x^{12} + 277 x^{11} + 160 x^{10} + 72 x^{9} - 42 x^{8} - 69 x^{7} - 31 x^{6} - 22 x^{5} + 3 x^{4} + 4 x^{3} + x^{2} + x - 1$ |
$22$ |
[2,10] |
$5^{11}\cdot 64661^{2}\cdot 92179^{2}$ |
$3$ |
$17.3039922569$ |
$172632.35964036407$ |
|
|
? |
$C_2\times S_{11}$ (as 22T47) |
trivial |
$2$ |
$11$ |
$38336.3977164$ |
22.2.176...672.1 |
$x^{22} - 5 x^{21} + 17 x^{20} - 40 x^{19} + 70 x^{18} - 93 x^{17} + 99 x^{16} - 86 x^{15} + 53 x^{14} + 37 x^{13} - 283 x^{12} + 778 x^{11} - 1493 x^{10} + 2198 x^{9} - 2575 x^{8} + 2425 x^{7} - 1840 x^{6} + 1108 x^{5} - 512 x^{4} + 173 x^{3} - 33 x^{2} + x + 1$ |
$22$ |
[2,10] |
$2^{16}\cdot 37^{5}\cdot 4441^{4}$ |
$3$ |
$17.3188364535$ |
$5527.862135514047$ |
|
|
? |
$C_2^{11}.A_{11}$ (as 22T52) |
trivial |
$2$ |
$11$ |
$51691.3054088$ |
22.4.189...683.1 |
$x^{22} - x^{21} + x^{20} + x^{19} + x^{18} + 5 x^{17} - 11 x^{16} + 6 x^{15} + 19 x^{14} - 22 x^{13} - 4 x^{12} + 6 x^{11} + 13 x^{10} + 26 x^{9} - 75 x^{8} - 11 x^{7} + 101 x^{6} - 32 x^{5} - 59 x^{4} + 28 x^{3} + 15 x^{2} - 6 x - 1$ |
$22$ |
[4,9] |
$-\,47147\cdot 200601609583^{2}$ |
$2$ |
$17.3745944722$ |
$97251036.43154505$ |
|
|
? |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$12$ |
$64048.1745685$ |
22.0.261...704.1 |
$x^{22} + 6 x^{20} + 16 x^{18} + 18 x^{16} + 4 x^{14} + 6 x^{12} + 25 x^{10} + 3 x^{8} - 19 x^{6} - 4 x^{4} + 4 x^{2} + 1$ |
$22$ |
[0,11] |
$-\,2^{22}\cdot 971^{2}\cdot 25709231^{2}$ |
$3$ |
$17.6294938054$ |
|
|
|
? |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$10$ |
$24986.318925$ |
22.6.261...704.1 |
$x^{22} - 6 x^{20} + 16 x^{18} - 18 x^{16} + 4 x^{14} - 6 x^{12} + 25 x^{10} - 3 x^{8} - 19 x^{6} + 4 x^{4} + 4 x^{2} - 1$ |
$22$ |
[6,8] |
$2^{22}\cdot 971^{2}\cdot 25709231^{2}$ |
$3$ |
$17.6294938054$ |
|
|
|
? |
$C_2^{10}.S_{11}$ (as 22T51) |
trivial |
$2$ |
$13$ |
$107375.053215$ |
22.2.286...056.1 |
$x^{22} - 5 x^{20} + 9 x^{18} - 6 x^{16} - 12 x^{14} + 37 x^{12} - 45 x^{10} + 75 x^{8} - 54 x^{6} - 17 x^{4} + 44 x^{2} - 16$ |
$22$ |
[2,10] |
$2^{24}\cdot 11^{4}\cdot 19^{4}\cdot 547^{4}$ |
$4$ |
$17.7034135973$ |
|
|
|
|
$C_2^{10}.A_{11}$ (as 22T49) |
trivial |
$2$ |
$11$ |
$97800.0774856$ |
22.0.298...003.1 |
$x^{22} - x^{21} - 4 x^{20} + 3 x^{19} + 11 x^{18} - 6 x^{17} - 18 x^{16} + 2 x^{15} + 26 x^{14} - 8 x^{13} - 18 x^{12} + 23 x^{11} + 12 x^{10} - 27 x^{9} - 30 x^{8} + 23 x^{7} + 19 x^{6} + 3 x^{5} + 5 x^{4} - 26 x^{3} + 8 x^{2} + 2 x + 1$ |
$22$ |
[0,11] |
$-\,3^{11}\cdot 167^{10}$ |
$2$ |
$17.7372503584$ |
$22.38302928559939$ |
|
|
|
$D_{22}$ (as 22T3) |
trivial |
$6$ |
$10$ |
$138999.076948$ |
22.2.302...024.1 |
$x^{22} + 3 x^{20} - 11 x^{16} - 24 x^{14} - 24 x^{12} + x^{10} + 11 x^{8} - 9 x^{6} - 5 x^{4} + 5 x^{2} - 1$ |
$22$ |
[2,10] |
$2^{22}\cdot 1583^{2}\cdot 2731^{2}\cdot 6217^{2}$ |
$4$ |
$17.7482593697$ |
|
|
|
✓ |
$C_2^{10}.S_{11}$ (as 22T51) |
trivial |
$2$ |
$11$ |
$45090.7591736$ |
22.6.302...024.1 |
$x^{22} - x^{18} - x^{16} - 2 x^{14} + x^{10} + 2 x^{8} + 2 x^{6} - 1$ |
$22$ |
[6,8] |
$2^{22}\cdot 1583^{2}\cdot 2731^{2}\cdot 6217^{2}$ |
$4$ |
$17.7482593697$ |
|
|
|
✓ |
$C_2^{10}.S_{11}$ (as 22T51) |
trivial |
$2$ |
$13$ |
$118028.692249$ |
22.0.310...627.1 |
$x^{22} - 2 x^{21} + 4 x^{20} - 2 x^{18} + 9 x^{17} - 4 x^{16} + 6 x^{15} + 4 x^{14} - 2 x^{13} + 10 x^{12} + 7 x^{10} + 4 x^{9} + 2 x^{8} + 11 x^{7} + x^{6} + 3 x^{5} + 4 x^{4} + 2 x^{3} + 3 x^{2} - x + 1$ |
$22$ |
[0,11] |
$-\,3^{11}\cdot 211441^{2}\cdot 625831^{2}$ |
$3$ |
$17.7672158985$ |
$630062.6932401251$ |
|
|
? |
$C_2\times S_{11}$ (as 22T47) |
trivial |
$6$ |
$10$ |
$73023.7380593$ |
22.2.311...696.1 |
$x^{22} + 2 x^{16} - x^{14} - x^{12} + x^{10} + x^{8} - 2 x^{6} - x^{4} + 2 x^{2} - 1$ |
$22$ |
[2,10] |
$2^{22}\cdot 1559^{2}\cdot 17480927^{2}$ |
$3$ |
$17.7706651762$ |
|
|
|
✓ |
$C_2^{10}.S_{11}$ (as 22T51) |
trivial |
$2$ |
$11$ |
$52464.2585693$ |
22.0.439...467.1 |
$x^{22} - x^{21} + 2 x^{20} + x^{19} + 2 x^{18} - x^{17} + 4 x^{15} - 6 x^{14} - 6 x^{13} - 3 x^{12} - x^{11} - 2 x^{10} - 8 x^{9} + 8 x^{8} + 5 x^{7} + 7 x^{6} + 8 x^{5} + 8 x^{4} + 6 x^{3} + 4 x^{2} + 2 x + 1$ |
$22$ |
[0,11] |
$-\,3^{11}\cdot 19457^{2}\cdot 8095783^{2}$ |
$3$ |
$18.050953563$ |
$687429.2323526837$ |
|
|
? |
$C_2\times S_{11}$ (as 22T47) |
trivial |
$6$ |
$10$ |
$136255.877931$ |
22.6.452...625.1 |
$x^{22} - 3 x^{21} - 5 x^{20} + 20 x^{19} + 6 x^{18} - 46 x^{17} - 22 x^{16} + 88 x^{15} + 102 x^{14} - 250 x^{13} - 116 x^{12} + 460 x^{11} - 50 x^{10} - 559 x^{9} + 321 x^{8} + 395 x^{7} - 287 x^{6} - 315 x^{5} + 200 x^{4} + 136 x^{3} + 14 x^{2} - 70 x + 5$ |
$22$ |
[6,8] |
$5^{5}\cdot 7^{6}\cdot 83^{4}\cdot 127^{4}\cdot 997$ |
$5$ |
$18.0748826004$ |
$146075.47938051051$ |
|
|
? |
$C_2^{11}.A_{11}$ (as 22T52) |
trivial |
$2$ |
$13$ |
$180581.627765$ |
22.2.107...089.1 |
$x^{22} - x^{21} + x^{20} - 11 x^{19} - 5 x^{18} + 22 x^{17} + 22 x^{16} + 62 x^{15} - 83 x^{14} - 148 x^{13} + 44 x^{12} + 72 x^{11} + 52 x^{10} + 25 x^{9} + 50 x^{8} - 75 x^{7} - 65 x^{6} + 60 x^{5} - 17 x^{3} + 17 x^{2} - 7 x + 1$ |
$22$ |
[2,10] |
$167^{10}\cdot 639361$ |
$2$ |
$18.8028300461$ |
$10333.116035349647$ |
|
|
? |
$C_2^{10}.D_{22}$ (as 22T32) |
trivial |
$2$ |
$11$ |
$116549.459796$ |
22.6.111...149.1 |
$x^{22} - 11 x^{21} + 44 x^{20} - 55 x^{19} - 111 x^{18} + 372 x^{17} - 61 x^{16} - 838 x^{15} + 563 x^{14} + 1153 x^{13} - 1030 x^{12} - 1191 x^{11} + 1050 x^{10} + 987 x^{9} - 634 x^{8} - 630 x^{7} + 192 x^{6} + 264 x^{5} - 3 x^{4} - 53 x^{3} - 10 x^{2} + x - 1$ |
$22$ |
[6,8] |
$83\cdot 199\cdot 937\cdot 1583^{2}\cdot 2731^{2}\cdot 6217^{2}$ |
$6$ |
$18.8334111471$ |
$644951594.8448861$ |
|
|
✓ |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$13$ |
$231636.713172$ |
22.0.131...371.1 |
$x^{22} + 44 x^{18} - 22 x^{17} + 55 x^{16} + 121 x^{15} + 187 x^{14} + 11 x^{13} + 594 x^{12} + 328 x^{11} + 836 x^{10} + 770 x^{9} + 814 x^{8} + 528 x^{7} + 374 x^{6} + 143 x^{5} + 11 x^{4} - 33 x^{3} - 11 x^{2} + 1$ |
$22$ |
[0,11] |
$-\,11^{27}$ |
$1$ |
$18.970240678$ |
$20.6986330715433$ |
|
|
? |
$F_{11}$ (as 22T4) |
trivial |
$2$ |
$10$ |
$302171.954912$ |
22.8.147...499.1 |
$x^{22} - 11 x^{21} + 44 x^{20} - 55 x^{19} - 112 x^{18} + 381 x^{17} - 87 x^{16} - 834 x^{15} + 674 x^{14} + 1020 x^{13} - 1213 x^{12} - 834 x^{11} + 1220 x^{10} + 511 x^{9} - 776 x^{8} - 247 x^{7} + 323 x^{6} + 85 x^{5} - 89 x^{4} - 18 x^{3} + 16 x^{2} + x - 1$ |
$22$ |
[8,7] |
$-\,97\cdot 2381^{2}\cdot 2467\cdot 104446171^{2}$ |
$4$ |
$19.0750493033$ |
$243947516.5618645$ |
|
|
✓ |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$14$ |
$439864.358869$ |
22.0.152...375.1 |
$x^{22} - 4 x^{21} + 18 x^{20} - 48 x^{19} + 125 x^{18} - 249 x^{17} + 478 x^{16} - 766 x^{15} + 1216 x^{14} - 1618 x^{13} + 2242 x^{12} - 2454 x^{11} + 2995 x^{10} - 2616 x^{9} + 2692 x^{8} - 1937 x^{7} + 1684 x^{6} - 1102 x^{5} + 757 x^{4} - 253 x^{3} + 163 x^{2} + 2 x + 1$ |
$22$ |
[0,11] |
$-\,5^{4}\cdot 7^{11}\cdot 83^{4}\cdot 127^{4}$ |
$4$ |
$19.1015026172$ |
$2844.1679033165196$ |
|
|
? |
$C_2\times A_{11}$ (as 22T46) |
trivial |
$2$ |
$10$ |
$69206.6233764$ |
22.6.184...625.1 |
$x^{22} - 7 x^{21} + 16 x^{20} - 3 x^{19} - 51 x^{18} + 101 x^{17} - 62 x^{16} - 50 x^{15} + 49 x^{14} + 124 x^{13} - 271 x^{12} + 166 x^{11} + 113 x^{10} - 102 x^{9} - 51 x^{8} - 34 x^{7} + 128 x^{6} - 78 x^{5} - 37 x^{4} + 36 x^{3} + 14 x^{2} - 8 x + 1$ |
$22$ |
[6,8] |
$5^{4}\cdot 7^{4}\cdot 83^{4}\cdot 127^{4}\cdot 997^{2}$ |
$5$ |
$19.2655473485$ |
$89805.47415981455$ |
|
|
? |
$C_2^{10}.A_{11}$ (as 22T49) |
trivial |
$2$ |
$13$ |
$416442.121837$ |