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 |
$6$ |
$10$ |
$4402.38521796$ |
22.0.641...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 |
$6$ |
$10$ |
$18267.9467933$ |
22.0.492...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 |
$2$ |
$10$ |
$33482.7947011$ |
22.0.144...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 |
$4$ |
$10$ |
$148004.116661$ |
22.0.261...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 |
$2$ |
$10$ |
$24986.318925$ |
22.0.298...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 |
$6$ |
$10$ |
$138999.076948$ |
22.0.310...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 |
$6$ |
$10$ |
$73023.7380593$ |
22.0.439...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 |
$6$ |
$10$ |
$136255.877931$ |
22.0.131...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 |
$2$ |
$10$ |
$302171.954912$ |
22.0.152...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 |
$2$ |
$10$ |
$69206.6233764$ |
22.0.394...623.1 |
$x^{22} - x^{21} + x^{20} - x^{19} + x^{18} - x^{17} + x^{16} - x^{15} + x^{14} - x^{13} + x^{12} - x^{11} + x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$ |
$22$ |
[0,11] |
$-\,23^{21}$ |
$1$ |
$19.944865695$ |
$19.944865695037844$ |
✓ |
✓ |
✓ |
$C_{22}$ (as 22T1) |
$[3]$ |
$46$ |
$10$ |
$1038656.82438$ |
22.0.458...896.1 |
$x^{22} + 2 x^{20} + 3 x^{18} - 2 x^{16} - 7 x^{14} - 5 x^{12} + 4 x^{10} + 11 x^{8} - 2 x^{6} - 6 x^{4} + x^{2} + 1$ |
$22$ |
[0,11] |
$-\,2^{28}\cdot 11^{4}\cdot 19^{4}\cdot 547^{4}$ |
$4$ |
$20.081203729$ |
|
|
|
? |
$C_2\times A_{11}$ (as 22T46) |
trivial |
$4$ |
$10$ |
$460879.840354$ |
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 |
$6$ |
$10$ |
$1362288.49255$ |
22.0.660...523.1 |
$x^{22} - x^{21} + 5 x^{20} + 2 x^{19} + 12 x^{18} + 13 x^{17} + 14 x^{16} + 63 x^{15} - 7 x^{14} + 68 x^{13} + 31 x^{12} + 19 x^{11} + 40 x^{10} - 71 x^{9} + 84 x^{8} - 79 x^{7} + 41 x^{6} - 38 x^{5} + 21 x^{4} - 11 x^{3} + 4 x^{2} - x + 1$ |
$22$ |
[0,11] |
$-\,3^{11}\cdot 610429790897^{2}$ |
$2$ |
$20.4165358902$ |
$1353251.407791989$ |
|
|
? |
$C_2\times S_{11}$ (as 22T47) |
trivial |
$6$ |
$10$ |
$399685.929551$ |
22.0.707...496.1 |
$x^{22} - 9 x^{20} + 37 x^{18} - 94 x^{16} + 166 x^{14} - 214 x^{12} + 207 x^{10} - 149 x^{8} + 81 x^{6} - 34 x^{4} + 12 x^{2} + 1$ |
$22$ |
[0,11] |
$-\,2^{22}\cdot 167^{10}$ |
$2$ |
$20.4812125382$ |
$25.84569596664017$ |
|
|
? |
$D_{22}$ (as 22T3) |
trivial |
$4$ |
$10$ |
$743434.07758$ |
22.0.707...496.2 |
$x^{22} + 3 x^{20} + 4 x^{18} + 4 x^{16} + 11 x^{14} + 10 x^{12} + 4 x^{10} + 12 x^{8} + 7 x^{6} + 6 x^{4} + 4 x^{2} + 1$ |
$22$ |
[0,11] |
$-\,2^{22}\cdot 167^{10}$ |
$2$ |
$20.4812125382$ |
|
|
|
? |
$C_2^{10}.D_{22}$ (as 22T32) |
trivial |
$2$ |
$10$ |
$290901.068764$ |
22.0.707...496.3 |
$x^{22} + x^{20} - 7 x^{18} - 6 x^{16} + 23 x^{14} + x^{12} - 24 x^{10} + 21 x^{8} - 17 x^{6} + 9 x^{4} - 2 x^{2} + 1$ |
$22$ |
[0,11] |
$-\,2^{22}\cdot 167^{10}$ |
$2$ |
$20.4812125382$ |
|
|
|
? |
$C_2^{10}.D_{22}$ (as 22T32) |
trivial |
$2$ |
$10$ |
$200949.419629$ |
22.0.707...496.4 |
$x^{22} - 3 x^{20} + 11 x^{18} - 22 x^{16} + 45 x^{14} - 62 x^{12} + 67 x^{10} - 46 x^{8} + 12 x^{6} + 6 x^{4} - 5 x^{2} + 1$ |
$22$ |
[0,11] |
$-\,2^{22}\cdot 167^{10}$ |
$2$ |
$20.481212538204982$ |
|
|
|
? |
$C_2^{10}.D_{22}$ (as 22T32) |
trivial |
$2$ |
$10$ |
$324083.01609232236$ |
22.0.734...664.1 |
$x^{22} + 13 x^{20} + 75 x^{18} + 255 x^{16} + 572 x^{14} + 895 x^{12} + 999 x^{10} + 790 x^{8} + 425 x^{6} + 140 x^{4} + 21 x^{2} + 1$ |
$22$ |
[0,11] |
$-\,2^{22}\cdot 211441^{2}\cdot 625831^{2}$ |
$3$ |
$20.5158137635$ |
|
|
|
✓ |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$10$ |
$131820.824712$ |
22.0.115...227.1 |
$x^{22} - 2 x^{21} + 5 x^{20} - 6 x^{19} + 10 x^{18} - 13 x^{17} + 3 x^{16} - 4 x^{15} - 15 x^{14} + 9 x^{13} - 23 x^{12} + 35 x^{11} + 5 x^{10} + 25 x^{9} + 40 x^{8} + 18 x^{7} + 38 x^{6} + 20 x^{4} - x^{3} + 6 x^{2} - x + 1$ |
$22$ |
[0,11] |
$-\,3^{11}\cdot 43^{2}\cdot 547^{2}\cdot 34374601^{2}$ |
$4$ |
$20.944896254$ |
$1557425.7511557334$ |
|
|
? |
$C_2\times S_{11}$ (as 22T47) |
trivial |
$6$ |
$10$ |
$583781.984765$ |
22.0.117...984.1 |
$x^{22} + 2 x^{20} - x^{16} - 7 x^{14} - 14 x^{12} - x^{10} + 9 x^{8} + 15 x^{6} + 22 x^{4} + 10 x^{2} + 1$ |
$22$ |
[0,11] |
$-\,2^{22}\cdot 2089^{2}\cdot 79966751^{2}$ |
$3$ |
$20.9550593338$ |
|
|
|
? |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$10$ |
$229900.23166$ |
22.0.213...691.1 |
$x^{22} - 4 x^{21} + 7 x^{20} - 12 x^{19} + 24 x^{18} - 33 x^{17} + 48 x^{16} - 51 x^{15} + 12 x^{14} - 2 x^{13} + 44 x^{12} + 193 x^{11} - 198 x^{10} - 426 x^{9} + 168 x^{8} + 372 x^{7} + 15 x^{6} - 99 x^{5} - 36 x^{4} - 36 x^{3} - 9 x^{2} + 18 x + 9$ |
$22$ |
[0,11] |
$-\,3^{20}\cdot 11^{19}$ |
$2$ |
$21.5343212171$ |
$23.496328849167636$ |
|
|
? |
$F_{11}$ (as 22T4) |
trivial |
$2$ |
$10$ |
$1473183.5094$ |
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 |
$2$ |
$10$ |
$685583.046278$ |
22.0.874...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 |
$2$ |
$10$ |
$9094108.72092$ |
22.0.100...443.1 |
$x^{22} - x^{21} + 7 x^{20} - 4 x^{19} + 31 x^{18} - 18 x^{17} + 77 x^{16} - 41 x^{15} + 140 x^{14} - 96 x^{13} + 153 x^{12} - 129 x^{11} + 145 x^{10} - 148 x^{9} + 84 x^{8} - 72 x^{7} + 94 x^{6} - 20 x^{5} + 39 x^{4} + 12 x^{3} + 18 x^{2} + 4 x + 1$ |
$22$ |
[0,11] |
$-\,3^{11}\cdot 29^{2}\cdot 131^{2}\cdot 5399^{2}\cdot 367163^{2}$ |
$5$ |
$25.6556241538$ |
$4753148.607259087$ |
|
|
? |
$C_2\times S_{11}$ (as 22T47) |
$[2]$ |
$6$ |
$10$ |
$2461752.74517$ |
22.0.118...832.1 |
$x^{22} + 9 x^{20} + 37 x^{18} + 74 x^{16} + 22 x^{14} - 217 x^{12} - 442 x^{10} - 261 x^{8} + 291 x^{6} + 663 x^{4} + 501 x^{2} + 167$ |
$22$ |
[0,11] |
$-\,2^{22}\cdot 167^{11}$ |
$2$ |
$25.8456959666$ |
|
|
|
? |
$C_2^{10}.D_{11}$ (as 22T29) |
trivial |
$2$ |
$10$ |
$2715893.41308$ |
22.0.118...832.2 |
$x^{22} - 6 x^{20} + 19 x^{18} - 15 x^{16} - 90 x^{14} + 259 x^{12} - 217 x^{10} + 142 x^{8} - 495 x^{6} + 761 x^{4} - 501 x^{2} + 167$ |
$22$ |
[0,11] |
$-\,2^{22}\cdot 167^{11}$ |
$2$ |
$25.8456959666$ |
|
|
|
|
$C_2^{10}.D_{11}$ (as 22T29) |
trivial |
$2$ |
$10$ |
$3187515.86093$ |
22.0.118...832.3 |
$x^{22} - 9 x^{20} + 30 x^{18} - 35 x^{16} - 36 x^{14} + 140 x^{12} - 130 x^{10} + 98 x^{8} - 330 x^{6} + 636 x^{4} - 531 x^{2} + 167$ |
$22$ |
[0,11] |
$-\,2^{22}\cdot 167^{11}$ |
$2$ |
$25.84569596664017$ |
|
|
|
? |
$C_2^{10}.D_{11}$ (as 22T29) |
$[2]$ |
$2$ |
$10$ |
$1380820.0993235877$ |
22.0.118...832.4 |
$x^{22} - 10 x^{20} + 53 x^{18} - 164 x^{16} + 331 x^{14} - 402 x^{12} + 191 x^{10} + 310 x^{8} - 747 x^{6} + 812 x^{4} - 501 x^{2} + 167$ |
$22$ |
[0,11] |
$-\,2^{22}\cdot 167^{11}$ |
$2$ |
$25.84569596664017$ |
|
|
|
? |
$C_2^{10}.D_{11}$ (as 22T29) |
trivial |
$2$ |
$10$ |
$3260196.2888900195$ |
22.0.133...083.1 |
$x^{22} - x^{21} + 8 x^{20} + x^{19} + 33 x^{18} + 20 x^{17} + 97 x^{16} + 111 x^{15} + 195 x^{14} + 258 x^{13} + 328 x^{12} + 369 x^{11} + 392 x^{10} + 323 x^{9} + 362 x^{8} + 155 x^{7} + 199 x^{6} + 67 x^{5} + 63 x^{4} + 12 x^{3} + 11 x^{2} + 2 x + 1$ |
$22$ |
[0,11] |
$-\,3^{11}\cdot 8674315276967^{2}$ |
$2$ |
$25.9874596265$ |
$5101269.041219155$ |
|
|
? |
$C_2\times S_{11}$ (as 22T47) |
trivial |
$6$ |
$10$ |
$6808139.27799$ |
22.0.134...816.1 |
$x^{22} + 12 x^{20} + 64 x^{18} + 200 x^{16} + 403 x^{14} + 544 x^{12} + 510 x^{10} + 358 x^{8} + 197 x^{6} + 73 x^{4} + 14 x^{2} + 1$ |
$22$ |
[0,11] |
$-\,2^{22}\cdot 1792166448977^{2}$ |
$2$ |
$26.0000079857$ |
|
|
|
✓ |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
trivial |
$2$ |
$10$ |
$3155709.44058$ |
22.0.223...627.1 |
$x^{22} - 2 x^{21} + 3 x^{20} + 8 x^{19} - 22 x^{18} + 38 x^{17} - 4 x^{16} - 57 x^{15} + 146 x^{14} - 127 x^{13} + 42 x^{12} + 144 x^{11} - 154 x^{10} + 123 x^{9} - 19 x^{8} - 35 x^{7} + 41 x^{6} - 58 x^{5} + 35 x^{4} - 12 x^{3} + 7 x^{2} - 2 x + 1$ |
$22$ |
[0,11] |
$-\,3^{11}\cdot 1831^{8}$ |
$2$ |
$26.606806584$ |
$74.11477585475112$ |
|
|
? |
$C_2\times \PSL(2,11)$ (as 22T13) |
trivial |
$6$ |
$10$ |
$19742415.8494$ |
22.0.223...627.2 |
$x^{22} - 2 x^{21} + x^{20} - 10 x^{19} + 18 x^{18} + 2 x^{17} + 31 x^{16} - 76 x^{15} - 19 x^{14} - 8 x^{13} + 188 x^{12} - 50 x^{11} - 76 x^{10} - 135 x^{9} + 130 x^{8} + 29 x^{7} + 42 x^{6} - 76 x^{5} + 11 x^{4} - 8 x^{3} + 13 x^{2} - 4 x + 1$ |
$22$ |
[0,11] |
$-\,3^{11}\cdot 1831^{8}$ |
$2$ |
$26.606806584$ |
$74.11477585475112$ |
|
|
? |
$C_2\times \PSL(2,11)$ (as 22T13) |
trivial |
$6$ |
$10$ |
$19742415.8494$ |
22.0.155...507.1 |
$x^{22} - 11 x^{21} + 76 x^{20} - 375 x^{19} + 1474 x^{18} - 4773 x^{17} + 13158 x^{16} - 31314 x^{15} + 65238 x^{14} - 119692 x^{13} + 194559 x^{12} - 280546 x^{11} + 359279 x^{10} - 407518 x^{9} + 408092 x^{8} - 358073 x^{7} + 272834 x^{6} - 177710 x^{5} + 97035 x^{4} - 42912 x^{3} + 14655 x^{2} - 3477 x + 467$ |
$22$ |
[0,11] |
$-\,23\cdot 2879\cdot 3371\cdot 56509^{2}\cdot 14792861^{2}$ |
$5$ |
$29.061716771$ |
$13659947365.223434$ |
|
|
✓ |
$C_2^{10}.(C_2\times S_{11})$ (as 22T53) |
$[2]$ |
$2$ |
$10$ |
$3264151.35122$ |
22.0.158...676.1 |
$x^{22} - 11 x^{21} + 66 x^{20} - 275 x^{19} + 880 x^{18} - 2277 x^{17} + 4917 x^{16} - 9042 x^{15} + 14355 x^{14} - 19855 x^{13} + 24068 x^{12} - 25650 x^{11} + 24035 x^{10} - 19723 x^{9} + 14058 x^{8} - 8646 x^{7} + 4653 x^{6} - 2343 x^{5} + 1210 x^{4} - 605 x^{3} + 231 x^{2} - 44 x + 10$ |
$22$ |
[0,11] |
$-\,2^{2}\cdot 3^{21}\cdot 11^{18}\cdot 683$ |
$4$ |
$29.0861442411$ |
$1291.0043009390063$ |
|
|
? |
$C_2\times C_2^{10}.F_{11}$ (as 22T37) |
$[2]$ |
$2$ |
$10$ |
$18825595.7955$ |
22.0.191...811.1 |
$x^{22} - 11 x^{21} + 66 x^{20} - 275 x^{19} + 847 x^{18} - 1980 x^{17} + 3454 x^{16} - 4070 x^{15} + 1100 x^{14} + 9482 x^{13} - 30690 x^{12} + 60224 x^{11} - 77803 x^{10} + 49665 x^{9} + 48642 x^{8} - 188375 x^{7} + 271315 x^{6} - 233860 x^{5} + 132748 x^{4} - 52624 x^{3} + 14960 x^{2} - 2816 x + 256$ |
$22$ |
[0,11] |
$-\,11^{31}$ |
$1$ |
$29.3370854252$ |
$29.33708542518522$ |
|
✓ |
|
$D_{11}$ (as 22T2) |
trivial |
$2$ |
$10$ |
$167976253.311$ |
22.0.304...547.1 |
$x^{22} - x^{21} + 11 x^{20} - 8 x^{19} + 73 x^{18} - 46 x^{17} + 301 x^{16} - 145 x^{15} + 883 x^{14} - 355 x^{13} + 1776 x^{12} - 498 x^{11} + 2527 x^{10} - 574 x^{9} + 2324 x^{8} - 251 x^{7} + 1358 x^{6} - 161 x^{5} + 400 x^{4} + 20 x^{3} + 51 x^{2} - 6 x + 1$ |
$22$ |
[0,11] |
$-\,3^{11}\cdot 23^{20}$ |
$2$ |
$29.9567726697$ |
$29.956772669723485$ |
✓ |
✓ |
? |
$C_{22}$ (as 22T1) |
$[23]$ |
$6$ |
$10$ |
$1038656.82438$ |
22.0.328...603.1 |
$x^{22} - 2 x^{21} + 14 x^{20} - 22 x^{19} + 110 x^{18} - 154 x^{17} + 537 x^{16} - 588 x^{15} + 1719 x^{14} - 1556 x^{13} + 3922 x^{12} - 2650 x^{11} + 6120 x^{10} - 3124 x^{9} + 6945 x^{8} - 2284 x^{7} + 4957 x^{6} - 987 x^{5} + 2301 x^{4} - 102 x^{3} + 153 x^{2} + 9$ |
$22$ |
[0,11] |
$-\,3^{15}\cdot 4784137656827^{2}$ |
$2$ |
$30.0621038474$ |
|
✓ |
|
? |
$C_2\times S_{11}$ (as 22T47) |
$[16]$ |
$6$ |
$10$ |
$2614417.99814$ |
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 |
$4$ |
$10$ |
$95678654.2598$ |