| 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 |
$6$ |
$10$ |
$622.138184002$ |
| 22.0.625...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 |
$6$ |
$10$ |
$4402.38521796$ |
| 22.0.110...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 |
$6$ |
$10$ |
$18267.9467933$ |
| 22.2.172...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 |
$2$ |
$11$ |
$38336.3977164$ |
| 22.0.310...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 |
$6$ |
$10$ |
$136255.877931$ |
| 22.6.304...125.1 |
$x^{22} - 8 x^{19} - 4 x^{16} + 116 x^{15} - 47 x^{14} - 228 x^{13} + 179 x^{12} + 177 x^{11} - 108 x^{10} + 58 x^{9} + 78 x^{8} + 4 x^{7} + 37 x^{6} - 13 x^{5} - 40 x^{4} - x^{3} + 10 x^{2} + x - 1$ |
$22$ |
[6,8] |
$5^{11}\cdot 971^{2}\cdot 25709231^{2}$ |
$3$ |
$19.7103732789$ |
$353296.357899427$ |
|
|
? |
$C_2\times S_{11}$ (as 22T47) |
trivial |
$2$ |
$13$ |
$376545.621481$ |
| 22.6.334...125.1 |
$x^{22} - 3 x^{20} - 4 x^{19} - 13 x^{18} + x^{17} + 41 x^{16} + 85 x^{15} - 10 x^{14} - 177 x^{13} + 9 x^{12} + 233 x^{11} - 32 x^{10} - 26 x^{9} + 38 x^{8} - 74 x^{7} + 18 x^{6} + 22 x^{5} - 25 x^{4} + 6 x^{2} - 1$ |
$22$ |
[6,8] |
$5^{11}\cdot 14851^{2}\cdot 1762627^{2}$ |
$3$ |
$19.7955824892$ |
$361778.7554362473$ |
|
|
? |
$C_2\times S_{11}$ (as 22T47) |
trivial |
$2$ |
$13$ |
$408757.310974$ |
| 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 |
$6$ |
$10$ |
$399685.929551$ |
| 22.0.115...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 |
$6$ |
$10$ |
$583781.984765$ |
| 22.10.854...125.1 |
$x^{22} - 2 x^{21} - 4 x^{20} + 14 x^{18} + 27 x^{17} - 40 x^{16} - 66 x^{15} + 4 x^{14} + 154 x^{13} + 292 x^{12} - 44 x^{11} - 237 x^{10} + 44 x^{9} + 22 x^{8} - 93 x^{7} - 3 x^{6} + 33 x^{5} - 4 x^{4} - 2 x^{3} + 7 x^{2} - x - 1$ |
$22$ |
[10,6] |
$5^{11}\cdot 211441^{2}\cdot 625831^{2}$ |
$3$ |
$22.9373770944$ |
$813407.4393285323$ |
|
|
? |
$C_2\times S_{11}$ (as 22T47) |
trivial |
$2$ |
$15$ |
$5205736.25321$ |
| 22.10.121...125.1 |
$x^{22} - x^{21} - 4 x^{20} - x^{19} - 6 x^{18} + 7 x^{17} + 10 x^{16} + 54 x^{15} + 178 x^{14} + 64 x^{13} - 301 x^{12} - 359 x^{11} - 56 x^{10} + 64 x^{9} + 32 x^{8} + 45 x^{7} + 27 x^{6} + 16 x^{5} - 4 x^{4} - 12 x^{3} + 4 x^{2} + 2 x - 1$ |
$22$ |
[10,6] |
$5^{11}\cdot 19457^{2}\cdot 8095783^{2}$ |
$3$ |
$23.3036808442$ |
$887467.322866031$ |
|
|
? |
$C_2\times S_{11}$ (as 22T47) |
trivial |
$2$ |
$15$ |
$5475014.69169$ |
| 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) |
$[2]$ |
$6$ |
$10$ |
$2461752.74517$ |
| 22.0.133...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 |
$6$ |
$10$ |
$6808139.27799$ |
| 22.14.181...125.1 |
$x^{22} - x^{21} - 13 x^{20} + 54 x^{18} + 93 x^{17} - 138 x^{16} - 339 x^{15} + 439 x^{14} + 258 x^{13} - 887 x^{12} + 343 x^{11} + 764 x^{10} - 601 x^{9} - 162 x^{8} + 341 x^{7} - 73 x^{6} - 118 x^{5} + 5 x^{4} + 25 x^{3} + 10 x^{2} - x - 1$ |
$22$ |
[14,4] |
$5^{11}\cdot 610429790897^{2}$ |
$2$ |
$26.3576344966$ |
$1747040.0552033717$ |
|
|
? |
$C_2\times S_{11}$ (as 22T47) |
trivial |
$2$ |
$17$ |
$51273605.8554$ |
| 22.14.319...125.1 |
$x^{22} - 2 x^{21} - 7 x^{20} + 14 x^{19} + 18 x^{18} - 67 x^{17} - 101 x^{16} + 234 x^{15} + 497 x^{14} - 273 x^{13} - 893 x^{12} + 23 x^{11} + 753 x^{10} + 147 x^{9} - 418 x^{8} - 88 x^{7} + 226 x^{6} + 6 x^{5} - 90 x^{4} + 7 x^{3} + 16 x^{2} - x - 1$ |
$22$ |
[14,4] |
$5^{11}\cdot 43^{2}\cdot 547^{2}\cdot 34374601^{2}$ |
$4$ |
$27.0397447932$ |
$2010627.9990602438$ |
|
|
? |
$C_2\times S_{11}$ (as 22T47) |
trivial |
$2$ |
$17$ |
$73525321.2665$ |
| 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) |
$[16]$ |
$6$ |
$10$ |
$2614417.99814$ |
| 22.0.420...803.1 |
$x^{22} - 3 x^{21} + 17 x^{20} - 32 x^{19} + 133 x^{18} - 221 x^{17} + 675 x^{16} - 925 x^{15} + 2270 x^{14} - 2774 x^{13} + 5421 x^{12} - 5457 x^{11} + 8435 x^{10} - 7261 x^{9} + 8780 x^{8} - 5447 x^{7} + 4182 x^{6} - 1619 x^{5} + 1047 x^{4} - 323 x^{3} + 152 x^{2} - 13 x + 1$ |
$22$ |
[0,11] |
$-\,3^{11}\cdot 421^{2}\cdot 115692385433^{2}$ |
$3$ |
$30.4009186045$ |
$12087989.19596965$ |
✓ |
|
? |
$C_2\times S_{11}$ (as 22T47) |
$[28]$ |
$6$ |
$10$ |
$1227458.81752$ |
| 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 |
$2$ |
$19$ |
$2040269368.26$ |
| 22.22.115...125.1 |
$x^{22} - 3 x^{21} - 33 x^{20} + 88 x^{19} + 421 x^{18} - 1001 x^{17} - 2683 x^{16} + 5647 x^{15} + 9370 x^{14} - 17186 x^{13} - 18923 x^{12} + 29509 x^{11} + 23007 x^{10} - 28981 x^{9} - 17000 x^{8} + 15763 x^{7} + 7336 x^{6} - 4249 x^{5} - 1613 x^{4} + 425 x^{3} + 118 x^{2} - 13 x - 1$ |
$22$ |
[22,0] |
$5^{11}\cdot 421^{2}\cdot 115692385433^{2}$ |
$3$ |
$39.2474171549$ |
$15605526.948375214$ |
|
|
? |
$C_2\times S_{11}$ (as 22T47) |
trivial |
$2$ |
$21$ |
$25661717777.2$ |
| 22.22.147...125.1 |
$x^{22} - x^{21} - 34 x^{20} + 25 x^{19} + 435 x^{18} - 199 x^{17} - 2682 x^{16} + 491 x^{15} + 8835 x^{14} + 378 x^{13} - 16217 x^{12} - 3399 x^{11} + 16648 x^{10} + 5347 x^{9} - 9307 x^{8} - 3533 x^{7} + 2728 x^{6} + 1048 x^{5} - 402 x^{4} - 126 x^{3} + 31 x^{2} + 5 x - 1$ |
$22$ |
[22,0] |
$5^{11}\cdot 55029067682009^{2}$ |
$2$ |
$39.6853069296$ |
$16587505.490882136$ |
|
|
? |
$C_2\times S_{11}$ (as 22T47) |
trivial |
$2$ |
$21$ |
$26137547532.3$ |
