| 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 |
| 11.3.109...096.1 |
$x^{11} + 11 x^{9} - 88 x^{8} + 99 x^{7} - 1034 x^{6} + 3971 x^{5} - 6072 x^{4} + 27412 x^{3} - 77198 x^{2} + 77352 x - 25912$ |
$11$ |
[3,4] |
$2^{16}\cdot 3^{12}\cdot 11^{12}$ |
$3$ |
$124.286075145$ |
$251.1032857588493$ |
|
|
|
$\PSL(2,11)$ (as 11T5) |
trivial |
$2$ |
$6$ |
$899199572.54$ |
| 11.3.109...096.2 |
$x^{11} - 22 x^{9} - 88 x^{8} + 1672 x^{6} + 4202 x^{5} + 4224 x^{4} - 28028 x^{3} - 77528 x^{2} - 138864 x - 70480$ |
$11$ |
[3,4] |
$2^{16}\cdot 3^{12}\cdot 11^{12}$ |
$3$ |
$124.286075145$ |
$251.1032857588493$ |
|
|
|
$\PSL(2,11)$ (as 11T5) |
trivial |
$2$ |
$6$ |
$899199572.54$ |
| 11.1.747...936.1 |
$x^{11} - 22 x^{2} - 36$ |
$11$ |
[1,5] |
$-\,2^{11}\cdot 3^{19}\cdot 11^{12}$ |
$3$ |
$182.479160373$ |
$938.1461036405288$ |
|
|
? |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$5$ |
$411234416.486$ |
| 11.1.201...272.1 |
$x^{11} - 48114 x^{2} - 236196$ |
$11$ |
[1,5] |
$-\,2^{11}\cdot 3^{22}\cdot 11^{12}$ |
$3$ |
$246.227895127$ |
$938.1461036405288$ |
|
|
? |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$5$ |
$2899138776.52$ |
| 11.3.102...000.1 |
$x^{11} - 55 x^{9} + 1210 x^{7} - 13310 x^{5} + 73205 x^{3} - 161051 x - 37500$ |
$11$ |
[3,4] |
$2^{10}\cdot 3^{8}\cdot 5^{11}\cdot 11^{12}$ |
$4$ |
$285.55887371$ |
$884.5792590790442$ |
|
|
? |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$6$ |
$16422422385.4$ |
| 11.1.124...912.1 |
$x^{11} + 44 x^{7} - 6272$ |
$11$ |
[1,5] |
$-\,2^{12}\cdot 7^{13}\cdot 11^{12}$ |
$3$ |
$290.544952775$ |
$2499.9338468264264$ |
|
|
? |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$5$ |
$4258772580.55$ |
| 11.1.159...768.2 |
$x^{11} + 16038 x^{3} - 209952$ |
$11$ |
[1,5] |
$-\,2^{33}\cdot 3^{10}\cdot 11^{12}$ |
$3$ |
$297.09909551$ |
$728.1349738318734$ |
|
|
? |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$5$ |
$8826880240.33$ |
| 11.3.226...656.1 |
$x^{11} - 66 x^{9} - 594 x^{8} - 1782 x^{7} - 32076 x^{4} - 104247 x^{3} - 128304 x^{2} - 144342 x - 100602$ |
$11$ |
[3,4] |
$2^{24}\cdot 3^{16}\cdot 11^{12}$ |
$3$ |
$306.797642147$ |
$1398.9857667876156$ |
|
|
|
$A_{11}$ (as 11T7) |
trivial |
$2$ |
$6$ |
$59534253860.2$ |
| 11.1.477...304.1 |
$x^{11} - 44 x^{8} - 393216$ |
$11$ |
[1,5] |
$-\,2^{33}\cdot 3^{11}\cdot 11^{12}$ |
$3$ |
$328.303860169$ |
$1598.7749512075377$ |
|
|
? |
$S_{11}$ (as 11T8) |
trivial |
$2$ |
$5$ |
$16881878101.6$ |
| 11.1.490...383.1 |
$x^{11} - 26411 x^{2} - 151263$ |
$11$ |
[1,5] |
$-\,3^{18}\cdot 7^{9}\cdot 11^{12}$ |
$3$ |
$405.744339486$ |
$1199.6528218367284$ |
|
|
? |
$S_{11}$ (as 11T8) |
$[2]$ |
$2$ |
$5$ |
$15057228670.3$ |
| 12.0.566...664.1 |
$x^{12} - 6 x^{11} + 33 x^{10} - 66 x^{9} + 660 x^{8} - 1782 x^{7} + 8261 x^{6} - 41250 x^{5} + 90288 x^{4} - 143286 x^{3} + 300069 x^{2} - 151362 x + 109935$ |
$12$ |
[0,6] |
$2^{22}\cdot 3^{16}\cdot 11^{12}$ |
$3$ |
$169.606574732$ |
$251.1032857588493$ |
|
|
|
$\PSL(2,11)$ (as 12T179) |
$[6]$ |
$2$ |
$5$ |
$426728491.749$ |
| 22.0.181...792.1 |
$x^{22} + 22 x^{20} + 231 x^{18} - 77 x^{17} + 1639 x^{16} - 913 x^{15} + 8855 x^{14} - 4796 x^{13} + 43703 x^{12} - 8698 x^{11} + 165286 x^{10} - 1177 x^{9} + 523688 x^{8} + 166903 x^{7} + 1297219 x^{6} + 434522 x^{5} + 2198856 x^{4} + 519860 x^{3} + 2214300 x^{2} + 161128 x + 1129696$ |
$22$ |
[0,11] |
$-\,2^{10}\cdot 7^{11}\cdot 11^{23}$ |
$3$ |
$44.4743441632$ |
$91.63507115281386$ |
|
|
|
$F_{11}\wr C_2$ (as 22T31) |
trivial |
$2$ |
$10$ |
$163923304373$ |
| 22.6.274...000.1 |
$x^{22} - 3168 x^{12} - 1440 x^{11} + 2509056 x^{2} + 2280960 x - 2073600$ |
$22$ |
[6,8] |
$2^{24}\cdot 3^{20}\cdot 5^{21}\cdot 11^{24}$ |
$4$ |
$367.626104278$ |
|
|
|
|
$A_{11}\wr C_2$ (as 22T54) |
trivial |
$2$ |
$13$ |
$222997401637000000000$ |
