| 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 |
| 11.3.656...000.1 |
$x^{11} - 2 x^{10} - 5 x^{9} - 50 x^{8} + 70 x^{7} + 232 x^{6} + 796 x^{5} - 1400 x^{4} - 5075 x^{3} - 10950 x^{2} + 2805 x + 90$ |
$11$ |
[3,4] |
$2^{18}\cdot 3^{8}\cdot 5^{18}$ |
$3$ |
$96.2411740906$ |
$270.8346732868732$ |
|
|
|
$M_{11}$ (as 11T6) |
trivial |
$2$ |
$6$ |
$107079411.141$ |
| 11.3.364...081.1 |
$x^{11} + 20 x^{9} - 26 x^{8} + 72 x^{7} - 137 x^{6} + 199 x^{5} - 212 x^{4} + 98 x^{3} - 11 x^{2} + x - 1$ |
$11$ |
[3,4] |
$661^{8}$ |
$1$ |
$112.474897717$ |
$180.36869686739456$ |
|
|
? |
$M_{11}$ (as 11T6) |
$[2]$ |
$2$ |
$6$ |
$6961764.90605$ |
| 11.3.294...000.1 |
$x^{11} - 2 x^{10} - 114 x^{9} + 144 x^{8} + 4806 x^{7} - 2592 x^{6} - 83592 x^{5} - 5832 x^{4} + 330237 x^{3} - 406782 x^{2} - 708588$ |
$11$ |
[3,4] |
$2^{18}\cdot 3^{8}\cdot 5^{6}\cdot 149^{6}$ |
$4$ |
$254.813544347$ |
$1580.3166898272689$ |
|
|
? |
$M_{11}$ (as 11T6) |
trivial |
$2$ |
$6$ |
$25994623180.1$ |
| 11.3.743...000.1 |
$x^{11} - 4 x^{10} + 6 x^{9} + 342 x^{8} - 306 x^{7} - 5664 x^{6} - 1416 x^{5} + 39900 x^{4} + 57765 x^{3} - 148040 x^{2} - 600880 x - 580650$ |
$11$ |
[3,4] |
$2^{18}\cdot 3^{16}\cdot 5^{6}\cdot 59^{6}$ |
$4$ |
$341.794236968$ |
$2126.806114514094$ |
|
|
? |
$M_{11}$ (as 11T6) |
trivial |
$2$ |
$6$ |
$142999381266$ |
| 11.3.111...000.1 |
$x^{11} - x^{10} - 129 x^{9} + 153 x^{8} + 6129 x^{7} - 7857 x^{6} - 122715 x^{5} + 139239 x^{4} + 712962 x^{3} + 564246 x^{2} + 3188646 x - 25154874$ |
$11$ |
[3,4] |
$2^{18}\cdot 3^{8}\cdot 5^{6}\cdot 401^{6}$ |
$4$ |
$437.265397234$ |
$3518.021893657963$ |
|
|
|
$M_{11}$ (as 11T6) |
trivial |
$2$ |
$6$ |
$1105007576070$ |
| 11.3.253...000.1 |
$x^{11} - x^{10} - 95 x^{9} + 135 x^{8} + 3480 x^{7} - 8412 x^{6} - 30408 x^{5} - 12180 x^{4} + 973740 x^{3} - 6637580 x^{2} + 27421202 x - 41776622$ |
$11$ |
[3,4] |
$2^{18}\cdot 3^{10}\cdot 5^{10}\cdot 109^{6}$ |
$4$ |
$471.07705849$ |
$3037.6605853937153$ |
|
|
? |
$M_{11}$ (as 11T6) |
trivial |
$2$ |
$6$ |
$300300836741$ |
| 11.3.152...000.1 |
$x^{11} - 2 x^{10} - 84 x^{9} + 120 x^{8} + 3495 x^{7} - 12042 x^{6} + 14304 x^{5} - 428892 x^{4} + 5153040 x^{3} - 49404320 x^{2} + 221690590 x - 331642560$ |
$11$ |
[3,4] |
$2^{18}\cdot 3^{10}\cdot 5^{6}\cdot 631^{6}$ |
$4$ |
$683.732527024$ |
$7020.628811125454$ |
|
|
|
$M_{11}$ (as 11T6) |
trivial |
$2$ |
$6$ |
$12101726961000$ |
| 11.3.270...000.1 |
$x^{11} - 126 x^{9} - 36 x^{8} + 5814 x^{7} + 2988 x^{6} - 111096 x^{5} - 63000 x^{4} + 547245 x^{3} - 614340 x^{2} + 4618620 x + 22234500$ |
$11$ |
[3,4] |
$2^{18}\cdot 3^{10}\cdot 5^{6}\cdot 1019^{6}$ |
$4$ |
$888.013936687$ |
$9492.897631128913$ |
|
|
? |
$M_{11}$ (as 11T6) |
trivial |
$2$ |
$6$ |
$21010110421500$ |
| 11.3.143...000.1 |
$x^{11} - 3 x^{10} - 105 x^{9} + 195 x^{8} + 4305 x^{7} - 3891 x^{6} - 71907 x^{5} - 4035 x^{4} + 323490 x^{3} - 689790 x^{2} - 16446186 x - 55091502$ |
$11$ |
[3,4] |
$2^{18}\cdot 3^{10}\cdot 5^{18}\cdot 79^{6}$ |
$4$ |
$1274.02970515$ |
$9161.182347194237$ |
|
|
|
$M_{11}$ (as 11T6) |
trivial |
$2$ |
$6$ |
$180714787324000$ |
| 11.3.387...000.1 |
$x^{11} - 4 x^{10} - 318 x^{9} - 156 x^{8} - 15012 x^{7} + 643152 x^{6} - 5337282 x^{5} + 136254876 x^{4} - 762562533 x^{3} + 10531148484 x^{2} - 46920135888 x + 95047524720$ |
$11$ |
[3,4] |
$2^{18}\cdot 3^{8}\cdot 5^{6}\cdot 7^{8}\cdot 251^{6}$ |
$5$ |
$1394.36950417$ |
$11083.78642099185$ |
|
|
? |
$M_{11}$ (as 11T6) |
trivial |
$2$ |
$6$ |
$513874226540000$ |
| 11.3.819...000.1 |
$x^{11} - 2 x^{10} - 130 x^{9} + 280 x^{8} + 6230 x^{7} - 13784 x^{6} - 126712 x^{5} + 253960 x^{4} + 803165 x^{3} + 31690 x^{2} - 402336 x - 17870868$ |
$11$ |
[3,4] |
$2^{18}\cdot 5^{18}\cdot 659^{6}$ |
$3$ |
$1492.57959077$ |
$12714.561701589068$ |
|
|
? |
$M_{11}$ (as 11T6) |
trivial |
$2$ |
$6$ |
$122400933489000$ |
| 11.11.118...424.1 |
$x^{11} - 4 x^{10} - 5541 x^{9} - 17700 x^{8} + 8989656 x^{7} + 88565592 x^{6} - 3982035456 x^{5} - 53992425120 x^{4} + 177164975493 x^{3} + 3011149862548 x^{2} - 789230330881 x - 3422014984884$ |
$11$ |
[11,0] |
$2^{24}\cdot 3^{10}\cdot 337^{4}\cdot 310501^{4}$ |
$4$ |
$10157.6040123$ |
$303970.38325382833$ |
|
|
? |
$M_{11}$ (as 11T6) |
trivial |
$2$ |
$10$ |
$71167879092500000000$ |
| 11.11.130...000.1 |
$x^{11} - 89045 x^{9} - 1016268 x^{8} + 1999274189 x^{7} + 17620911770 x^{6} - 14713278229518 x^{5} - 142840655647272 x^{4} + 38125562570421876 x^{3} + 562256553231789768 x^{2} - 26705329205451737544 x - 432518584183431877728$ |
$11$ |
[11,0] |
$2^{16}\cdot 3^{4}\cdot 5^{6}\cdot 11^{12}\cdot 13^{4}\cdot 17^{4}\cdot 347^{8}$ |
$7$ |
$67406.2536104$ |
$936774.2546036756$ |
|
|
|
$M_{11}$ (as 11T6) |
trivial |
$2$ |
$10$ |
$6854659729190000000000000$ |
