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 |
24.0.925...625.1 |
$x^{24} - x^{23} - 2 x^{22} + 3 x^{21} + x^{20} - 2 x^{19} + x^{18} + 34 x^{17} - 37 x^{16} - 59 x^{15} + 98 x^{14} + 17 x^{13} - 45 x^{12} + 34 x^{11} + 392 x^{10} - 472 x^{9} - 592 x^{8} + 1088 x^{7} + 64 x^{6} - 256 x^{5} + 256 x^{4} + 1536 x^{3} - 2048 x^{2} - 2048 x + 4096$ |
$24$ |
[0,12] |
$5^{12}\cdot 7^{20}\cdot 41^{6}$ |
$3$ |
$28.6371195818$ |
$72.46449954207208$ |
✓ |
|
? |
$C_6\times D_4$ (as 24T38) |
$[2, 2]$ |
$14$ |
$11$ |
$54448598.00948402$ |
24.0.132...784.1 |
$x^{24} - 2 x^{23} - x^{22} + 8 x^{21} - 5 x^{20} - 22 x^{19} + 39 x^{18} - 102 x^{17} + 107 x^{16} + 184 x^{15} - 573 x^{14} + 2 x^{13} + 1911 x^{12} - 1908 x^{11} + 766 x^{10} + 360 x^{9} - 740 x^{8} + 432 x^{7} - 136 x^{6} + 352 x^{5} - 272 x^{4} + 64 x^{3} + 96 x^{2} - 128 x + 64$ |
$24$ |
[0,12] |
$2^{36}\cdot 7^{20}\cdot 17^{6}$ |
$3$ |
$29.0673600744$ |
$59.02252990123237$ |
✓ |
|
|
$C_6\times D_4$ (as 24T38) |
$[6]$ |
$14$ |
$11$ |
$81519832.15193881$ |
24.0.448...689.1 |
$x^{24} - x^{23} - x^{21} - x^{20} + 6 x^{19} - 3 x^{18} - 10 x^{17} + 5 x^{16} - 13 x^{15} + 40 x^{14} + 3 x^{13} - 37 x^{12} + 6 x^{11} + 160 x^{10} - 104 x^{9} + 80 x^{8} - 320 x^{7} - 192 x^{6} + 768 x^{5} - 256 x^{4} - 512 x^{3} - 2048 x + 4096$ |
$24$ |
[0,12] |
$7^{20}\cdot 13^{12}\cdot 17^{6}$ |
$3$ |
$37.053759057$ |
$75.23925792699937$ |
✓ |
|
? |
$C_6\times D_4$ (as 24T38) |
$[4, 4]$ |
$14$ |
$11$ |
$357083207.82180834$ |