| 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 |
| 16.2.438...875.1 |
$x^{16} - 2 x^{15} + 4 x^{14} - 18 x^{13} + 18 x^{12} - 47 x^{11} + 72 x^{10} - 89 x^{9} + 122 x^{8} - 151 x^{7} + 145 x^{6} - 130 x^{5} + 126 x^{4} - 79 x^{3} + 33 x^{2} - 17 x + 3$ |
$16$ |
[2,7] |
$-\,5^{8}\cdot 7^{8}\cdot 11^{7}$ |
$3$ |
$16.8905317355$ |
$35.48747003412059$ |
|
|
? |
$\SL(2,7):C_2$ (as 16T1036) |
trivial |
$2$ |
$8$ |
$4626.0277119$ |
| 16.2.438...875.2 |
$x^{16} - 2 x^{15} + x^{14} + 6 x^{13} - 16 x^{12} + 22 x^{11} - 4 x^{10} - 45 x^{9} + 72 x^{8} - 53 x^{7} + 15 x^{6} + 39 x^{5} - 44 x^{4} - 11 x^{3} + 15 x^{2} + 4 x - 3$ |
$16$ |
[2,7] |
$-\,5^{8}\cdot 7^{8}\cdot 11^{7}$ |
$3$ |
$16.8905317355$ |
$35.48747003412059$ |
|
|
? |
$\SL(2,7):C_2$ (as 16T1036) |
trivial |
$2$ |
$8$ |
$4626.0277119$ |
| 16.16.166...469.1 |
$x^{16} - 7 x^{15} - 103 x^{14} + 796 x^{13} + 2610 x^{12} - 24580 x^{11} - 27038 x^{10} + 325744 x^{9} + 182643 x^{8} - 2128662 x^{7} - 1152953 x^{6} + 6545865 x^{5} + 4255837 x^{4} - 6862292 x^{3} - 2953069 x^{2} + 2685678 x - 406429$ |
$16$ |
[16,0] |
$107509^{7}$ |
$1$ |
$158.948747381$ |
$327.88565079917726$ |
|
|
? |
$\SL(2,7):C_2$ (as 16T1036) |
$[3]$ |
$2$ |
$15$ |
$1386340262300$ |
| 16.16.166...469.2 |
$x^{16} - 5 x^{15} - 120 x^{14} + 338 x^{13} + 5547 x^{12} - 6452 x^{11} - 119959 x^{10} + 11910 x^{9} + 1267786 x^{8} + 761152 x^{7} - 6187417 x^{6} - 7027611 x^{5} + 10037859 x^{4} + 18144166 x^{3} + 5329406 x^{2} - 1929681 x - 466947$ |
$16$ |
[16,0] |
$107509^{7}$ |
$1$ |
$158.948747381$ |
$327.88565079917726$ |
|
|
? |
$\SL(2,7):C_2$ (as 16T1036) |
$[3]$ |
$2$ |
$15$ |
$1386340262300$ |
| 16.0.108...384.1 |
$x^{16} + 272 x^{14} + 27654 x^{12} + 1414890 x^{10} + 40121951 x^{8} + 640305695 x^{6} + 5486452759 x^{4} + 22217587818 x^{2} + 32167660381$ |
$16$ |
[0,8] |
$2^{16}\cdot 107509^{7}$ |
$2$ |
$317.897494762$ |
$655.7713015983545$ |
✓ |
|
? |
$\SL(2,7):C_2$ (as 16T1036) |
$[6, 1987464]$ |
$2$ |
$7$ |
$4843194.42505$ |
| 16.0.108...384.2 |
$x^{16} + 285 x^{14} + 31524 x^{12} + 1790442 x^{10} + 57413856 x^{8} + 1067444681 x^{6} + 11253655334 x^{4} + 61487901005 x^{2} + 133178816421$ |
$16$ |
[0,8] |
$2^{16}\cdot 107509^{7}$ |
$2$ |
$317.897494762$ |
$655.7713015983545$ |
✓ |
|
? |
$\SL(2,7):C_2$ (as 16T1036) |
$[6, 1987464]$ |
$2$ |
$7$ |
$4843194.42505$ |
