| 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 |
| 16.4.233...864.1 |
$x^{16} - 8 x^{15} + 28 x^{14} - 52 x^{13} + 38 x^{12} + 52 x^{11} - 196 x^{10} + 320 x^{9} - 368 x^{8} + 320 x^{7} - 196 x^{6} + 52 x^{5} + 38 x^{4} - 52 x^{3} + 28 x^{2} - 8 x + 1$ |
$16$ |
[4,6] |
$2^{42}\cdot 3^{12}$ |
$2$ |
$14.0619218393$ |
$14.061921839317815$ |
|
|
? |
$C_2^2.D_4$ (as 16T37) |
trivial |
$2$ |
$9$ |
$1026.14642978$ |
| 16.0.934...456.8 |
$x^{16} - 8 x^{15} + 36 x^{14} - 104 x^{13} + 222 x^{12} - 336 x^{11} + 396 x^{10} - 400 x^{9} + 534 x^{8} - 888 x^{7} + 1344 x^{6} - 1536 x^{5} + 1268 x^{4} - 736 x^{3} + 264 x^{2} - 48 x + 4$ |
$16$ |
[0,8] |
$2^{44}\cdot 3^{12}$ |
$2$ |
$15.3346345019$ |
$18.23605645563822$ |
|
|
? |
$C_2^2.D_4$ (as 16T37) |
trivial |
$12$ |
$7$ |
$4738.13967163$ |
| 16.4.295...256.2 |
$x^{16} - 28 x^{12} - 80 x^{10} - 42 x^{8} + 64 x^{6} + 36 x^{4} + 16 x^{2} + 1$ |
$16$ |
[4,6] |
$2^{52}\cdot 3^{8}$ |
$2$ |
$16.4781371513$ |
$16.47813715125694$ |
|
|
? |
$C_2^2.D_4$ (as 16T37) |
trivial |
$2$ |
$9$ |
$4088.19912533$ |
| 16.4.239...736.2 |
$x^{16} - 16 x^{14} + 20 x^{12} + 8 x^{10} - 32 x^{8} + 16 x^{6} - 40 x^{4} + 16 x^{2} + 4$ |
$16$ |
[4,6] |
$2^{52}\cdot 3^{12}$ |
$2$ |
$21.6864480866$ |
$21.686448086636275$ |
|
|
? |
$C_2^2.D_4$ (as 16T37) |
trivial |
$2$ |
$9$ |
$46601.6852762$ |
| 16.0.679...264.3 |
$x^{16} - 16 x^{14} + 228 x^{12} - 1288 x^{10} + 3909 x^{8} - 6856 x^{6} + 7124 x^{4} - 4080 x^{2} + 1156$ |
$16$ |
[0,8] |
$2^{48}\cdot 17^{6}$ |
$2$ |
$23.1477259754$ |
$32.984845004941285$ |
|
|
? |
$C_2^2.D_4$ (as 16T37) |
$[2, 2]$ |
$8$ |
$7$ |
$51904.7959131$ |
| 16.0.957...944.82 |
$x^{16} - 8 x^{14} + 104 x^{12} - 512 x^{10} + 1888 x^{8} - 4288 x^{6} + 6080 x^{4} - 4864 x^{2} + 1600$ |
$16$ |
[0,8] |
$2^{54}\cdot 3^{12}$ |
$2$ |
$23.64923933252054$ |
$23.64923933252054$ |
|
|
? |
$C_2^2.D_4$ (as 16T37) |
$[2]$ |
$4$ |
$7$ |
$85283.83600686201$ |
| 16.0.365...000.1 |
$x^{16} + 28 x^{14} + 266 x^{12} + 1012 x^{10} + 1435 x^{8} + 908 x^{6} + 266 x^{4} + 32 x^{2} + 1$ |
$16$ |
[0,8] |
$2^{44}\cdot 3^{12}\cdot 5^{8}$ |
$3$ |
$34.2892851564$ |
$40.77706187633094$ |
✓ |
|
? |
$C_2^2.D_4$ (as 16T37) |
$[2, 8]$ |
$2$ |
$7$ |
$27938.6673263$ |
| 16.16.365...000.1 |
$x^{16} - 28 x^{14} + 266 x^{12} - 1012 x^{10} + 1435 x^{8} - 908 x^{6} + 266 x^{4} - 32 x^{2} + 1$ |
$16$ |
[16,0] |
$2^{44}\cdot 3^{12}\cdot 5^{8}$ |
$3$ |
$34.2892851564$ |
$40.77706187633094$ |
|
|
? |
$C_2^2.D_4$ (as 16T37) |
trivial |
$2$ |
$15$ |
$15464214.7165$ |
| 16.0.365...000.2 |
$x^{16} + 4 x^{14} + 62 x^{12} + 112 x^{10} + 931 x^{8} + 920 x^{6} + 3386 x^{4} - 6076 x^{2} + 2401$ |
$16$ |
[0,8] |
$2^{44}\cdot 3^{12}\cdot 5^{8}$ |
$3$ |
$34.2892851564$ |
$40.77706187633094$ |
✓ |
|
? |
$C_2^2.D_4$ (as 16T37) |
$[2, 2, 2]$ |
$2$ |
$7$ |
$58950.2572269$ |
| 16.0.365...000.3 |
$x^{16} - 4 x^{14} + 62 x^{12} - 112 x^{10} + 931 x^{8} - 920 x^{6} + 3386 x^{4} + 6076 x^{2} + 2401$ |
$16$ |
[0,8] |
$2^{44}\cdot 3^{12}\cdot 5^{8}$ |
$3$ |
$34.2892851564$ |
$40.77706187633094$ |
✓ |
|
? |
$C_2^2.D_4$ (as 16T37) |
$[2, 8]$ |
$2$ |
$7$ |
$33671.7128484$ |
| 16.16.118...625.1 |
$x^{16} - 47 x^{14} - 35 x^{13} + 789 x^{12} + 1045 x^{11} - 5823 x^{10} - 10250 x^{9} + 20071 x^{8} + 45250 x^{7} - 28530 x^{6} - 96075 x^{5} + 1845 x^{4} + 91600 x^{3} + 25800 x^{2} - 29000 x - 11600$ |
$16$ |
[16,0] |
$5^{12}\cdot 13^{8}\cdot 29^{6}$ |
$3$ |
$42.618526338$ |
$64.92293999494403$ |
|
|
|
$C_2^2.D_4$ (as 16T37) |
trivial |
$2$ |
$15$ |
$71853302.9688$ |
| 16.0.346...096.1 |
$x^{16} + 52 x^{14} + 1076 x^{12} + 11236 x^{10} + 61786 x^{8} + 168260 x^{6} + 182324 x^{4} + 32660 x^{2} + 529$ |
$16$ |
[0,8] |
$2^{42}\cdot 3^{12}\cdot 23^{6}$ |
$3$ |
$45.5714259609$ |
$67.43860803535995$ |
✓ |
|
? |
$C_2^2.D_4$ (as 16T37) |
$[2, 2, 2, 4]$ |
$2$ |
$7$ |
$147856.675539$ |
| 16.0.346...584.4 |
$x^{16} - 36 x^{14} + 742 x^{12} - 10440 x^{10} + 106132 x^{8} - 709920 x^{6} + 3431008 x^{4} - 11319552 x^{2} + 21381376$ |
$16$ |
[0,8] |
$2^{44}\cdot 13^{8}\cdot 17^{6}$ |
$3$ |
$70.18147794577077$ |
$100.00659134828328$ |
✓ |
|
|
$C_2^2.D_4$ (as 16T37) |
$[2, 8, 8]$ |
$2$ |
$7$ |
$1129313.0175622809$ |
| 16.0.346...584.5 |
$x^{16} + 36 x^{14} + 742 x^{12} + 10440 x^{10} + 106132 x^{8} + 709920 x^{6} + 3431008 x^{4} + 11319552 x^{2} + 21381376$ |
$16$ |
[0,8] |
$2^{44}\cdot 13^{8}\cdot 17^{6}$ |
$3$ |
$70.18147794577077$ |
$100.00659134828328$ |
✓ |
|
|
$C_2^2.D_4$ (as 16T37) |
$[6, 12]$ |
$2$ |
$7$ |
$2174593.0293103284$ |
