| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
| 16.0.153...104.170 |
$x^{16} - 12 x^{12} + 450 x^{8} + 972 x^{4} + 6561$ |
$16$ |
[0,8] |
$2^{58}\cdot 3^{12}$ |
$2$ |
$28.12384367863563$ |
$28.12384367863563$ |
|
|
? |
$Q_{16}:C_2$ (as 16T50) |
$[2]$ |
$[2]$ |
$8$ |
$7$ |
$290180.7746031396$ |
| 16.0.166...944.5 |
$x^{16} + 28 x^{12} + 200 x^{8} + 280 x^{4} + 4$ |
$16$ |
[0,8] |
$2^{58}\cdot 7^{8}$ |
$2$ |
$32.64245050608851$ |
$32.64245050608851$ |
|
|
|
$C_4^2:C_2^2$ (as 16T138) |
$[4]$ |
$[4]$ |
$2$ |
$7$ |
$649472.6502563054$ |
| 16.0.134...464.1 |
$x^{16} + 40 x^{14} + 608 x^{12} + 4520 x^{10} + 17782 x^{8} + 36792 x^{6} + 36288 x^{4} + 12312 x^{2} + 81$ |
$16$ |
[0,8] |
$2^{58}\cdot 3^{4}\cdot 7^{8}$ |
$3$ |
$42.9598808302$ |
$56.53838276009771$ |
✓ |
|
? |
$Q_{16}:C_2$ (as 16T50) |
$[2, 6, 6]$ |
$[2, 6, 6]$ |
$2$ |
$7$ |
$44651.6325002$ |
| 16.16.134...464.1 |
$x^{16} - 40 x^{14} + 608 x^{12} - 4520 x^{10} + 17782 x^{8} - 36792 x^{6} + 36288 x^{4} - 12312 x^{2} + 81$ |
$16$ |
[16,0] |
$2^{58}\cdot 3^{4}\cdot 7^{8}$ |
$3$ |
$42.9598808302$ |
$56.53838276009771$ |
|
|
? |
$Q_{16}:C_2$ (as 16T50) |
trivial |
$[2, 2, 2]$ |
$2$ |
$15$ |
$129617382.619$ |
| 18.18.389...112.1 |
$x^{18} - 146687112 x^{16} - 37892719296 x^{15} + 8408618911888512 x^{14} + 4325813678364681744 x^{13} - 243604861180754026285992 x^{12} - 192688273988213296086844512 x^{11} + 3797668582351192771935287035158 x^{10} + 4155203541072329873982601967541328 x^{9} - 30824703601196378502940767667441818360 x^{8} - 44117476415146499319729949379490251620992 x^{7} + 112503359565037178406650855732715578314837728 x^{6} + 209476226244754241024858216530145737787244951984 x^{5} - 121787795931109896131166351794082151507555501395576 x^{4} - 371916116695980755216640900185153166330681546329851680 x^{3} - 57935826570177631099916455044945775522459483676836854543 x^{2} + 201710684116538249174185560612387919784188057130327410730544 x + 93572448667401892834025834694441537328078001525771364657373312$ |
$18$ |
[18,0] |
$2^{60}\cdot 3^{28}\cdot 7^{9}\cdot 103^{6}\cdot 271^{6}\cdot 3030020153113^{6}$ |
$6$ |
$64652943.4195$ |
|
|
|
? |
$C_3^4:Q_{16}:C_2$ (as 18T395) |
not computed |
not computed |
$2$ |
$17$ |
|
