| 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 |
Unit signature rank |
| 20.6.149...088.1 |
$x^{20} - 3 x^{18} - 9 x^{16} + 3 x^{14} - 18 x^{12} + 120 x^{10} + 540 x^{8} + 666 x^{6} + 330 x^{4} + 54 x^{2} - 3$ |
$20$ |
(6, 7) |
$-\,2^{20}\cdot 3^{19}\cdot 223^{6}$ |
$3$ |
$28.7598519836$ |
|
|
|
? |
$C_2^9.(C_2\times S_5)$ (as 20T800) |
trivial |
$[2]$ |
$2$ |
$12$ |
$7067436.90335$ |
$5$ |
| 20.6.149...088.2 |
$x^{20} + 6 x^{18} - 3 x^{16} + 54 x^{12} - 105 x^{10} + 87 x^{8} - 12 x^{6} - 30 x^{4} + 18 x^{2} - 3$ |
$20$ |
(6, 7) |
$-\,2^{20}\cdot 3^{19}\cdot 223^{6}$ |
$3$ |
$28.7598519836$ |
|
|
|
? |
$C_2^9.(C_2\times S_5)$ (as 20T800) |
trivial |
$[2]$ |
$2$ |
$12$ |
$9505372.16371$ |
$5$ |
| 20.2.121...000.1 |
$x^{20} - 3$ |
$20$ |
(2, 9) |
$-\,2^{40}\cdot 3^{19}\cdot 5^{20}$ |
$3$ |
$56.7930493584$ |
$72.30039804795702$ |
|
|
✓ |
$D_4\times F_5$ (as 20T42) |
$[2]$ |
$[2, 2]$ |
$2$ |
$10$ |
$3729139104.85$ |
$1$ |
| 20.2.128...579.1 |
$x^{20} - 3 x - 3$ |
$20$ |
(2, 9) |
$-\,3^{19}\cdot 11\cdot 317\cdot 24391\cdot 1302657414478831561$ |
$5$ |
$56.949613428$ |
$29889667002706.793$ |
|
|
✓ |
$S_{20}$ (as 20T1117) |
trivial |
$[2]$ |
$2$ |
$10$ |
$6899010527.48$ |
$1$ |
| 20.2.149...656.1 |
$x^{20} - 6 x - 3$ |
$20$ |
(2, 9) |
$-\,2^{18}\cdot 3^{19}\cdot 509\cdot 96370438990419405533$ |
$4$ |
$72.2312730255$ |
|
|
|
? |
$S_{20}$ (as 20T1117) |
trivial |
$[2]$ |
$2$ |
$10$ |
$193180156776$ |
$1$ |
| 20.0.566...496.1 |
$x^{20} - 6 x + 6$ |
$20$ |
(0, 10) |
$2^{20}\cdot 3^{19}\cdot 13\cdot 3576426233309158402509851$ |
$4$ |
$109.05983062$ |
|
|
|
✓ |
$S_{20}$ (as 20T1117) |
$[2]$ |
$[2]$ |
$2$ |
$9$ |
$2645107811650$ |
$0$ |
| 20.0.638...421.1 |
$x^{20} - 3 x + 6$ |
$20$ |
(0, 10) |
$3^{19}\cdot 8377\cdot 757339037557\cdot 8665446098234267$ |
$4$ |
$109.716938619$ |
$2.1054749754151156e+16$ |
|
|
✓ |
$S_{20}$ (as 20T1117) |
$[2]$ |
$[2]$ |
$2$ |
$9$ |
$4991680191810$ |
$0$ |
| 20.0.638...000.1 |
$x^{20} + 6$ |
$20$ |
(0, 10) |
$2^{59}\cdot 3^{19}\cdot 5^{20}$ |
$3$ |
$109.716939211$ |
$154.9792959172223$ |
|
|
✓ |
$D_4\times F_5$ (as 20T42) |
$[2]$ |
$[2]$ |
$2$ |
$9$ |
$3249681118900$ |
$0$ |
| 20.2.489...371.1 |
$x^{20} - 9 x + 6$ |
$20$ |
(2, 9) |
$-\,3^{19}\cdot 7\cdot 13\cdot 257\cdot 1579\cdot 3224847061\cdot 3537102887772821$ |
$7$ |
$121.476106893$ |
$5.828031933129955e+16$ |
|
|
? |
$S_{20}$ (as 20T1117) |
trivial |
$[2]$ |
$2$ |
$10$ |
$47794776531200$ |
$1$ |
| 20.2.240...179.1 |
$x^{20} - 9 x - 3$ |
$20$ |
(2, 9) |
$-\,3^{19}\cdot 11\cdot 5101\cdot 3217829\cdot 26435864551\cdot 4335710551573$ |
$6$ |
$147.59050898$ |
$4.085051882499857e+17$ |
|
|
✓ |
$S_{20}$ (as 20T1117) |
trivial |
$[2]$ |
$2$ |
$10$ |
$142233639483000$ |
$1$ |
| 21.1.789...469.1 |
$x^{21} - 3 x - 9$ |
$21$ |
(1, 10) |
$3^{19}\cdot 29\cdot 55867813\cdot 4191305915922243109905102391$ |
$4$ |
$153.313911936$ |
$7.399795308226999e+18$ |
|
|
? |
$S_{21}$ (as 21T164) |
trivial |
trivial |
$2$ |
$10$ |
$868990488950000$ |
$1$ |
| 21.1.789...469.1 |
$x^{21} + 6 x - 9$ |
$21$ |
(1, 10) |
$3^{19}\cdot 13\cdot 113\cdot 2253311\cdot 16878613\cdot 121546765019059840121$ |
$6$ |
$153.314148351$ |
$7.399915122124316e+18$ |
|
|
? |
$S_{21}$ (as 21T164) |
trivial |
trivial |
$2$ |
$10$ |
$1908348601180000$ |
$1$ |
