| 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 |
| 20.0.148...713.1 |
$x^{20} - 5 x^{19} + 16 x^{18} - 46 x^{17} + 108 x^{16} - 214 x^{15} + 395 x^{14} - 698 x^{13} + 1123 x^{12} - 1588 x^{11} + 2057 x^{10} - 2588 x^{9} + 3128 x^{8} - 3348 x^{7} + 2932 x^{6} - 1996 x^{5} + 1016 x^{4} - 371 x^{3} + 92 x^{2} - 14 x + 1$ |
$20$ |
[0,10] |
$3^{5}\cdot 11^{19}$ |
$2$ |
$12.8411336046$ |
$16.89988223383312$ |
|
|
? |
$C_5\times D_4$ (as 20T12) |
trivial |
$22$ |
$9$ |
$5805.73215178$ |
| 20.0.173...125.1 |
$x^{20} - 5 x^{19} + 15 x^{18} - 36 x^{17} + 74 x^{16} - 131 x^{15} + 201 x^{14} - 267 x^{13} + 304 x^{12} - 291 x^{11} + 230 x^{10} - 116 x^{9} - 15 x^{8} + 80 x^{7} - 63 x^{6} + 21 x^{5} + 8 x^{4} - 19 x^{3} + 15 x^{2} - 6 x + 1$ |
$20$ |
[0,10] |
$5^{5}\cdot 11^{18}$ |
$2$ |
$12.9418367635$ |
$19.352559831033375$ |
|
|
? |
$C_5\times D_4$ (as 20T12) |
trivial |
$22$ |
$9$ |
$6060.61866235$ |
| 20.10.361...259.1 |
$x^{20} - 3 x^{19} - 7 x^{18} + 25 x^{17} + 4 x^{16} - 27 x^{15} + 17 x^{14} - 191 x^{13} + 37 x^{12} + 613 x^{11} - 33 x^{10} - 796 x^{9} - 208 x^{8} + 490 x^{7} + 329 x^{6} - 71 x^{5} - 145 x^{4} - 46 x^{3} + 5 x^{2} + 6 x + 1$ |
$20$ |
[10,5] |
$-\,3^{10}\cdot 11^{19}$ |
$2$ |
$16.8998822338$ |
$16.89988223383312$ |
|
|
? |
$C_5\times D_4$ (as 20T12) |
trivial |
$2$ |
$14$ |
$54412.0450771$ |
| 20.10.493...875.1 |
$x^{20} - 4 x^{19} - x^{18} + 28 x^{17} - 60 x^{16} + 45 x^{15} + 65 x^{14} - 215 x^{13} + 233 x^{12} - x^{11} - 318 x^{10} + 407 x^{9} - 158 x^{8} - 175 x^{7} + 270 x^{6} - 75 x^{5} - 110 x^{4} + 46 x^{3} + 24 x^{2} - 2 x - 1$ |
$20$ |
[10,5] |
$-\,5^{10}\cdot 11^{17}$ |
$2$ |
$17.1659872079$ |
$19.352559831033375$ |
|
|
? |
$C_5\times D_4$ (as 20T12) |
trivial |
$2$ |
$14$ |
$63613.3081038$ |
| 20.0.816...408.1 |
$x^{20} - 8 x^{19} + 40 x^{18} - 117 x^{17} + 251 x^{16} - 300 x^{15} + 303 x^{14} - 64 x^{13} + 654 x^{12} - 836 x^{11} + 1629 x^{10} + 352 x^{9} - 442 x^{8} + 1545 x^{7} + 3077 x^{6} + 1939 x^{5} + 1665 x^{4} + 2206 x^{3} + 406 x^{2} + 95 x + 661$ |
$20$ |
[0,10] |
$2^{10}\cdot 3^{15}\cdot 11^{18}$ |
$3$ |
$27.9003309928$ |
$39.45702648477223$ |
✓ |
|
? |
$C_5\times D_4$ (as 20T12) |
$[10]$ |
$2$ |
$9$ |
$125582.779517$ |
| 20.20.816...408.1 |
$x^{20} - 5 x^{19} - 18 x^{18} + 118 x^{17} + 63 x^{16} - 1022 x^{15} + 498 x^{14} + 4100 x^{13} - 4382 x^{12} - 7485 x^{11} + 12429 x^{10} + 3921 x^{9} - 14821 x^{8} + 3875 x^{7} + 6273 x^{6} - 3851 x^{5} - 190 x^{4} + 641 x^{3} - 150 x^{2} + 5 x + 1$ |
$20$ |
[20,0] |
$2^{10}\cdot 3^{15}\cdot 11^{18}$ |
$3$ |
$27.9003309928$ |
$39.45702648477223$ |
|
|
? |
$C_5\times D_4$ (as 20T12) |
trivial |
$2$ |
$19$ |
$71784662.2779$ |
| 20.0.118...912.1 |
$x^{20} - 4 x^{19} + 12 x^{18} - 32 x^{17} + 91 x^{16} - 126 x^{15} + 349 x^{14} - 606 x^{13} + 1765 x^{12} - 3140 x^{11} + 5896 x^{10} - 8688 x^{9} + 11729 x^{8} - 12648 x^{7} + 11673 x^{6} - 7892 x^{5} + 4643 x^{4} - 688 x^{3} - 849 x^{2} + 428 x + 463$ |
$20$ |
[0,10] |
$2^{15}\cdot 3^{10}\cdot 11^{19}$ |
$3$ |
$28.4221007773$ |
$47.80008531518983$ |
✓ |
|
? |
$C_5\times D_4$ (as 20T12) |
$[2, 4]$ |
$2$ |
$9$ |
$125582.779517$ |
| 20.20.118...912.1 |
$x^{20} - 8 x^{19} + 4 x^{18} + 118 x^{17} - 260 x^{16} - 490 x^{15} + 1920 x^{14} + 114 x^{13} - 5672 x^{12} + 3567 x^{11} + 7304 x^{10} - 8202 x^{9} - 3013 x^{8} + 6759 x^{7} - 980 x^{6} - 1898 x^{5} + 680 x^{4} + 134 x^{3} - 83 x^{2} + 5 x + 1$ |
$20$ |
[20,0] |
$2^{15}\cdot 3^{10}\cdot 11^{19}$ |
$3$ |
$28.4221007773$ |
$47.80008531518983$ |
|
|
? |
$C_5\times D_4$ (as 20T12) |
trivial |
$2$ |
$19$ |
$90377894.1176$ |
