| 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 |
| 20.20.488...704.1 |
$x^{20} - 10 x^{19} - 116 x^{18} + 1313 x^{17} + 4736 x^{16} - 67464 x^{15} - 71774 x^{14} + 1744748 x^{13} - 126850 x^{12} - 24570618 x^{11} + 14939336 x^{10} + 193331394 x^{9} - 163802315 x^{8} - 826609978 x^{7} + 787082462 x^{6} + 1707884929 x^{5} - 1813914636 x^{4} - 1179787402 x^{3} + 1644305872 x^{2} - 315124556 x - 58612856$ |
$20$ |
[20,0] |
$2^{16}\cdot 17^{15}\cdot 53^{13}$ |
$3$ |
$192.504108489$ |
$328.90735776316194$ |
|
|
|
$C_{20}:C_4$ (as 20T18) |
$[2]$ |
$2$ |
$19$ |
$293289608829000000$ |
| 20.0.781...264.1 |
$x^{20} - 4 x^{19} + 96 x^{18} + 122 x^{17} + 4620 x^{16} + 18596 x^{15} + 184045 x^{14} + 728624 x^{13} + 6000753 x^{12} + 13556428 x^{11} + 139124895 x^{10} + 136683460 x^{9} + 2117576320 x^{8} - 289614572 x^{7} + 18977386826 x^{6} - 37574492902 x^{5} + 70623059201 x^{4} - 324133328144 x^{3} + 72454618799 x^{2} - 66338130030 x + 1082598671174$ |
$20$ |
[0,10] |
$2^{20}\cdot 17^{15}\cdot 53^{13}$ |
$3$ |
$221.129152751$ |
$328.90735776316194$ |
✓ |
|
? |
$C_{20}:C_4$ (as 20T18) |
$[2, 2, 2, 6, 6, 5562]$ |
$2$ |
$9$ |
$4097659676.87$ |
| 20.20.258...312.1 |
$x^{20} - 4 x^{19} - 211 x^{18} + 1138 x^{17} + 12703 x^{16} - 81202 x^{15} - 279760 x^{14} + 2366808 x^{13} + 1504150 x^{12} - 31913924 x^{11} + 22954298 x^{10} + 194714572 x^{9} - 295344111 x^{8} - 469380944 x^{7} + 1107126565 x^{6} + 182743098 x^{5} - 1481772709 x^{4} + 491417950 x^{3} + 577682706 x^{2} - 321816380 x + 25224604$ |
$20$ |
[20,0] |
$2^{16}\cdot 17^{15}\cdot 53^{14}$ |
$3$ |
$234.776052566$ |
$328.90735776316194$ |
|
|
|
$C_{20}:C_4$ (as 20T18) |
$[4]$ |
$2$ |
$19$ |
$1146610929550000000$ |
| 20.0.414...992.1 |
$x^{20} - 4 x^{19} + 177 x^{18} - 4 x^{17} + 8449 x^{16} + 23822 x^{15} + 168540 x^{14} + 596526 x^{13} + 2612317 x^{12} + 7067238 x^{11} + 38130743 x^{10} + 75736410 x^{9} + 321304814 x^{8} + 864149074 x^{7} + 1787066994 x^{6} + 245640690 x^{5} + 6843858589 x^{4} - 4594563420 x^{3} + 14977761454 x^{2} - 24323038390 x + 15554125329$ |
$20$ |
[0,10] |
$2^{20}\cdot 17^{15}\cdot 53^{14}$ |
$3$ |
$269.686865375$ |
$328.90735776316194$ |
✓ |
|
? |
$C_{20}:C_4$ (as 20T18) |
$[2, 2, 6, 12, 22248]$ |
$2$ |
$9$ |
$8009866748.83$ |
