| 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 |
| 20.2.120...008.2 |
$x^{20} - 2 x^{19} - 8 x^{18} + 20 x^{17} + 5 x^{16} - 38 x^{15} + 38 x^{14} - 58 x^{13} + 72 x^{12} - 70 x^{11} + 96 x^{10} - 34 x^{9} - 47 x^{8} - 30 x^{7} + 64 x^{6} + 22 x^{5} - 19 x^{4} - 14 x^{3} + 2 x - 1$ |
$20$ |
[2,9] |
$-\,2^{30}\cdot 47^{9}$ |
$2$ |
$15.9951762372$ |
$25.146651949529847$ |
|
|
? |
$C_2^4:D_5$ (as 20T38) |
trivial |
$2$ |
$10$ |
$7339.72832281$ |
| 20.2.120...008.3 |
$x^{20} - 2 x^{19} + 6 x^{18} - 18 x^{17} + 26 x^{16} - 60 x^{15} + 124 x^{14} - 168 x^{13} + 269 x^{12} - 414 x^{11} + 540 x^{10} - 668 x^{9} + 728 x^{8} - 786 x^{7} + 788 x^{6} - 642 x^{5} + 396 x^{4} - 138 x^{3} + 44 x^{2} - 8 x + 1$ |
$20$ |
[2,9] |
$-\,2^{30}\cdot 47^{9}$ |
$2$ |
$15.9951762372$ |
$25.146651949529847$ |
|
|
? |
$C_2^4:D_5$ (as 20T38) |
trivial |
$2$ |
$10$ |
$7842.51365505$ |
| 20.0.195...129.1 |
$x^{20} - 2 x^{19} + 10 x^{18} - 11 x^{17} + 15 x^{16} + 14 x^{15} - 5 x^{14} - 64 x^{13} + 214 x^{12} - 320 x^{11} + 303 x^{10} - 212 x^{9} + 188 x^{8} - 75 x^{7} + 21 x^{6} - 7 x^{5} + 23 x^{4} - 24 x^{3} + 16 x^{2} - 5 x + 1$ |
$20$ |
[0,10] |
$3^{6}\cdot 401^{9}$ |
$2$ |
$20.6324757858$ |
$34.68429039204925$ |
|
|
? |
$C_2^4:D_5$ (as 20T38) |
$[2]$ |
$2$ |
$9$ |
$33411.4738636$ |
| 20.4.195...129.1 |
$x^{20} - 5 x^{19} + 17 x^{18} - 48 x^{17} + 113 x^{16} - 220 x^{15} + 335 x^{14} - 345 x^{13} + 118 x^{12} + 376 x^{11} - 1035 x^{10} + 1466 x^{9} - 1251 x^{8} + 459 x^{7} + 176 x^{6} - 145 x^{5} - 8 x^{4} - 16 x^{3} + 23 x^{2} + 3 x + 3$ |
$20$ |
[4,8] |
$3^{6}\cdot 401^{9}$ |
$2$ |
$20.6324757858$ |
$34.68429039204925$ |
|
|
? |
$C_2^4:D_5$ (as 20T38) |
trivial |
$2$ |
$11$ |
$323981.65654$ |
| 20.8.175...161.1 |
$x^{20} - 5 x^{19} - 2 x^{18} + 41 x^{17} - 7 x^{16} - 203 x^{15} + 110 x^{14} + 512 x^{13} - 313 x^{12} - 799 x^{11} + 548 x^{10} + 791 x^{9} - 684 x^{8} - 632 x^{7} + 531 x^{6} + 467 x^{5} - 136 x^{4} - 190 x^{3} - 42 x^{2} + 2 x + 1$ |
$20$ |
[8,6] |
$3^{8}\cdot 401^{9}$ |
$2$ |
$23.0283843622$ |
$34.68429039204925$ |
|
|
? |
$C_2^4:D_5$ (as 20T38) |
trivial |
$2$ |
$13$ |
$1214073.35747$ |
| 20.0.175...161.1 |
$x^{20} - 9 x^{19} + 43 x^{18} - 133 x^{17} + 293 x^{16} - 525 x^{15} + 893 x^{14} - 1457 x^{13} + 2102 x^{12} - 2770 x^{11} + 3616 x^{10} - 4338 x^{9} + 4157 x^{8} - 3013 x^{7} + 1702 x^{6} - 747 x^{5} + 166 x^{4} + 36 x^{3} + 32 x^{2} - 80 x + 32$ |
$20$ |
[0,10] |
$3^{8}\cdot 401^{9}$ |
$2$ |
$23.0283843622$ |
$34.68429039204925$ |
|
|
? |
$C_2^4:D_5$ (as 20T38) |
$[2]$ |
$2$ |
$9$ |
$110300.954595$ |
| 20.4.158...449.1 |
$x^{20} - 12 x^{18} - x^{17} + 35 x^{16} - 22 x^{15} + 21 x^{14} + 186 x^{13} - 18 x^{12} + 170 x^{11} + 445 x^{10} - 384 x^{9} - 144 x^{8} + 113 x^{7} - 835 x^{6} + 127 x^{5} + 203 x^{4} - 504 x^{3} + 322 x^{2} - 249 x + 57$ |
$20$ |
[4,8] |
$3^{10}\cdot 401^{9}$ |
$2$ |
$25.7025134472$ |
$34.68429039204925$ |
|
|
? |
$C_2^4:D_5$ (as 20T38) |
$[2]$ |
$2$ |
$11$ |
$1949572.20243$ |
| 20.8.158...449.1 |
$x^{20} - 5 x^{19} + 13 x^{18} - 43 x^{17} + 110 x^{16} - 202 x^{15} + 294 x^{14} - 136 x^{13} - 148 x^{12} + 50 x^{11} + 152 x^{10} - 79 x^{9} - 314 x^{8} + 67 x^{7} + 89 x^{6} + 55 x^{5} - 6 x^{4} - 7 x^{3} - 7 x^{2} - 2 x + 1$ |
$20$ |
[8,6] |
$3^{10}\cdot 401^{9}$ |
$2$ |
$25.7025134472$ |
$34.68429039204925$ |
|
|
? |
$C_2^4:D_5$ (as 20T38) |
$[2]$ |
$2$ |
$13$ |
$2212993.78287$ |
| 20.20.651...536.1 |
$x^{20} - 8 x^{19} - 10 x^{18} + 220 x^{17} - 279 x^{16} - 1984 x^{15} + 4826 x^{14} + 6348 x^{13} - 27246 x^{12} + 1368 x^{11} + 65496 x^{10} - 41248 x^{9} - 63708 x^{8} + 62344 x^{7} + 18102 x^{6} - 25596 x^{5} - 2245 x^{4} + 3688 x^{3} + 260 x^{2} - 128 x - 4$ |
$20$ |
[20,0] |
$2^{18}\cdot 1429^{9}$ |
$2$ |
$49.0559283726$ |
$106.92053123698928$ |
|
|
? |
$C_2^4:D_5$ (as 20T38) |
trivial |
$2$ |
$19$ |
$117630359267$ |
| 20.20.651...536.2 |
$x^{20} - 37 x^{18} + 581 x^{16} - 5055 x^{14} + 26694 x^{12} - 88133 x^{10} + 180741 x^{8} - 221377 x^{6} + 149427 x^{4} - 48302 x^{2} + 5716$ |
$20$ |
[20,0] |
$2^{18}\cdot 1429^{9}$ |
$2$ |
$49.0559283726$ |
$106.92053123698928$ |
|
|
? |
$C_2^4:D_5$ (as 20T38) |
trivial |
$2$ |
$19$ |
$36062412269.7$ |
