| 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 |
| 20.0.722...936.1 |
$x^{20} - 4 x^{19} + 8 x^{18} - 12 x^{17} + 16 x^{16} - 36 x^{15} + 52 x^{14} + 16 x^{13} - 64 x^{12} - 56 x^{11} + 200 x^{10} + 192 x^{9} + 136 x^{8} + 208 x^{7} + 64 x^{6} - 96 x^{5} + 64 x^{4} + 192 x^{3} + 64 x^{2} + 32$ |
$20$ |
[0,10] |
$2^{30}\cdot 7^{10}\cdot 47^{8}$ |
$3$ |
$34.9086582577$ |
$70.95657033042767$ |
|
|
? |
$D_5\times A_4$ (as 20T37) |
trivial |
$2$ |
$9$ |
$13684855.6842$ |
| 20.0.320...625.1 |
$x^{20} - 2 x^{19} + 2 x^{18} + 2 x^{17} - 6 x^{16} + 4 x^{15} + 39 x^{14} - 126 x^{13} + 137 x^{12} + 47 x^{11} - 321 x^{10} + 359 x^{9} + 246 x^{8} - 1174 x^{7} + 2192 x^{6} - 1341 x^{5} - 8 x^{4} + 2400 x^{3} - 576 x^{2} + 1024$ |
$20$ |
[0,10] |
$5^{10}\cdot 13^{10}\cdot 47^{8}$ |
$3$ |
$37.6093494711$ |
$84.75451298300825$ |
|
|
? |
$D_5\times A_4$ (as 20T37) |
$[2]$ |
$2$ |
$9$ |
$14363449.2462$ |
| 20.4.315...089.1 |
$x^{20} - 2 x^{19} + 2 x^{18} + 4 x^{17} - 10 x^{16} + 104 x^{15} + 675 x^{14} + 770 x^{13} + 1759 x^{12} - 195 x^{11} - 4565 x^{10} + 3085 x^{9} + 10111 x^{8} + 16588 x^{7} + 38727 x^{6} + 13729 x^{5} - 45405 x^{4} - 23166 x^{3} - 94770 x^{2} + 59049$ |
$20$ |
[4,8] |
$47^{8}\cdot 163^{10}$ |
$2$ |
$59.5570181003$ |
$204.56939710422668$ |
|
|
? |
$D_5\times A_4$ (as 20T37) |
trivial |
$2$ |
$11$ |
$8004059626.39$ |
| 20.4.100...689.1 |
$x^{20} - 3 x^{17} - 63 x^{15} + 1011 x^{14} - 1728 x^{13} + 5107 x^{12} - 4020 x^{11} - 11221 x^{10} + 11955 x^{9} - 5805 x^{8} + 840 x^{7} + 1068 x^{6} - 1584 x^{5} - 803 x^{4} - 180 x^{3} - 23 x^{2} + 1$ |
$20$ |
[4,8] |
$3^{10}\cdot 47^{8}\cdot 61^{10}$ |
$3$ |
$63.1051332397$ |
$184.0049245858974$ |
|
|
? |
$D_5\times A_4$ (as 20T37) |
trivial |
$2$ |
$11$ |
$13453127150.8$ |
| 20.0.202...376.1 |
$x^{20} - 6 x^{19} - 2 x^{18} + 64 x^{17} - 14 x^{16} - 436 x^{15} + 478 x^{14} + 806 x^{13} - 353 x^{12} - 3450 x^{11} + 4838 x^{10} - 4132 x^{9} + 8903 x^{8} - 13704 x^{7} + 21364 x^{6} - 16984 x^{5} + 18589 x^{4} - 20038 x^{3} + 35838 x^{2} - 13398 x + 17123$ |
$20$ |
[0,10] |
$2^{30}\cdot 7^{10}\cdot 401^{8}$ |
$3$ |
$82.2908906025$ |
$207.26018102939304$ |
|
|
? |
$D_5\times A_4$ (as 20T37) |
trivial |
$2$ |
$9$ |
$99133769895.8$ |
| 20.0.179...976.1 |
$x^{20} - 6 x^{19} - 10 x^{18} + 104 x^{17} + 34 x^{16} - 876 x^{15} + 466 x^{14} + 2726 x^{13} - 57 x^{12} - 8874 x^{11} + 5254 x^{10} + 820 x^{9} + 9099 x^{8} - 7864 x^{7} + 23172 x^{6} - 27568 x^{5} + 44861 x^{4} - 60510 x^{3} + 126562 x^{2} - 54390 x + 58471$ |
$20$ |
[0,10] |
$2^{30}\cdot 7^{14}\cdot 199^{8}$ |
$3$ |
$91.7603057675$ |
$201.93885914428654$ |
|
|
? |
$D_5\times A_4$ (as 20T37) |
trivial |
$2$ |
$9$ |
$483814559041$ |
| 20.20.885...649.1 |
$x^{20} - x^{19} - 58 x^{18} + 41 x^{17} + 1325 x^{16} - 653 x^{15} - 15442 x^{14} + 5251 x^{13} + 99299 x^{12} - 23893 x^{11} - 357547 x^{10} + 66887 x^{9} + 703666 x^{8} - 120039 x^{7} - 712988 x^{6} + 132265 x^{5} + 330432 x^{4} - 70240 x^{3} - 51122 x^{2} + 11872 x - 643$ |
$20$ |
[20,0] |
$163^{10}\cdot 401^{8}$ |
$2$ |
$140.394970925$ |
$597.5357895604798$ |
|
|
? |
$D_5\times A_4$ (as 20T37) |
trivial |
$2$ |
$19$ |
$1694909520630000$ |
| 20.20.281...249.1 |
$x^{20} - 4 x^{19} - 49 x^{18} + 183 x^{17} + 916 x^{16} - 3140 x^{15} - 8616 x^{14} + 26624 x^{13} + 44550 x^{12} - 121756 x^{11} - 129120 x^{10} + 305362 x^{9} + 203500 x^{8} - 406080 x^{7} - 160387 x^{6} + 260630 x^{5} + 54133 x^{4} - 67485 x^{3} - 9972 x^{2} + 5958 x + 873$ |
$20$ |
[20,0] |
$3^{10}\cdot 61^{10}\cdot 401^{8}$ |
$3$ |
$148.759014957$ |
$537.4681132751847$ |
|
|
|
$D_5\times A_4$ (as 20T37) |
trivial |
$2$ |
$19$ |
$3231166245160000$ |
