| 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 |
| 20.0.453...625.1 |
$x^{20} - 3 x^{19} + 2 x^{18} - 3 x^{17} + 11 x^{16} + 3 x^{15} - 4 x^{14} - 13 x^{13} - 24 x^{12} + 51 x^{11} - 30 x^{10} - 23 x^{9} + 88 x^{8} - 132 x^{7} + 53 x^{6} + 124 x^{5} - 84 x^{4} + 4 x^{3} - 2 x^{2} - 15 x + 25$ |
$20$ |
[0,10] |
$5^{8}\cdot 47^{12}$ |
$2$ |
$19.1799166927$ |
$40.13824648753661$ |
|
|
? |
$C_2^4:D_5$ (as 20T45) |
trivial |
$2$ |
$9$ |
$30253.9562768$ |
| 20.0.564...376.1 |
$x^{20} - 2 x^{19} - 2 x^{18} + 12 x^{17} - 21 x^{16} + 26 x^{15} + 78 x^{14} - 18 x^{13} + 360 x^{12} + 482 x^{11} + 614 x^{10} + 594 x^{9} + 565 x^{8} + 686 x^{7} + 1552 x^{6} + 1286 x^{5} - 133 x^{4} - 970 x^{3} - 402 x^{2} + 102 x + 115$ |
$20$ |
[0,10] |
$2^{30}\cdot 47^{10}$ |
$2$ |
$19.3907194297$ |
$25.146651949529847$ |
|
|
? |
$C_2^4:D_5$ (as 20T45) |
$[2]$ |
$2$ |
$9$ |
$34812.3985182$ |
| 20.4.705...561.1 |
$x^{20} - 3 x^{19} + 7 x^{18} - 22 x^{17} + 43 x^{16} - 116 x^{15} + 153 x^{14} - 180 x^{13} + 224 x^{12} - 370 x^{11} + 674 x^{10} + 728 x^{9} - 2447 x^{8} + 1852 x^{7} - 3783 x^{6} + 9203 x^{5} - 16447 x^{4} + 29044 x^{3} - 35670 x^{2} + 22901 x - 5791$ |
$20$ |
[4,8] |
$3^{8}\cdot 401^{10}$ |
$2$ |
$31.0756834003$ |
$34.68429039204925$ |
|
|
? |
$C_2^4:D_5$ (as 20T45) |
$[4]$ |
$2$ |
$11$ |
$2775127.35933$ |
| 20.4.705...561.2 |
$x^{20} - 5 x^{19} - 4 x^{18} + 49 x^{17} - 6 x^{16} - 317 x^{15} + 337 x^{14} + 929 x^{13} - 2250 x^{12} + 1536 x^{11} - 1083 x^{10} + 4072 x^{9} - 4986 x^{8} + 2361 x^{7} - 2813 x^{6} + 3137 x^{5} - 686 x^{4} - 147 x^{3} - 186 x^{2} + 19 x + 51$ |
$20$ |
[4,8] |
$3^{8}\cdot 401^{10}$ |
$2$ |
$31.0756834003$ |
$34.68429039204925$ |
|
|
|
$C_2^4:D_5$ (as 20T45) |
$[4]$ |
$2$ |
$11$ |
$13089361.5818$ |
| 20.4.705...561.3 |
$x^{20} + 13 x^{18} + 9 x^{16} - 297 x^{14} - 601 x^{12} + 800 x^{10} + 1809 x^{8} - 1089 x^{6} - 6305 x^{4} + 1390 x^{2} + 1521$ |
$20$ |
[4,8] |
$3^{8}\cdot 401^{10}$ |
$2$ |
$31.0756834003$ |
$34.68429039204925$ |
|
|
? |
$C_2^4:D_5$ (as 20T45) |
$[2, 2]$ |
$2$ |
$11$ |
$3064534.69564$ |
| 20.4.172...801.1 |
$x^{20} - 2 x^{19} - 14 x^{18} + 30 x^{17} + 85 x^{16} - 97 x^{15} - 775 x^{14} - 843 x^{13} + 1743 x^{12} + 2570 x^{11} + 4868 x^{10} - 45 x^{9} + 5801 x^{8} + 1900 x^{7} + 10393 x^{6} + 5475 x^{5} + 7697 x^{4} + 4197 x^{3} + 2745 x^{2} + 567 x + 81$ |
$20$ |
[4,8] |
$401^{12}$ |
$1$ |
$36.46587371$ |
$89.6103718449757$ |
|
|
|
$C_2^4:D_5$ (as 20T45) |
$[3]$ |
$2$ |
$11$ |
$35976171.7676$ |
| 20.20.533...801.1 |
$x^{20} - 4 x^{19} - 73 x^{18} + 266 x^{17} + 2099 x^{16} - 7034 x^{15} - 30388 x^{14} + 95007 x^{13} + 233926 x^{12} - 704949 x^{11} - 910055 x^{10} + 2903891 x^{9} + 1308453 x^{8} - 6301742 x^{7} + 1117774 x^{6} + 5673768 x^{5} - 3759592 x^{4} - 115897 x^{3} + 632356 x^{2} - 144650 x + 7067$ |
$20$ |
[20,0] |
$7^{12}\cdot 199^{12}$ |
$2$ |
$76.9787172477$ |
$228.01495760534868$ |
|
|
? |
$C_2^4:D_5$ (as 20T45) |
trivial |
$2$ |
$19$ |
$4352158906050$ |
| 20.20.595...416.1 |
$x^{20} - 77 x^{18} + 2322 x^{16} - 36486 x^{14} + 334817 x^{12} - 1886957 x^{10} + 6629588 x^{8} - 14361184 x^{6} + 18445640 x^{4} - 12777520 x^{2} + 3655744$ |
$20$ |
[20,0] |
$2^{24}\cdot 1429^{10}$ |
$2$ |
$86.8464577169$ |
$106.92053123698928$ |
|
|
|
$C_2^4:D_5$ (as 20T45) |
$[4]$ |
$2$ |
$19$ |
$38855057911700$ |
