| 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 |
| 20.0.648...000.1 |
$x^{20} - 7 x^{19} + 26 x^{18} - 63 x^{17} + 102 x^{16} - 83 x^{15} - 72 x^{14} + 381 x^{13} - 463 x^{12} + 72 x^{11} + 1550 x^{10} - 4118 x^{9} + 5799 x^{8} - 5627 x^{7} + 4748 x^{6} - 2617 x^{5} + 1252 x^{4} - 451 x^{3} + 88 x^{2} - 27 x + 9$ |
$20$ |
[0,10] |
$2^{16}\cdot 5^{18}\cdot 11^{10}$ |
$3$ |
$24.5806488689$ |
$46.793049035559065$ |
|
|
|
$D_5\wr C_2$ (as 20T50) |
$[2]$ |
$2$ |
$9$ |
$784798.952025$ |
| 20.0.250...000.1 |
$x^{20} + 30 x^{16} - 2 x^{15} + 10 x^{13} + 275 x^{12} - 20 x^{11} + 2 x^{10} + 150 x^{9} + 790 x^{8} + 100 x^{7} + 30 x^{6} + 254 x^{5} + 425 x^{4} + 230 x^{3} + 50 x^{2} - 20 x + 4$ |
$20$ |
[0,10] |
$2^{28}\cdot 5^{30}$ |
$2$ |
$29.5050938534$ |
$38.982178030461924$ |
|
|
|
$D_5\wr C_2$ (as 20T50) |
trivial |
$4$ |
$9$ |
$12937342.471$ |
| 20.0.250...000.2 |
$x^{20} + 45 x^{16} - 8 x^{15} + 130 x^{13} + 400 x^{12} + 80 x^{11} + 72 x^{10} + 1050 x^{9} + 1105 x^{8} + 650 x^{7} + 1670 x^{6} + 2016 x^{5} + 1525 x^{4} + 1190 x^{3} + 550 x^{2} + 180 x + 164$ |
$20$ |
[0,10] |
$2^{28}\cdot 5^{30}$ |
$2$ |
$29.5050938534$ |
$56.44548403227803$ |
|
|
|
$D_5\wr C_2$ (as 20T50) |
trivial |
$4$ |
$9$ |
$16526624.2831$ |
| 20.4.456...000.1 |
$x^{20} - 9 x^{19} + 34 x^{18} - 67 x^{17} + 66 x^{16} + 11 x^{15} - 408 x^{14} + 2049 x^{13} - 5479 x^{12} + 6738 x^{11} + 3064 x^{10} - 27034 x^{9} + 56319 x^{8} - 60333 x^{7} - 20328 x^{6} + 149377 x^{5} - 65918 x^{4} - 107895 x^{3} - 168442 x^{2} + 346539 x - 18749$ |
$20$ |
[4,8] |
$2^{16}\cdot 5^{10}\cdot 61^{10}$ |
$3$ |
$30.4070239512$ |
$30.407023951240983$ |
|
|
|
$D_5\wr C_2$ (as 20T50) |
trivial |
$2$ |
$11$ |
$9876199.95752$ |
| 20.4.456...000.2 |
$x^{20} - 4 x^{19} + 10 x^{18} - 20 x^{17} + 71 x^{16} - 218 x^{15} + 246 x^{14} - 202 x^{13} + 648 x^{12} - 926 x^{11} - 138 x^{10} + 1338 x^{9} + 896 x^{8} - 846 x^{7} - 8502 x^{6} + 16842 x^{5} - 13793 x^{4} + 5786 x^{3} - 1200 x^{2} + 90 x + 1$ |
$20$ |
[4,8] |
$2^{16}\cdot 5^{10}\cdot 61^{10}$ |
$3$ |
$30.4070239512$ |
$30.407023951240983$ |
|
|
|
$D_5\wr C_2$ (as 20T50) |
trivial |
$2$ |
$11$ |
$46607660.7666$ |
| 20.0.241...625.1 |
$x^{20} + 20 x^{18} + 170 x^{16} - 8 x^{15} + 800 x^{14} - 120 x^{13} + 2275 x^{12} - 720 x^{11} + 4047 x^{10} - 2200 x^{9} + 4720 x^{8} - 3600 x^{7} + 4145 x^{6} - 3014 x^{5} + 2975 x^{4} - 1070 x^{3} + 1175 x^{2} - 70 x + 199$ |
$20$ |
[0,10] |
$5^{30}\cdot 11^{10}$ |
$2$ |
$37.0809924355$ |
$45.71065554658032$ |
|
|
? |
$D_5\wr C_2$ (as 20T50) |
$[2]$ |
$2$ |
$9$ |
$19342033.3142$ |
| 20.20.452...000.1 |
$x^{20} - 4 x^{19} - 63 x^{18} + 270 x^{17} + 1426 x^{16} - 6704 x^{15} - 14858 x^{14} + 81952 x^{13} + 68447 x^{12} - 533244 x^{11} - 58627 x^{10} + 1820396 x^{9} - 439446 x^{8} - 3049052 x^{7} + 801892 x^{6} + 2635222 x^{5} - 246308 x^{4} - 1037404 x^{3} - 147832 x^{2} + 66168 x + 7604$ |
$20$ |
[20,0] |
$2^{16}\cdot 3^{16}\cdot 5^{18}\cdot 29^{10}$ |
$4$ |
$96.1154056409$ |
$182.97047051958532$ |
|
|
|
$D_5\wr C_2$ (as 20T50) |
$[2]$ |
$2$ |
$19$ |
$42038324782300$ |
| 20.20.256...000.1 |
$x^{20} - 80 x^{18} + 2720 x^{16} - 84 x^{15} - 51200 x^{14} + 5040 x^{13} + 582400 x^{12} - 120960 x^{11} - 4098224 x^{10} + 1478400 x^{9} + 17496960 x^{8} - 9676800 x^{7} - 42205440 x^{6} + 32580096 x^{5} + 48076800 x^{4} - 49489920 x^{3} - 14233600 x^{2} + 25927680 x - 6385664$ |
$20$ |
[20,0] |
$2^{16}\cdot 5^{30}\cdot 29^{10}$ |
$3$ |
$104.828169436$ |
$187.114396643148$ |
|
|
|
$D_5\wr C_2$ (as 20T50) |
$[2]$ |
$2$ |
$19$ |
$94753821362700$ |
