| 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 |
| 20.0.159...669.1 |
$x^{20} - 6 x^{19} + 11 x^{18} - 13 x^{16} - 19 x^{15} + 50 x^{14} + 8 x^{13} - 42 x^{12} - 38 x^{11} + 42 x^{10} + 31 x^{9} + 17 x^{8} - 59 x^{7} + 6 x^{6} + 2 x^{5} - x^{4} + 15 x^{3} - 2 x^{2} - 3 x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 1609^{4}\cdot 4021$ |
$3$ |
$11.4838772002$ |
$4405.606314685869$ |
|
|
? |
$C_2^8.(D_4\times S_5)$ (as 20T887) |
trivial |
$6$ |
$9$ |
$427.42684139$ |
| 20.0.302...896.1 |
$x^{20} + x^{18} - 4 x^{17} + 2 x^{16} - 4 x^{15} + 7 x^{14} - 6 x^{13} + 8 x^{12} - 6 x^{11} + 7 x^{10} - 6 x^{9} + 4 x^{8} - 2 x^{7} - 2 x^{5} - x^{4} + x^{2} + 1$ |
$20$ |
[0,10] |
$2^{20}\cdot 3^{10}\cdot 220873^{2}$ |
$3$ |
$11.8578208872$ |
|
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
trivial |
$12$ |
$9$ |
$1171.34610492$ |
| 20.0.330...241.1 |
$x^{20} - 2 x^{19} + 3 x^{18} - 6 x^{17} + 8 x^{16} - 9 x^{15} + 11 x^{14} - 10 x^{13} + 6 x^{12} - 5 x^{11} + x^{10} + 4 x^{9} - 4 x^{8} + 5 x^{7} - 5 x^{6} + 3 x^{5} - x^{4} + x^{2} - x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 236438047^{2}$ |
$2$ |
$11.9105650042$ |
$26632.95216456486$ |
|
|
? |
$C_2\times S_{10}$ (as 20T1021) |
trivial |
$6$ |
$9$ |
$622.109043514$ |
| 20.0.357...081.1 |
$x^{20} - 3 x^{19} + 2 x^{18} + 3 x^{17} - 2 x^{16} - 9 x^{15} + 18 x^{14} - 13 x^{13} - x^{12} + 6 x^{11} + 10 x^{10} - 26 x^{9} + 20 x^{8} - 6 x^{7} + x^{6} + 5 x^{5} - 10 x^{4} + 6 x^{3} - 2 x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 7^{10}\cdot 11^{8}$ |
$3$ |
$11.958225022$ |
$31.204971875395575$ |
|
|
? |
$C_5\times D_{10}$ (as 20T24) |
trivial |
$6$ |
$9$ |
$635.552521857$ |
| 20.0.393...825.1 |
$x^{20} - 5 x^{19} + 11 x^{18} - 9 x^{17} - 9 x^{16} + 34 x^{15} - 42 x^{14} + 21 x^{13} + 18 x^{12} - 46 x^{11} + 42 x^{10} - 16 x^{9} - 13 x^{8} + 25 x^{7} - 12 x^{6} - 4 x^{5} + 22 x^{4} - 21 x^{3} + 15 x^{2} - 6 x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 5^{2}\cdot 7\cdot 43^{2}\cdot 151\cdot 36943^{2}$ |
$6$ |
$12.0160420289$ |
$158702.37677804325$ |
|
|
? |
$C_2^{10}.S_5\wr C_2$ (as 20T1045) |
trivial |
$6$ |
$9$ |
$734.197779319$ |
| 20.0.609...061.1 |
$x^{20} - 3 x^{19} - x^{18} + 15 x^{17} - 17 x^{16} - 16 x^{15} + 56 x^{14} - 48 x^{13} - 12 x^{12} + 77 x^{11} - 107 x^{10} + 87 x^{9} - 8 x^{8} - 109 x^{7} + 201 x^{6} - 214 x^{5} + 158 x^{4} - 84 x^{3} + 32 x^{2} - 8 x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 73^{2}\cdot 13921^{2}\cdot 99901$ |
$4$ |
$12.2811333919$ |
$551876.8692371515$ |
|
|
? |
$C_2^{10}.S_5\wr C_2$ (as 20T1045) |
trivial |
$6$ |
$9$ |
$870.501962188$ |
| 20.0.129...337.1 |
$x^{20} - 5 x^{19} + 6 x^{18} + 11 x^{17} - 38 x^{16} + 35 x^{15} + 11 x^{14} - 60 x^{13} + 79 x^{12} - 69 x^{11} + 39 x^{10} + 5 x^{9} - 49 x^{8} + 68 x^{7} - 41 x^{6} - 7 x^{5} + 32 x^{4} - 27 x^{3} + 14 x^{2} - 5 x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 31^{8}\cdot 256393$ |
$3$ |
$12.7511869483$ |
$13680.534461057585$ |
|
|
? |
$C_2^{10}.(C_5\times D_5)$ (as 20T647) |
trivial |
$6$ |
$9$ |
$1277.33889125$ |
| 20.0.465...625.1 |
$x^{20} - x^{19} + 2 x^{18} + x^{17} + 2 x^{16} + 2 x^{15} + 7 x^{14} + x^{13} + 14 x^{12} - 2 x^{11} + 23 x^{10} - 6 x^{9} + 22 x^{8} - 4 x^{7} + 21 x^{6} - 7 x^{5} + 13 x^{4} - 12 x^{3} + 3 x^{2} - 2 x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 5^{10}\cdot 13^{4}\cdot 41^{4}$ |
$4$ |
$13.5953712478$ |
$89.41476388158725$ |
|
|
? |
$C_2^2\times S_5$ (as 20T117) |
trivial |
$6$ |
$9$ |
$2424.23048073$ |
| 20.0.492...024.1 |
$x^{20} + 2 x^{18} + x^{16} - 4 x^{14} - 8 x^{12} - 5 x^{10} + 6 x^{8} + 14 x^{6} + 12 x^{4} + 5 x^{2} + 1$ |
$20$ |
[0,10] |
$2^{20}\cdot 3^{10}\cdot 11^{4}\cdot 7369^{2}$ |
$4$ |
$13.6335832912$ |
|
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
trivial |
$12$ |
$9$ |
$5086.93249334$ |
| 20.0.492...024.4 |
$x^{20} + 5 x^{18} + 14 x^{16} + 25 x^{14} + 34 x^{12} + 38 x^{10} + 38 x^{8} + 31 x^{6} + 18 x^{4} + 6 x^{2} + 1$ |
$20$ |
[0,10] |
$2^{20}\cdot 3^{10}\cdot 11^{4}\cdot 7369^{2}$ |
$4$ |
$13.6335832912$ |
|
|
|
✓ |
$C_2^8.S_5^2:C_2^2$ (as 20T1040) |
trivial |
$6$ |
$9$ |
$2624.48747318$ |
| 20.0.492...024.5 |
$x^{20} + 5 x^{18} + 14 x^{16} + 27 x^{14} + 41 x^{12} + 47 x^{10} + 43 x^{8} + 30 x^{6} + 15 x^{4} + 5 x^{2} + 1$ |
$20$ |
[0,10] |
$2^{20}\cdot 3^{10}\cdot 11^{4}\cdot 7369^{2}$ |
$4$ |
$13.6335832912$ |
|
|
|
✓ |
$C_2^8.S_5^2:C_2^2$ (as 20T1040) |
trivial |
$6$ |
$9$ |
$2463.47198002$ |
| 20.0.494...625.1 |
$x^{20} - x^{19} + 2 x^{18} - 5 x^{17} + 5 x^{16} - 8 x^{15} + 11 x^{14} - 10 x^{13} + 9 x^{12} - 15 x^{11} + 6 x^{10} - 6 x^{9} + 8 x^{8} + 4 x^{7} + 3 x^{6} + 9 x^{5} + 5 x^{4} + 4 x^{3} + x^{2} + x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 5^{10}\cdot 199^{2}\cdot 1471^{2}$ |
$4$ |
$13.636163644$ |
$2095.4557976726687$ |
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
trivial |
$6$ |
$9$ |
$2740.01327388$ |
| 20.0.518...368.1 |
$x^{20} - 6 x^{19} + 20 x^{18} - 48 x^{17} + 89 x^{16} - 134 x^{15} + 175 x^{14} - 207 x^{13} + 237 x^{12} - 278 x^{11} + 331 x^{10} - 386 x^{9} + 426 x^{8} - 419 x^{7} + 372 x^{6} - 281 x^{5} + 181 x^{4} - 95 x^{3} + 37 x^{2} - 9 x + 1$ |
$20$ |
[0,10] |
$2^{12}\cdot 3^{10}\cdot 13^{7}\cdot 43^{4}$ |
$4$ |
$13.6694955888$ |
$272.34911951448595$ |
|
|
? |
$A_5^2:(C_2\times D_4)$ (as 20T658) |
trivial |
$6$ |
$9$ |
$3440.36919796$ |
| 20.0.528...784.3 |
$x^{20} - 6 x^{18} + 19 x^{16} - 41 x^{14} + 66 x^{12} - 80 x^{10} + 74 x^{8} - 49 x^{6} + 23 x^{4} - 7 x^{2} + 1$ |
$20$ |
[0,10] |
$2^{20}\cdot 3^{10}\cdot 31^{8}$ |
$3$ |
$13.6815499565$ |
|
|
|
? |
$C_2^8.(C_5\times D_{10})$ (as 20T538) |
trivial |
$6$ |
$9$ |
$2812.91246826$ |
| 20.0.528...784.4 |
$x^{20} + 4 x^{18} + 10 x^{16} + 15 x^{14} + 17 x^{12} + 15 x^{10} + 13 x^{8} + 12 x^{6} + 10 x^{4} + 5 x^{2} + 1$ |
$20$ |
[0,10] |
$2^{20}\cdot 3^{10}\cdot 31^{8}$ |
$3$ |
$13.6815499565$ |
|
|
|
? |
$C_2^8.(C_5\times D_{10})$ (as 20T538) |
trivial |
$6$ |
$9$ |
$2471.2827235$ |
| 20.0.574...153.1 |
$x^{20} - 4 x^{17} + 6 x^{14} - 4 x^{11} + 2 x^{10} + x^{8} - 4 x^{7} - 3 x^{5} + 2 x^{4} + 3 x^{2} + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 7\cdot 13^{5}\cdot 1723\cdot 217211089$ |
$5$ |
$13.7391457577$ |
$10107993.610639602$ |
|
|
? |
$A_5^4.D_4^2.C_2$ (as 20T1103) |
trivial |
$6$ |
$9$ |
$3377.50034261$ |
| 20.0.671...917.1 |
$x^{20} - 10 x^{19} + 54 x^{18} - 201 x^{17} + 570 x^{16} - 1296 x^{15} + 2439 x^{14} - 3879 x^{13} + 5293 x^{12} - 6265 x^{11} + 6486 x^{10} - 5904 x^{9} + 4736 x^{8} - 3341 x^{7} + 2060 x^{6} - 1097 x^{5} + 496 x^{4} - 185 x^{3} + 53 x^{2} - 10 x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 1777^{4}\cdot 114013$ |
$3$ |
$13.8466856087$ |
$24653.667130875278$ |
|
|
✓ |
$C_2^8.(D_4\times S_5)$ (as 20T887) |
trivial |
$6$ |
$9$ |
$2908.2079646$ |
| 20.0.722...989.1 |
$x^{20} - 7 x^{19} + 26 x^{18} - 73 x^{17} + 170 x^{16} - 346 x^{15} + 622 x^{14} - 944 x^{13} + 1183 x^{12} - 1208 x^{11} + 995 x^{10} - 691 x^{9} + 396 x^{8} - 166 x^{7} + 19 x^{6} + 42 x^{5} + 19 x^{4} - 19 x^{3} - 2 x^{2} + x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 37^{2}\cdot 109^{5}\cdot 241^{2}$ |
$4$ |
$13.8975782662$ |
$1707.5886507001621$ |
|
|
? |
$S_5^2:D_4$ (as 20T781) |
trivial |
$6$ |
$9$ |
$3087.8504129$ |
| 20.0.752...625.1 |
$x^{20} - 3 x^{19} + 4 x^{18} - 5 x^{17} + 8 x^{16} - 11 x^{15} + 13 x^{14} - 16 x^{13} + 22 x^{12} - 22 x^{11} + 15 x^{10} - 20 x^{9} + 27 x^{8} - 17 x^{7} + 12 x^{6} - 14 x^{5} + 8 x^{4} - 4 x^{3} + 4 x^{2} - 2 x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 5^{10}\cdot 601^{4}$ |
$3$ |
$13.9258118741$ |
$94.94735383358507$ |
|
|
? |
$D_5^2:C_2^2$ (as 20T100) |
trivial |
$6$ |
$9$ |
$3129.89439802$ |
| 20.0.915...464.1 |
$x^{20} - 4 x^{19} + 5 x^{18} - 11 x^{16} + 19 x^{15} + x^{14} - 48 x^{13} + 104 x^{12} - 145 x^{11} + 158 x^{10} - 167 x^{9} + 182 x^{8} - 189 x^{7} + 175 x^{6} - 133 x^{5} + 82 x^{4} - 42 x^{3} + 17 x^{2} - 5 x + 1$ |
$20$ |
[0,10] |
$2^{8}\cdot 3^{10}\cdot 8821^{4}$ |
$3$ |
$14.0629421438$ |
$547.1696884958392$ |
|
|
? |
$C_2^8.D_5^2:C_2^2$ (as 20T760) |
trivial |
$6$ |
$9$ |
$4222.32085816$ |
| 20.0.967...824.1 |
$x^{20} - 2 x^{18} + 4 x^{12} + 8 x^{10} - 14 x^{8} - 8 x^{6} + 15 x^{4} + 8 x^{2} + 1$ |
$20$ |
[0,10] |
$2^{24}\cdot 3^{10}\cdot 13^{4}\cdot 43^{4}$ |
$4$ |
$14.1019439354$ |
$347.60943715688273$ |
|
|
? |
$C_2^8.A_5^2:C_2^3$ (as 20T1028) |
trivial |
$6$ |
$9$ |
$5919.94430523$ |
| 20.0.116...641.1 |
$x^{20} - 3 x^{19} + 3 x^{18} - 4 x^{17} + 9 x^{16} - 10 x^{15} + x^{14} + 10 x^{13} - 14 x^{12} + 8 x^{11} + 16 x^{10} - 34 x^{9} + 36 x^{8} - 29 x^{7} + 24 x^{6} - 12 x^{5} + 8 x^{4} - 6 x^{3} + 3 x^{2} - x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 7^{10}\cdot 17^{8}$ |
$3$ |
$14.2327629428$ |
$18.894443627691185$ |
|
|
? |
$C_2\times D_{10}$ (as 20T8) |
trivial |
$6$ |
$9$ |
$4706.41314047$ |
| 20.0.139...824.1 |
$x^{20} - 2 x^{18} + 5 x^{16} - x^{14} - x^{12} + 7 x^{10} - 2 x^{6} + 4 x^{4} + 4 x^{2} + 1$ |
$20$ |
[0,10] |
$2^{12}\cdot 3^{10}\cdot 4903^{4}$ |
$3$ |
$14.3638547037$ |
$1914.7592348233552$ |
|
|
? |
$C_2^8.A_5^2:C_2^2$ (as 20T1008) |
trivial |
$6$ |
$9$ |
$4480.37888591$ |
| 20.0.345...064.1 |
$x^{20} - 2 x^{18} - 2 x^{15} - 6 x^{14} + 8 x^{13} + 14 x^{12} - 4 x^{11} - x^{10} - 6 x^{9} - x^{8} - 8 x^{7} + 4 x^{6} + 2 x^{5} - x^{4} + 4 x^{2} - 2 x + 1$ |
$20$ |
[0,10] |
$2^{20}\cdot 3^{10}\cdot 29^{4}\cdot 53^{4}$ |
$4$ |
$15.0288377726$ |
$135.8086889709197$ |
|
|
? |
$D_5^2:C_2^2$ (as 20T100) |
trivial |
$12$ |
$9$ |
$17343.1636986$ |
| 20.0.522...677.1 |
$x^{20} - 2 x^{19} + 2 x^{18} - x^{17} - 2 x^{15} - 9 x^{14} + 3 x^{12} + x^{11} + 22 x^{9} + 45 x^{8} + 41 x^{7} + 29 x^{6} + 18 x^{5} + 7 x^{4} - 2 x^{3} - 3 x^{2} + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 13^{5}\cdot 47^{8}$ |
$3$ |
$15.342128242$ |
$42.81354925721529$ |
|
|
? |
$D_4\times D_5$ (as 20T21) |
trivial |
$6$ |
$9$ |
$8452.6678373$ |
| 20.0.649...921.1 |
$x^{20} - 2 x^{17} - x^{16} - 3 x^{15} + x^{14} + 3 x^{13} + 7 x^{12} - x^{11} + 6 x^{10} - 7 x^{9} + 7 x^{8} - 18 x^{7} + 3 x^{6} - 9 x^{5} + 11 x^{4} - x^{3} + 4 x^{2} - x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 1483^{2}\cdot 2236369^{2}$ |
$3$ |
$15.5106175275$ |
$99747.71015416845$ |
|
|
? |
$C_2\times S_{10}$ (as 20T1021) |
trivial |
$6$ |
$9$ |
$8617.1364564$ |
| 20.0.685...625.1 |
$x^{20} - 3 x^{19} + 4 x^{18} - 7 x^{17} + 15 x^{16} - 24 x^{15} + 34 x^{14} - 47 x^{13} + 67 x^{12} - 78 x^{11} + 72 x^{10} - 81 x^{9} + 81 x^{8} - 54 x^{7} + 45 x^{6} - 37 x^{5} + 20 x^{4} - 11 x^{3} + 6 x^{2} - 3 x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 5^{10}\cdot 1039^{2}\cdot 1049^{2}$ |
$4$ |
$15.5519457669$ |
$4043.3482412475923$ |
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
trivial |
$6$ |
$9$ |
$9161.21223923$ |
| 20.0.686...001.1 |
$x^{20} + x^{18} - 2 x^{17} + 2 x^{16} + 2 x^{15} + 6 x^{14} + 4 x^{13} + x^{12} - 2 x^{11} + 14 x^{10} + 10 x^{9} + 5 x^{8} - x^{7} + 12 x^{6} + 15 x^{5} - 2 x^{3} + 9 x^{2} + 3 x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 3409004107^{2}$ |
$2$ |
$15.5533297544$ |
$101128.6918782202$ |
|
|
? |
$C_2\times S_{10}$ (as 20T1021) |
trivial |
$6$ |
$9$ |
$9979.28108523$ |
| 20.0.686...801.1 |
$x^{20} - x^{19} - x^{18} + 6 x^{17} - 5 x^{16} - 5 x^{15} + 17 x^{14} - 9 x^{13} - 10 x^{12} + 24 x^{11} - 13 x^{10} - 9 x^{9} + 30 x^{8} - 26 x^{7} + x^{6} + 25 x^{5} - 16 x^{4} - 4 x^{3} + 11 x^{2} - 4 x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 7^{8}\cdot 17^{10}$ |
$3$ |
$15.5533628545$ |
$18.894443627691185$ |
|
|
? |
$C_2\times D_{10}$ (as 20T8) |
trivial |
$6$ |
$9$ |
$12584.3597894$ |
| 20.0.690...625.1 |
$x^{20} - 3 x^{19} + 8 x^{18} - 15 x^{17} + 28 x^{16} - 46 x^{15} + 63 x^{14} - 81 x^{13} + 92 x^{12} - 98 x^{11} + 89 x^{10} - 66 x^{9} + 54 x^{8} - 28 x^{7} + x^{6} - 3 x^{5} - 5 x^{4} + 10 x^{3} - x^{2} + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 5^{10}\cdot 61^{2}\cdot 17939^{2}$ |
$4$ |
$15.5581672565$ |
$4051.442335761426$ |
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
trivial |
$6$ |
$9$ |
$8167.64790374$ |
| 20.0.114...744.1 |
$x^{20} + 3 x^{18} + 3 x^{16} - 6 x^{14} - 11 x^{12} - 7 x^{10} - 3 x^{8} + 6 x^{6} + 19 x^{4} + 7 x^{2} + 1$ |
$20$ |
[0,10] |
$2^{32}\cdot 3^{10}\cdot 7^{4}\cdot 37^{4}$ |
$4$ |
$15.9539627328$ |
|
|
|
|
$A_5^2:C_2^3$ (as 20T548) |
trivial |
$12$ |
$9$ |
$44820.5144024$ |
| 20.0.114...744.2 |
$x^{20} - 7 x^{16} - 2 x^{14} + 29 x^{12} - 54 x^{10} + 77 x^{8} - 44 x^{6} - 4 x^{4} + 16 x^{2} + 16$ |
$20$ |
[0,10] |
$2^{32}\cdot 3^{10}\cdot 7^{4}\cdot 37^{4}$ |
$4$ |
$15.9539627328$ |
$487.3068781324951$ |
|
|
? |
$C_2^8.A_5^2:C_2^3$ (as 20T1028) |
trivial |
$6$ |
$9$ |
$21174.0969976$ |
| 20.0.117...792.1 |
$x^{20} - 9 x^{19} + 45 x^{18} - 163 x^{17} + 464 x^{16} - 1081 x^{15} + 2121 x^{14} - 3545 x^{13} + 5100 x^{12} - 6329 x^{11} + 6805 x^{10} - 6329 x^{9} + 5100 x^{8} - 3545 x^{7} + 2121 x^{6} - 1081 x^{5} + 464 x^{4} - 163 x^{3} + 45 x^{2} - 9 x + 1$ |
$20$ |
[0,10] |
$2^{16}\cdot 3^{10}\cdot 13^{13}$ |
$3$ |
$15.9752551367$ |
$20.646295463608727$ |
|
|
? |
$D_{10}:C_4$ (as 20T19) |
trivial |
$6$ |
$9$ |
$19012.2439561$ |
| 20.0.147...464.1 |
$x^{20} - 2 x^{18} + x^{16} - 3 x^{14} - 9 x^{12} + 8 x^{10} + 22 x^{8} + 12 x^{6} + 1$ |
$20$ |
[0,10] |
$2^{20}\cdot 3^{10}\cdot 47^{8}$ |
$3$ |
$16.1595687355$ |
|
|
|
? |
$C_2^9.D_{10}$ (as 20T430) |
trivial |
$6$ |
$9$ |
$20577.4746256$ |
| 20.0.147...464.2 |
$x^{20} + 5 x^{18} + 19 x^{16} + 51 x^{14} + 94 x^{12} + 132 x^{10} + 128 x^{8} + 63 x^{6} + 7 x^{4} - 2 x^{2} + 1$ |
$20$ |
[0,10] |
$2^{20}\cdot 3^{10}\cdot 47^{8}$ |
$3$ |
$16.1595687355$ |
|
|
|
? |
$C_2^9.D_{10}$ (as 20T430) |
trivial |
$6$ |
$9$ |
$18222.0554621$ |
| 20.0.147...464.4 |
$x^{20} - x^{18} + 11 x^{14} - 27 x^{12} - 8 x^{10} + 76 x^{8} - 82 x^{6} + 34 x^{4} - 4 x^{2} + 1$ |
$20$ |
[0,10] |
$2^{20}\cdot 3^{10}\cdot 47^{8}$ |
$3$ |
$16.159568735513513$ |
|
|
|
? |
$C_2^9.D_{10}$ (as 20T430) |
trivial |
$6$ |
$9$ |
$17984.519664041843$ |
| 20.0.148...797.1 |
$x^{20} + x^{16} - 4 x^{15} + 9 x^{12} - 21 x^{11} + 14 x^{10} + x^{8} - 5 x^{6} + 4 x^{5} + x^{4} - x^{3} - x^{2} + x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 13^{5}\cdot 19^{4}\cdot 151^{4}$ |
$4$ |
$16.1656277916$ |
$334.50112107435456$ |
|
|
? |
$D_4\times S_5$ (as 20T174) |
trivial |
$6$ |
$9$ |
$16956.6944135$ |
| 20.0.154...184.1 |
$x^{20} + 9 x^{18} + 34 x^{16} + 73 x^{14} + 120 x^{12} + 142 x^{10} + 134 x^{8} + 89 x^{6} + 47 x^{4} + 11 x^{2} + 1$ |
$20$ |
[0,10] |
$2^{28}\cdot 3^{10}\cdot 13^{4}\cdot 43^{4}$ |
$4$ |
$16.1988798008$ |
|
|
|
? |
$A_5^2:C_2^3$ (as 20T548) |
trivial |
$12$ |
$9$ |
$46673.003502$ |
| 20.0.176...264.1 |
$x^{20} - 2 x^{19} + 2 x^{18} - 4 x^{17} + 6 x^{16} - 8 x^{15} + 12 x^{14} - 8 x^{13} - 5 x^{12} - 6 x^{11} + 14 x^{10} + 12 x^{9} + 14 x^{8} - 4 x^{7} - 12 x^{6} - 16 x^{5} - 7 x^{4} + 2 x^{3} + 2 x^{2} + 4 x + 4$ |
$20$ |
[0,10] |
$2^{32}\cdot 3^{10}\cdot 17^{8}$ |
$3$ |
$16.3075301064$ |
$38.517882206335926$ |
|
|
|
$C_2^2\times A_5$ (as 20T64) |
trivial |
$12$ |
$9$ |
$51384.9781866$ |
| 20.0.254...625.1 |
$x^{20} - x^{19} + 6 x^{18} + x^{17} + 17 x^{16} + 14 x^{15} + 40 x^{14} + 59 x^{13} + 64 x^{12} + 113 x^{11} + 106 x^{10} + 135 x^{9} + 86 x^{8} + 106 x^{7} + 7 x^{6} + 40 x^{5} + 14 x^{4} - 85 x^{3} + 40 x^{2} - 25 x + 25$ |
$20$ |
[0,10] |
$3^{10}\cdot 5^{16}\cdot 7^{10}$ |
$3$ |
$16.6067883548$ |
$37.133907649370514$ |
|
|
? |
$D_5\times D_{10}$ (as 20T59) |
trivial |
$6$ |
$9$ |
$27201.1631786$ |
| 20.0.267...512.1 |
$x^{20} - 9 x^{19} + 42 x^{18} - 135 x^{17} + 322 x^{16} - 563 x^{15} + 685 x^{14} - 484 x^{13} - 76 x^{12} + 770 x^{11} - 1177 x^{10} + 996 x^{9} - 365 x^{8} - 306 x^{7} + 697 x^{6} - 721 x^{5} + 518 x^{4} - 274 x^{3} + 109 x^{2} - 30 x + 4$ |
$20$ |
[0,10] |
$2^{4}\cdot 3^{10}\cdot 4903^{5}$ |
$3$ |
$16.6487679361$ |
$5827.6106981440025$ |
|
|
|
$C_2^{10}.\SOPlus(4,4)$ (as 20T1023) |
trivial |
$6$ |
$9$ |
$52175.1150233$ |
| 20.10.361...259.1 |
$x^{20} - 3 x^{19} - 7 x^{18} + 25 x^{17} + 4 x^{16} - 27 x^{15} + 17 x^{14} - 191 x^{13} + 37 x^{12} + 613 x^{11} - 33 x^{10} - 796 x^{9} - 208 x^{8} + 490 x^{7} + 329 x^{6} - 71 x^{5} - 145 x^{4} - 46 x^{3} + 5 x^{2} + 6 x + 1$ |
$20$ |
[10,5] |
$-\,3^{10}\cdot 11^{19}$ |
$2$ |
$16.8998822338$ |
$16.89988223383312$ |
|
|
? |
$C_5\times D_4$ (as 20T12) |
trivial |
$2$ |
$14$ |
$54412.0450771$ |
| 20.0.961...000.1 |
$x^{20} - 4 x^{17} - 3 x^{16} + 2 x^{15} + 10 x^{14} + 8 x^{13} + x^{12} - 10 x^{11} - 10 x^{10} + 2 x^{9} + x^{8} - 2 x^{7} - 6 x^{6} - 2 x^{5} + 9 x^{4} + 4 x^{3} + 2 x + 1$ |
$20$ |
[0,10] |
$2^{24}\cdot 3^{10}\cdot 5^{4}\cdot 353^{4}$ |
$4$ |
$17.7478424226$ |
$637.4269600462906$ |
|
|
|
$A_5^2:C_2^2$ (as 20T458) |
trivial |
$12$ |
$9$ |
$159607.526546$ |
| 20.0.121...625.1 |
$x^{20} + 2 x^{18} - 8 x^{17} + 8 x^{16} - 14 x^{15} + 26 x^{14} - 43 x^{13} + 62 x^{12} - 52 x^{11} + 99 x^{10} - 104 x^{9} + 89 x^{8} - 91 x^{7} + 67 x^{6} - 84 x^{5} + 22 x^{4} - 14 x^{3} + 29 x^{2} + 5 x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 5^{10}\cdot 4588681^{2}$ |
$3$ |
$17.9561992646$ |
$8296.397712260425$ |
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
trivial |
$6$ |
$9$ |
$34456.4237695$ |
| 20.4.336...249.1 |
$x^{20} - 10 x^{19} + 47 x^{18} - 138 x^{17} + 283 x^{16} - 428 x^{15} + 450 x^{14} - 148 x^{13} - 409 x^{12} + 374 x^{11} + 1036 x^{10} - 2975 x^{9} + 3655 x^{8} - 2634 x^{7} + 947 x^{6} + 305 x^{5} - 612 x^{4} + 322 x^{3} - 67 x^{2} + x + 1$ |
$20$ |
[4,8] |
$3^{10}\cdot 7^{10}\cdot 17^{10}$ |
$3$ |
$18.8944436277$ |
$18.894443627691185$ |
|
|
? |
$C_2\times D_{10}$ (as 20T8) |
trivial |
$2$ |
$11$ |
$58001.1435756$ |
| 20.0.348...056.1 |
$x^{20} + 18 x^{18} + 135 x^{16} + 540 x^{14} + 1231 x^{12} + 1604 x^{10} + 1167 x^{8} + 462 x^{6} + 106 x^{4} + 16 x^{2} + 1$ |
$20$ |
[0,10] |
$2^{20}\cdot 3^{10}\cdot 59^{2}\cdot 402107^{2}$ |
$4$ |
$18.9282292608$ |
|
|
|
? |
$S_5^2:C_2^2$ (as 20T656) |
trivial |
$12$ |
$9$ |
$182622.47508$ |
| 20.0.379...000.1 |
$x^{20} - 2 x^{19} + 4 x^{18} + x^{16} - 4 x^{15} + 2 x^{14} - 2 x^{13} + 5 x^{12} + 4 x^{11} + 6 x^{10} - 4 x^{9} - 3 x^{8} - 2 x^{7} + 6 x^{6} - 4 x^{5} + 17 x^{4} - 8 x^{3} - 2 x + 1$ |
$20$ |
[0,10] |
$2^{20}\cdot 3^{10}\cdot 5^{10}\cdot 89^{4}$ |
$4$ |
$19.0087529575$ |
$275.12324972060804$ |
|
|
|
$A_5^2:C_2^3$ (as 20T548) |
trivial |
$6$ |
$9$ |
$212672.802641$ |
| 20.0.399...464.1 |
$x^{20} + 24 x^{18} + 234 x^{16} + 1198 x^{14} + 3467 x^{12} + 5684 x^{10} + 5047 x^{8} + 2260 x^{6} + 467 x^{4} + 38 x^{2} + 1$ |
$20$ |
[0,10] |
$2^{20}\cdot 3^{10}\cdot 71^{8}$ |
$3$ |
$19.0587302172$ |
$104.85696952505783$ |
✓ |
|
? |
$C_5\times D_{10}$ (as 20T24) |
trivial |
$12$ |
$9$ |
$264102.546071$ |
| 20.4.452...625.1 |
$x^{20} - 3 x^{17} - 23 x^{16} + 46 x^{15} - 62 x^{14} + 306 x^{13} - 395 x^{12} + 394 x^{11} - 779 x^{10} + 893 x^{9} - 548 x^{8} + 25 x^{7} - 264 x^{6} + 420 x^{5} - 391 x^{4} + 51 x^{3} + 118 x^{2} - 17 x - 11$ |
$20$ |
[4,8] |
$3^{10}\cdot 5^{10}\cdot 601^{5}$ |
$3$ |
$19.1762749293$ |
$94.94735383358507$ |
|
|
? |
$D_5^2:C_2^2$ (as 20T92) |
trivial |
$2$ |
$11$ |
$72349.8991655$ |
| 20.4.636...625.1 |
$x^{20} - 10 x^{18} + 27 x^{16} - 30 x^{14} + 91 x^{12} - 85 x^{10} + 140 x^{8} - 120 x^{6} + 125 x^{4} - 55 x^{2} + 25$ |
$20$ |
[4,8] |
$3^{10}\cdot 5^{18}\cdot 7^{10}$ |
$3$ |
$19.5066481854$ |
$37.133907649370514$ |
|
|
? |
$D_5\times D_{10}$ (as 20T59) |
trivial |
$2$ |
$11$ |
$115359.797336$ |
