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 |
20.10.361...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 |
$2$ |
$14$ |
$54412.0450771$ |
20.10.393...375.1 |
$x^{20} - x^{19} - x^{18} + 11 x^{17} - 53 x^{16} + 61 x^{15} - 54 x^{14} - 3 x^{13} + 266 x^{12} - 79 x^{11} - 167 x^{10} - 9 x^{9} - 215 x^{8} - 42 x^{7} + 305 x^{6} - 155 x^{5} + 17 x^{4} + 43 x^{3} - 30 x^{2} + 3 x + 1$ |
$20$ |
[10,5] |
$-\,5^{10}\cdot 3319^{5}$ |
$2$ |
$16.9721481969$ |
$128.82158204276178$ |
|
|
? |
$D_5\wr C_2$ (as 20T48) |
trivial |
$2$ |
$14$ |
$53457.8405658$ |
20.10.417...375.1 |
$x^{20} - 2 x^{19} - 11 x^{18} + 23 x^{17} + 31 x^{16} - 111 x^{15} + 48 x^{14} + 275 x^{13} - 467 x^{12} - 341 x^{11} + 1168 x^{10} + 107 x^{9} - 1480 x^{8} + 268 x^{7} + 1065 x^{6} - 330 x^{5} - 456 x^{4} + 70 x^{3} + 45 x^{2} - 13 x + 1$ |
$20$ |
[10,5] |
$-\,5^{10}\cdot 3359^{5}$ |
$2$ |
$17.0230550318$ |
$129.59552461408535$ |
|
|
? |
$D_5\wr C_2$ (as 20T48) |
trivial |
$2$ |
$14$ |
$55116.0718093$ |
20.10.493...875.1 |
$x^{20} - 4 x^{19} - x^{18} + 28 x^{17} - 60 x^{16} + 45 x^{15} + 65 x^{14} - 215 x^{13} + 233 x^{12} - x^{11} - 318 x^{10} + 407 x^{9} - 158 x^{8} - 175 x^{7} + 270 x^{6} - 75 x^{5} - 110 x^{4} + 46 x^{3} + 24 x^{2} - 2 x - 1$ |
$20$ |
[10,5] |
$-\,5^{10}\cdot 11^{17}$ |
$2$ |
$17.1659872079$ |
$19.352559831033375$ |
|
|
? |
$C_5\times D_4$ (as 20T12) |
trivial |
$2$ |
$14$ |
$63613.3081038$ |
20.10.897...152.1 |
$x^{20} - 12 x^{18} + 63 x^{16} - 194 x^{14} + 385 x^{12} - 493 x^{10} + 371 x^{8} - 100 x^{6} - 80 x^{4} + 83 x^{2} - 23$ |
$20$ |
[10,5] |
$-\,2^{10}\cdot 23\cdot 641^{2}\cdot 5519^{4}$ |
$4$ |
$17.6872075229$ |
$33086.76993763445$ |
|
|
? |
$C_2^{10}.C_2\wr S_5$ (as 20T1015) |
trivial |
$2$ |
$14$ |
$88065.812548$ |
20.10.185...896.1 |
$x^{20} - 7 x^{18} + 18 x^{16} - 38 x^{14} + 84 x^{12} - 60 x^{10} - 128 x^{8} + 261 x^{6} - 186 x^{4} + 63 x^{2} - 9$ |
$20$ |
[10,5] |
$-\,2^{10}\cdot 3^{6}\cdot 17^{4}\cdot 4153^{4}$ |
$4$ |
$18.3406002338$ |
$2320.0213627026787$ |
|
|
? |
$C_2^9.C_2^5.S_5$ (as 20T992) |
trivial |
$2$ |
$14$ |
$136001.268357$ |
20.10.248...056.1 |
$x^{20} - 2 x^{18} - 6 x^{16} + 19 x^{14} - 30 x^{12} - 28 x^{10} + 105 x^{8} - x^{6} - 37 x^{4} + 12 x^{2} - 1$ |
$20$ |
[10,5] |
$-\,2^{10}\cdot 11^{16}\cdot 727^{2}$ |
$3$ |
$18.611551871$ |
$703.2778998665901$ |
|
|
? |
$C_2^{10}.C_2\wr C_5$ (as 20T846) |
trivial |
$2$ |
$14$ |
$152135.358854$ |
20.10.248...056.2 |
$x^{20} + x^{18} - 16 x^{16} - 17 x^{14} + 74 x^{12} + 90 x^{10} - 94 x^{8} - 112 x^{6} + 26 x^{4} + 5 x^{2} - 1$ |
$20$ |
[10,5] |
$-\,2^{10}\cdot 11^{16}\cdot 727^{2}$ |
$3$ |
$18.611551871$ |
$703.2778998665901$ |
|
|
? |
$C_2^{10}.C_2\wr C_5$ (as 20T846) |
trivial |
$2$ |
$14$ |
$153214.090592$ |
20.10.248...056.3 |
$x^{20} - 3 x^{18} - 8 x^{16} + 27 x^{14} + 9 x^{12} - 71 x^{10} + 35 x^{8} + 49 x^{6} - 58 x^{4} + 19 x^{2} - 1$ |
$20$ |
[10,5] |
$-\,2^{10}\cdot 11^{16}\cdot 727^{2}$ |
$3$ |
$18.611551871$ |
$703.2778998665901$ |
|
|
? |
$C_2^{10}.C_2\wr C_5$ (as 20T846) |
trivial |
$2$ |
$14$ |
$150230.99101$ |
20.10.248...056.4 |
$x^{20} + x^{18} - 31 x^{16} + 59 x^{14} + 3 x^{12} - 86 x^{10} + 63 x^{8} + 15 x^{6} - 35 x^{4} + 12 x^{2} - 1$ |
$20$ |
[10,5] |
$-\,2^{10}\cdot 11^{16}\cdot 727^{2}$ |
$3$ |
$18.611551871$ |
$703.2778998665901$ |
|
|
? |
$C_2^{10}.C_2\wr C_5$ (as 20T846) |
trivial |
$2$ |
$14$ |
$150748.473735$ |
20.10.350...248.1 |
$x^{20} - 10 x^{18} + 42 x^{16} - 113 x^{14} + 236 x^{12} - 329 x^{10} + 191 x^{8} + 128 x^{6} - 249 x^{4} + 119 x^{2} - 17$ |
$20$ |
[10,5] |
$-\,2^{10}\cdot 3^{4}\cdot 17^{5}\cdot 4153^{4}$ |
$4$ |
$18.9331931457$ |
$3579.512641707566$ |
|
|
? |
$C_2^9.C_2^5.S_5$ (as 20T992) |
trivial |
$2$ |
$14$ |
$182092.772888$ |
20.10.367...119.1 |
$x^{20} - 10 x^{19} + 37 x^{18} - 48 x^{17} - 57 x^{16} + 252 x^{15} - 222 x^{14} - 204 x^{13} + 562 x^{12} - 304 x^{11} - 307 x^{10} + 517 x^{9} - 173 x^{8} - 184 x^{7} + 202 x^{6} - 49 x^{5} - 37 x^{4} + 34 x^{3} - 7 x^{2} - 3 x + 1$ |
$20$ |
[10,5] |
$-\,317\cdot 443\cdot 673^{2}\cdot 4903^{4}$ |
$4$ |
$18.9787250672$ |
$680722.2920464703$ |
|
|
✓ |
$C_2^{10}.C_2\wr S_5$ (as 20T1015) |
trivial |
$2$ |
$14$ |
$183861.307452$ |
20.10.379...947.1 |
$x^{20} - x^{19} - 7 x^{18} + 17 x^{17} + 5 x^{16} - 57 x^{15} + 55 x^{14} + 38 x^{13} - 176 x^{12} + 108 x^{11} + 241 x^{10} - 244 x^{9} - 92 x^{8} + 195 x^{7} - 120 x^{6} - 73 x^{5} + 130 x^{4} + 16 x^{3} - 34 x^{2} - 2 x + 1$ |
$20$ |
[10,5] |
$-\,7^{6}\cdot 43^{5}\cdot 1217^{4}$ |
$3$ |
$19.0087973844$ |
$605.2412742039327$ |
|
|
? |
$C_2^9.C_2^5.S_5$ (as 20T992) |
trivial |
$2$ |
$14$ |
$228565.419572$ |
20.10.434...144.1 |
$x^{20} - 8 x^{18} + 23 x^{16} - 33 x^{14} + 25 x^{12} + 10 x^{10} - 40 x^{8} + 21 x^{6} + x^{4} - 1$ |
$20$ |
[10,5] |
$-\,2^{14}\cdot 307^{4}\cdot 739^{4}$ |
$3$ |
$19.137163166$ |
|
|
|
? |
$C_2^{10}.A_{10}$ (as 20T1106) |
trivial |
$2$ |
$14$ |
$198289.220847$ |
20.10.464...816.1 |
$x^{20} - 10 x^{19} + 37 x^{18} - 46 x^{17} - 81 x^{16} + 358 x^{15} - 434 x^{14} - 60 x^{13} + 775 x^{12} - 1046 x^{11} + 945 x^{10} - 638 x^{9} - 310 x^{8} + 1564 x^{7} - 1908 x^{6} + 1168 x^{5} - 339 x^{4} - 2 x^{3} + 34 x^{2} - 10 x + 1$ |
$20$ |
[10,5] |
$-\,2^{20}\cdot 83^{4}\cdot 983^{4}$ |
$3$ |
$19.2024356191$ |
|
|
|
? |
$C_2^9.C_2^5.S_5$ (as 20T992) |
trivial |
$2$ |
$14$ |
$270387.319194$ |
20.10.464...816.2 |
$x^{20} - 6 x^{19} + 8 x^{18} + 26 x^{17} - 98 x^{16} + 82 x^{15} + 111 x^{14} - 194 x^{13} - 100 x^{12} + 70 x^{11} + 1277 x^{10} - 2956 x^{9} + 2439 x^{8} + 390 x^{7} - 2506 x^{6} + 2138 x^{5} - 732 x^{4} - 12 x^{3} + 74 x^{2} - 12 x - 1$ |
$20$ |
[10,5] |
$-\,2^{20}\cdot 83^{4}\cdot 983^{4}$ |
$3$ |
$19.2024356191$ |
|
|
|
? |
$C_2^9.C_2^5.S_5$ (as 20T992) |
trivial |
$2$ |
$14$ |
$254610.712489$ |
20.10.748...419.1 |
$x^{20} - 3 x^{19} - 4 x^{18} + 23 x^{17} + 3 x^{16} - 108 x^{15} + 62 x^{14} + 353 x^{13} - 538 x^{12} - 333 x^{11} + 1385 x^{10} - 819 x^{9} - 865 x^{8} + 1401 x^{7} - 518 x^{6} - 210 x^{5} + 322 x^{4} - 267 x^{3} + 152 x^{2} - 37 x + 1$ |
$20$ |
[10,5] |
$-\,11^{17}\cdot 23^{6}$ |
$2$ |
$19.6653705073$ |
$90.89694638232187$ |
|
|
? |
$C_2^5.C_2\wr C_5$ (as 20T310) |
trivial |
$2$ |
$14$ |
$298913.61697$ |
20.10.106...651.1 |
$x^{20} - 5 x^{19} + 16 x^{18} - 38 x^{17} + 36 x^{16} + 53 x^{15} - 225 x^{14} + 425 x^{13} - 559 x^{12} + 338 x^{11} + 384 x^{10} - 897 x^{9} + 449 x^{8} + 347 x^{7} - 442 x^{6} + 31 x^{5} + 132 x^{4} - 33 x^{3} - 17 x^{2} + 4 x + 1$ |
$20$ |
[10,5] |
$-\,251^{4}\cdot 1931^{5}$ |
$2$ |
$20.0161392059$ |
$3652.835493495483$ |
|
|
|
$C_5\wr S_4$ (as 20T462) |
trivial |
$2$ |
$14$ |
$372281.376086$ |
20.10.123...112.1 |
$x^{20} - 8 x^{19} + 24 x^{18} - 30 x^{17} - 18 x^{16} + 200 x^{15} - 584 x^{14} + 960 x^{13} - 937 x^{12} + 480 x^{11} + 328 x^{10} - 1274 x^{9} + 1384 x^{8} - 422 x^{7} - 322 x^{6} + 272 x^{5} - 60 x^{4} + 18 x^{3} - 20 x^{2} + 8 x - 1$ |
$20$ |
[10,5] |
$-\,2^{30}\cdot 103\cdot 5783^{4}$ |
$3$ |
$20.165894611$ |
|
|
|
? |
$C_2^9.C_2^5.S_5$ (as 20T992) |
trivial |
$2$ |
$14$ |
$363110.453896$ |
20.10.144...864.1 |
$x^{20} - x^{18} - 15 x^{16} + 14 x^{14} + 69 x^{12} - 133 x^{10} - 110 x^{8} + 517 x^{6} - 495 x^{4} + 165 x^{2} - 11$ |
$20$ |
[10,5] |
$-\,2^{10}\cdot 11^{17}\cdot 23^{4}$ |
$3$ |
$20.3256455304$ |
$152.24694139566975$ |
|
|
? |
$C_2^5.C_2^8:C_{10}$ (as 20T749) |
trivial |
$2$ |
$14$ |
$432984.426207$ |
20.10.144...864.2 |
$x^{20} + x^{18} - 4 x^{16} - 36 x^{14} + 14 x^{12} + 254 x^{10} - 319 x^{8} - 33 x^{6} + 88 x^{4} + 44 x^{2} - 11$ |
$20$ |
[10,5] |
$-\,2^{10}\cdot 11^{17}\cdot 23^{4}$ |
$3$ |
$20.3256455304$ |
$152.24694139566975$ |
|
|
? |
$C_2^5.C_2^8:C_{10}$ (as 20T749) |
trivial |
$2$ |
$14$ |
$423472.987307$ |
20.10.155...456.1 |
$x^{20} - 12 x^{18} + 55 x^{16} - 117 x^{14} + 107 x^{12} - 24 x^{10} + 17 x^{8} - 57 x^{6} + 30 x^{4} - 1$ |
$20$ |
[10,5] |
$-\,2^{16}\cdot 149^{4}\cdot 1481^{4}$ |
$3$ |
$20.39728020118754$ |
|
|
|
|
$C_2^9.C_2^5.S_5$ (as 20T992) |
trivial |
$2$ |
$14$ |
$597656.3104754605$ |
20.10.160...000.1 |
$x^{20} - 2 x^{19} - 6 x^{18} + 22 x^{17} - 10 x^{16} - 88 x^{15} + 147 x^{14} + 84 x^{13} - 469 x^{12} + 240 x^{11} + 623 x^{10} - 708 x^{9} - 183 x^{8} + 732 x^{7} - 276 x^{6} - 262 x^{5} + 222 x^{4} - 10 x^{3} - 35 x^{2} + 6 x + 1$ |
$20$ |
[10,5] |
$-\,2^{20}\cdot 5^{10}\cdot 11^{4}\cdot 181^{4}$ |
$4$ |
$20.4328642571$ |
|
|
|
? |
$C_5\wr D_4$ (as 20T299) |
trivial |
$2$ |
$14$ |
$458094.158162$ |
20.10.186...136.1 |
$x^{20} - 6 x^{19} + 8 x^{18} + 12 x^{17} - 35 x^{16} + 30 x^{15} + 70 x^{14} - 366 x^{13} + 113 x^{12} + 1284 x^{11} - 1196 x^{10} - 1704 x^{9} + 2502 x^{8} + 510 x^{7} - 1986 x^{6} + 468 x^{5} + 563 x^{4} - 228 x^{3} - 76 x^{2} + 30 x + 7$ |
$20$ |
[10,5] |
$-\,2^{30}\cdot 53^{4}\cdot 59\cdot 139^{4}$ |
$4$ |
$20.584756216374213$ |
|
|
|
? |
$C_2^9.C_2^5.S_5$ (as 20T992) |
trivial |
$2$ |
$14$ |
$524943.8816056355$ |
20.10.195...679.1 |
$x^{20} - x^{19} - 13 x^{18} + 14 x^{17} + 70 x^{16} - 82 x^{15} - 203 x^{14} + 261 x^{13} + 351 x^{12} - 492 x^{11} - 397 x^{10} + 566 x^{9} + 346 x^{8} - 403 x^{7} - 262 x^{6} + 180 x^{5} + 142 x^{4} - 44 x^{3} - 36 x^{2} + 1$ |
$20$ |
[10,5] |
$-\,16493^{2}\cdot 520151\cdot 1175561^{2}$ |
$3$ |
$20.6329323741$ |
$100423911.52322002$ |
|
|
? |
$C_2^{10}.S_{10}$ (as 20T1110) |
trivial |
$2$ |
$14$ |
$434433.516854$ |
20.10.201...875.1 |
$x^{20} - 2 x^{19} - 11 x^{18} + 16 x^{17} + 40 x^{16} - 41 x^{15} - 71 x^{14} + 42 x^{13} + 39 x^{12} - 27 x^{11} + 159 x^{10} + 4 x^{9} - 369 x^{8} - 61 x^{7} + 444 x^{6} + 7 x^{5} - 200 x^{4} + 2 x^{3} + 29 x^{2} - x - 1$ |
$20$ |
[10,5] |
$-\,5^{10}\cdot 19^{5}\cdot 1699^{4}$ |
$3$ |
$20.6638898519$ |
$401.75241131821474$ |
|
|
? |
$D_{10}\wr C_2$ (as 20T168) |
trivial |
$2$ |
$14$ |
$464579.009458$ |
20.10.201...875.2 |
$x^{20} - 3 x^{19} - 10 x^{18} + 27 x^{17} + 45 x^{16} - 76 x^{15} - 145 x^{14} + 98 x^{13} + 274 x^{12} - 51 x^{11} - 339 x^{10} - 51 x^{9} + 274 x^{8} + 98 x^{7} - 145 x^{6} - 76 x^{5} + 45 x^{4} + 27 x^{3} - 10 x^{2} - 3 x + 1$ |
$20$ |
[10,5] |
$-\,5^{10}\cdot 19^{5}\cdot 1699^{4}$ |
$3$ |
$20.6638898519$ |
$838.7777321687686$ |
|
|
✓ |
$C_2^8.D_{10}\wr C_2$ (as 20T876) |
trivial |
$2$ |
$14$ |
$492393.298171$ |
20.10.201...875.3 |
$x^{20} - 6 x^{19} + 13 x^{18} - 6 x^{17} - 42 x^{16} + 139 x^{15} - 198 x^{14} + 49 x^{13} + 354 x^{12} - 720 x^{11} + 620 x^{10} + 45 x^{9} - 811 x^{8} + 756 x^{7} - 133 x^{6} + 66 x^{5} - 177 x^{4} + 91 x^{3} + 8 x^{2} - 9 x + 1$ |
$20$ |
[10,5] |
$-\,5^{10}\cdot 19^{5}\cdot 1699^{4}$ |
$3$ |
$20.6638898519$ |
$838.7777321687686$ |
|
|
? |
$C_2^8.D_{10}\wr C_2$ (as 20T876) |
trivial |
$2$ |
$14$ |
$496664.119055$ |
20.10.241...419.1 |
$x^{20} - 10 x^{19} + 34 x^{18} - 21 x^{17} - 135 x^{16} + 264 x^{15} + 122 x^{14} - 680 x^{13} + 158 x^{12} + 898 x^{11} - 439 x^{10} - 737 x^{9} + 429 x^{8} + 396 x^{7} - 229 x^{6} - 136 x^{5} + 74 x^{4} + 28 x^{3} - 15 x^{2} - 2 x + 1$ |
$20$ |
[10,5] |
$-\,11^{2}\cdot 41\cdot 3691\cdot 3628255063^{2}$ |
$4$ |
$20.8499704889$ |
$77715777.91109978$ |
|
|
✓ |
$C_2^{10}.S_{10}$ (as 20T1110) |
trivial |
$2$ |
$14$ |
$473763.087336$ |
20.10.274...224.1 |
$x^{20} - 12 x^{18} + 57 x^{16} - 132 x^{14} + 139 x^{12} - 19 x^{10} - 71 x^{8} + 30 x^{6} + 10 x^{4} - 3 x^{2} - 1$ |
$20$ |
[10,5] |
$-\,2^{20}\cdot 673^{2}\cdot 4903^{4}$ |
$3$ |
$20.985720323937798$ |
|
|
|
✓ |
$C_2^{10}.C_2\wr S_5$ (as 20T1015) |
trivial |
$2$ |
$14$ |
$533109.5446087791$ |
20.10.330...064.1 |
$x^{20} - x^{19} - 3 x^{18} + 7 x^{17} - 6 x^{16} + 11 x^{15} - 31 x^{14} - 68 x^{13} + 269 x^{12} - 140 x^{11} - 496 x^{10} + 705 x^{9} + 157 x^{8} - 799 x^{7} + 490 x^{6} + 374 x^{5} - 387 x^{4} + 57 x^{3} + 127 x^{2} - 25 x + 1$ |
$20$ |
[10,5] |
$-\,2^{10}\cdot 11^{18}\cdot 241^{2}$ |
$3$ |
$21.182153882$ |
$514.6447591533517$ |
|
|
? |
$C_2^{10}.C_2\wr C_5$ (as 20T846) |
trivial |
$2$ |
$14$ |
$617689.692878$ |
20.10.499...696.1 |
$x^{20} - 10 x^{18} + 18 x^{16} - 42 x^{14} + 23 x^{12} + 100 x^{10} - 52 x^{8} - 120 x^{6} + 72 x^{4} + 18 x^{2} - 9$ |
$20$ |
[10,5] |
$-\,2^{10}\cdot 3^{6}\cdot 401^{8}$ |
$3$ |
$21.6226601931$ |
$174.84722497415262$ |
|
|
? |
$C_2^6.C_2^8:D_5$ (as 20T849) |
trivial |
$2$ |
$14$ |
$838076.531091$ |
20.10.658...144.1 |
$x^{20} - 9 x^{18} + 18 x^{16} + 26 x^{14} - 80 x^{12} + 22 x^{10} - 93 x^{8} - 105 x^{6} + 780 x^{4} - 210 x^{2} - 241$ |
$20$ |
[10,5] |
$-\,2^{10}\cdot 11^{16}\cdot 241^{3}$ |
$3$ |
$21.9246011941$ |
$404.91912156279443$ |
|
|
? |
$C_2^{10}.C_2\wr C_5$ (as 20T846) |
trivial |
$2$ |
$14$ |
$840640.634638$ |
20.10.658...144.2 |
$x^{20} - 3 x^{19} - 7 x^{18} + 4 x^{17} + 59 x^{16} + 41 x^{15} - 155 x^{14} - 151 x^{13} + 146 x^{12} - 149 x^{11} - 667 x^{10} + 273 x^{9} + 1109 x^{8} + 143 x^{7} - 550 x^{6} - 211 x^{5} + 94 x^{4} + 83 x^{3} - 7 x^{2} - 9 x - 1$ |
$20$ |
[10,5] |
$-\,2^{10}\cdot 11^{16}\cdot 241^{3}$ |
$3$ |
$21.9246011941$ |
$404.91912156279443$ |
|
|
? |
$C_2^{10}.C_2\wr C_5$ (as 20T846) |
trivial |
$2$ |
$14$ |
$866308.68228$ |
20.10.658...144.3 |
$x^{20} - 2 x^{19} - 10 x^{18} + 30 x^{17} + 2 x^{16} - 119 x^{15} + 241 x^{14} - 159 x^{13} - 305 x^{12} + 1042 x^{11} - 1683 x^{10} + 1548 x^{9} - 250 x^{8} - 1523 x^{7} + 2507 x^{6} - 1857 x^{5} + 376 x^{4} + 492 x^{3} - 472 x^{2} + 75 x + 67$ |
$20$ |
[10,5] |
$-\,2^{10}\cdot 11^{16}\cdot 241^{3}$ |
$3$ |
$21.9246011941$ |
$1595.4108698395264$ |
|
|
? |
$C_2^{10}.C_2\wr C_5$ (as 20T846) |
trivial |
$2$ |
$14$ |
$826263.9163$ |
20.10.658...144.4 |
$x^{20} - 13 x^{18} + 64 x^{16} - 148 x^{14} + 212 x^{12} - 510 x^{10} + 1324 x^{8} - 1599 x^{6} + 476 x^{4} + 433 x^{2} - 241$ |
$20$ |
[10,5] |
$-\,2^{10}\cdot 11^{16}\cdot 241^{3}$ |
$3$ |
$21.924601194104245$ |
$404.91912156279443$ |
|
|
? |
$C_2^{10}.C_2\wr C_5$ (as 20T846) |
trivial |
$2$ |
$14$ |
$924306.9836138696$ |
20.10.806...875.1 |
$x^{20} - 2 x^{19} - 11 x^{18} + 29 x^{17} + 11 x^{16} - 122 x^{15} + 184 x^{14} + 47 x^{13} - 342 x^{12} + 569 x^{11} - 536 x^{10} - 1288 x^{9} + 403 x^{8} + 3536 x^{7} + 167 x^{6} - 3112 x^{5} - 1429 x^{4} + 1221 x^{3} + 772 x^{2} - 92 x - 1$ |
$20$ |
[10,5] |
$-\,5^{8}\cdot 151^{4}\cdot 331^{5}$ |
$3$ |
$22.1482996029$ |
|
|
|
? |
$C_5\wr S_4$ (as 20T462) |
trivial |
$2$ |
$14$ |
$1133873.36921$ |
20.10.909...744.1 |
$x^{20} - 9 x^{19} + 30 x^{18} - 26 x^{17} - 92 x^{16} + 235 x^{15} - 38 x^{14} - 277 x^{13} - 443 x^{12} + 1550 x^{11} + 245 x^{10} - 4064 x^{9} + 3041 x^{8} + 2955 x^{7} - 4618 x^{6} + 302 x^{5} + 2054 x^{4} - 768 x^{3} - 178 x^{2} + 108 x - 9$ |
$20$ |
[10,5] |
$-\,2^{10}\cdot 71^{5}\cdot 281^{6}$ |
$3$ |
$22.2813489897$ |
$6157.504577096202$ |
|
|
? |
$C_4^5.C_2^4.S_5$ (as 20T993) |
trivial |
$2$ |
$14$ |
$1259433.60319$ |
20.10.909...744.2 |
$x^{20} + 6 x^{18} + 8 x^{16} - 89 x^{14} - 80 x^{12} + 257 x^{10} + 245 x^{8} - 512 x^{6} + 23 x^{4} + 213 x^{2} - 71$ |
$20$ |
[10,5] |
$-\,2^{10}\cdot 71^{5}\cdot 281^{6}$ |
$3$ |
$22.2813489897$ |
$6157.504577096202$ |
|
|
? |
$C_4^5.C_2^4.S_5$ (as 20T993) |
trivial |
$2$ |
$14$ |
$1094061.94435$ |
20.10.976...056.1 |
$x^{20} - 2 x^{18} - 4 x^{16} + 7 x^{14} + x^{12} + 3 x^{10} + 3 x^{8} - 11 x^{6} + 4 x^{2} - 1$ |
$20$ |
[10,5] |
$-\,2^{20}\cdot 30516826559^{2}$ |
$2$ |
$22.360624706$ |
$677645.9190796186$ |
|
|
? |
$C_2^{10}.S_{10}$ (as 20T1110) |
trivial |
$2$ |
$14$ |
$1334502.89974$ |
20.10.108...464.1 |
$x^{20} - 10 x^{18} + 36 x^{16} - 48 x^{14} - 13 x^{12} + 78 x^{10} - 21 x^{8} - 52 x^{6} + 24 x^{4} + 8 x^{2} - 4$ |
$20$ |
[10,5] |
$-\,2^{38}\cdot 89^{8}$ |
$2$ |
$22.4756879837$ |
|
|
|
? |
$C_2^9.C_2^4.S_5$ (as 20T965) |
trivial |
$2$ |
$14$ |
$2261786.67414$ |
20.10.124...000.1 |
$x^{20} - 7 x^{18} + 20 x^{16} - 8 x^{14} - 145 x^{12} + 486 x^{10} - 688 x^{8} + 468 x^{6} - 146 x^{4} + 21 x^{2} - 1$ |
$20$ |
[10,5] |
$-\,2^{20}\cdot 5^{10}\cdot 3319^{4}$ |
$3$ |
$22.6316619964$ |
$364.3624569024641$ |
|
|
? |
$D_{10}\wr C_2$ (as 20T168) |
trivial |
$2$ |
$14$ |
$1180484.37704$ |
20.10.124...000.2 |
$x^{20} - 7 x^{18} + 16 x^{16} - 18 x^{14} + 29 x^{12} - 40 x^{10} + 31 x^{6} - 15 x^{4} + 3 x^{2} - 1$ |
$20$ |
[10,5] |
$-\,2^{20}\cdot 5^{10}\cdot 3319^{4}$ |
$3$ |
$22.6316619964$ |
|
|
|
? |
$C_2^8.D_{10}\wr C_2$ (as 20T876) |
trivial |
$2$ |
$14$ |
$1457843.89477$ |
20.10.124...000.3 |
$x^{20} - 11 x^{18} + 45 x^{16} - 92 x^{14} + 96 x^{12} - 36 x^{10} - 19 x^{8} + 38 x^{6} - 37 x^{4} + 15 x^{2} - 1$ |
$20$ |
[10,5] |
$-\,2^{20}\cdot 5^{10}\cdot 3319^{4}$ |
$3$ |
$22.6316619964$ |
|
|
|
? |
$C_2^8.D_{10}\wr C_2$ (as 20T876) |
trivial |
$2$ |
$14$ |
$1432300.48596$ |
20.10.124...000.4 |
$x^{20} - 3 x^{18} + 11 x^{14} - 31 x^{12} + 46 x^{10} - 44 x^{8} + 51 x^{6} - 45 x^{4} + 16 x^{2} - 1$ |
$20$ |
[10,5] |
$-\,2^{20}\cdot 5^{10}\cdot 3319^{4}$ |
$3$ |
$22.6316619964$ |
|
|
|
? |
$C_2^8.D_{10}\wr C_2$ (as 20T876) |
trivial |
$2$ |
$14$ |
$1484559.24325$ |
20.10.124...000.5 |
$x^{20} - 4 x^{18} - 4 x^{16} + 26 x^{14} - 26 x^{12} + 8 x^{10} - 20 x^{8} + 49 x^{6} - 39 x^{4} + 11 x^{2} - 1$ |
$20$ |
[10,5] |
$-\,2^{20}\cdot 5^{10}\cdot 3319^{4}$ |
$3$ |
$22.6316619964$ |
|
|
|
? |
$C_2^8.D_{10}\wr C_2$ (as 20T876) |
trivial |
$2$ |
$14$ |
$1342671.7554$ |
20.10.125...000.1 |
$x^{20} - 6 x^{18} + 10 x^{16} - 4 x^{14} + 7 x^{12} - 12 x^{10} - 14 x^{8} + 18 x^{6} + 7 x^{4} - 5 x^{2} - 1$ |
$20$ |
[10,5] |
$-\,2^{20}\cdot 5^{10}\cdot 11066329^{2}$ |
$3$ |
$22.6420296925$ |
|
|
|
? |
$C_2^{10}.S_5\wr C_2$ (as 20T1045) |
trivial |
$2$ |
$14$ |
$1149167.37308$ |
20.10.128...375.1 |
$x^{20} - 10 x^{19} + 35 x^{18} - 30 x^{17} - 107 x^{16} + 244 x^{15} + 49 x^{14} - 533 x^{13} + 171 x^{12} + 651 x^{11} - 306 x^{10} - 544 x^{9} + 218 x^{8} + 329 x^{7} - 53 x^{6} - 142 x^{5} - 12 x^{4} + 39 x^{3} + 5 x^{2} - 5 x - 1$ |
$20$ |
[10,5] |
$-\,5^{10}\cdot 19\cdot 61\cdot 929\cdot 11066329^{2}$ |
$5$ |
$22.672025294$ |
$7718561.447549342$ |
|
|
✓ |
$C_2^{10}.S_5\wr C_2$ (as 20T1045) |
trivial |
$2$ |
$14$ |
$1253501.62256$ |
20.10.130...000.1 |
$x^{20} - 8 x^{18} + 14 x^{16} + 29 x^{14} - 105 x^{12} + 88 x^{10} - 13 x^{8} + 8 x^{6} - 21 x^{4} + 9 x^{2} - 1$ |
$20$ |
[10,5] |
$-\,2^{20}\cdot 5^{10}\cdot 3359^{4}$ |
$3$ |
$22.6859514648$ |
$366.5514970641915$ |
|
|
? |
$D_{10}\wr C_2$ (as 20T168) |
trivial |
$2$ |
$14$ |
$1437381.57379$ |
20.10.181...000.1 |
$x^{20} - 10 x^{18} + 37 x^{16} - 57 x^{14} + 11 x^{12} + 67 x^{10} - 59 x^{8} - 6 x^{6} + 16 x^{4} - 1$ |
$20$ |
[10,5] |
$-\,2^{12}\cdot 5^{10}\cdot 491^{2}\cdot 434249^{2}$ |
$4$ |
$23.0666768507$ |
$92350.69225512064$ |
|
|
? |
$C_2^{10}.S_5\wr C_2$ (as 20T1045) |
trivial |
$2$ |
$14$ |
$1902127.36812$ |