| 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 |
| 20.12.356...449.1 |
$x^{20} - 13 x^{18} - 8 x^{17} + 28 x^{16} + 9 x^{15} - 18 x^{14} + 47 x^{13} + 73 x^{12} - 54 x^{11} - 155 x^{10} - 54 x^{9} + 73 x^{8} + 47 x^{7} - 18 x^{6} + 9 x^{5} + 28 x^{4} - 8 x^{3} - 13 x^{2} + 1$ |
$20$ |
[12,4] |
$61^{6}\cdot 167^{2}\cdot 397^{4}$ |
$3$ |
$18.9508502128$ |
$5620.1882832374085$ |
|
|
? |
$C_2^{10}.S_5$ (as 20T799) |
trivial |
$2$ |
$15$ |
$261799.053214$ |
| 20.12.461...441.1 |
$x^{20} - x^{19} - 6 x^{18} + 13 x^{17} - 4 x^{16} - 21 x^{15} - 17 x^{14} + 65 x^{13} + 252 x^{12} - 674 x^{11} + 87 x^{10} + 1178 x^{9} - 1094 x^{8} - 343 x^{7} + 983 x^{6} - 397 x^{5} - 148 x^{4} + 177 x^{3} - 54 x^{2} + 3 x + 1$ |
$20$ |
[12,4] |
$11^{18}\cdot 43^{2}\cdot 67^{2}$ |
$3$ |
$19.1958674527$ |
$464.5420646123548$ |
|
|
? |
$C_2^{10}:C_5$ (as 20T341) |
trivial |
$2$ |
$15$ |
$302532.721491$ |
| 20.12.493...664.1 |
$x^{20} - 8 x^{19} + 26 x^{18} - 40 x^{17} + 14 x^{16} + 76 x^{15} - 296 x^{14} + 658 x^{13} - 577 x^{12} - 362 x^{11} + 906 x^{10} - 866 x^{9} + 2214 x^{8} - 3458 x^{7} + 1784 x^{6} + 564 x^{5} - 1042 x^{4} + 542 x^{3} - 158 x^{2} + 22 x - 1$ |
$20$ |
[12,4] |
$2^{30}\cdot 11^{16}$ |
$2$ |
$19.2601267834$ |
$26.08313353110776$ |
|
|
? |
$C_2\wr C_5$ (as 20T41) |
trivial |
$2$ |
$15$ |
$311138.716179$ |
| 20.12.493...664.2 |
$x^{20} - 4 x^{19} - 4 x^{18} + 24 x^{17} + 18 x^{16} - 92 x^{15} - 52 x^{14} + 388 x^{13} - 411 x^{12} - 122 x^{11} + 92 x^{10} + 1352 x^{9} - 1651 x^{8} - 314 x^{7} + 986 x^{6} + 46 x^{5} - 275 x^{4} - 14 x^{3} + 32 x^{2} + 2 x - 1$ |
$20$ |
[12,4] |
$2^{30}\cdot 11^{16}$ |
$2$ |
$19.2601267834$ |
$26.08313353110776$ |
|
|
? |
$C_2\wr C_5$ (as 20T41) |
trivial |
$2$ |
$15$ |
$322822.36902$ |
| 20.12.103...125.1 |
$x^{20} - x^{19} - 5 x^{18} + 7 x^{17} - 13 x^{16} - 18 x^{15} + 90 x^{14} - 28 x^{13} - 89 x^{12} + 219 x^{11} - 175 x^{10} - 400 x^{9} + 452 x^{8} + 355 x^{7} - 406 x^{6} - 186 x^{5} + 178 x^{4} + 61 x^{3} - 34 x^{2} - 10 x + 1$ |
$20$ |
[12,4] |
$5^{13}\cdot 419^{2}\cdot 695771^{2}$ |
$3$ |
$19.9893437947$ |
$57091.003446773015$ |
|
|
? |
$C_2^8.S_5^2:C_4$ (as 20T1039) |
trivial |
$2$ |
$15$ |
$479519.086931$ |
| 20.12.119...184.1 |
$x^{20} - 20 x^{18} + 163 x^{16} - 717 x^{14} + 1904 x^{12} - 3263 x^{10} + 3779 x^{8} - 2996 x^{6} + 1540 x^{4} - 441 x^{2} + 49$ |
$20$ |
[12,4] |
$2^{12}\cdot 7^{6}\cdot 137^{4}\cdot 163^{4}$ |
$4$ |
$20.1339526866$ |
$1818.9577404473885$ |
|
|
? |
$C_4^4:S_5$ (as 20T568) |
trivial |
$2$ |
$15$ |
$486324.90054$ |
| 20.12.160...424.1 |
$x^{20} - 2 x^{19} - 16 x^{18} + 42 x^{17} + 57 x^{16} - 216 x^{15} + 38 x^{14} + 88 x^{13} + 368 x^{12} - 270 x^{11} - 388 x^{10} + 28 x^{9} + 583 x^{8} - 94 x^{7} - 568 x^{6} + 416 x^{5} + 27 x^{4} - 152 x^{3} + 72 x^{2} - 14 x + 1$ |
$20$ |
[12,4] |
$2^{30}\cdot 13^{4}\cdot 19^{2}\cdot 347^{4}$ |
$4$ |
$20.4303082381$ |
|
|
|
? |
$C_3^5.D_6$ (as 20T669) |
trivial |
$2$ |
$15$ |
$603471.181199$ |
| 20.12.201...625.1 |
$x^{20} - 5 x^{19} + 45 x^{17} - 85 x^{16} - 50 x^{15} + 380 x^{14} - 470 x^{13} - 185 x^{12} + 1120 x^{11} - 1151 x^{10} + 140 x^{9} + 880 x^{8} - 1085 x^{7} + 545 x^{6} + 75 x^{5} - 320 x^{4} + 235 x^{3} - 85 x^{2} + 15 x - 1$ |
$20$ |
[12,4] |
$5^{16}\cdot 6029^{4}$ |
$2$ |
$20.6645075523$ |
$339.5041957855234$ |
|
|
? |
$C_2\wr S_5$ (as 20T279) |
trivial |
$2$ |
$15$ |
$684074.076253$ |
| 20.12.201...969.1 |
$x^{20} - 10 x^{19} + 41 x^{18} - 84 x^{17} + 45 x^{16} + 252 x^{15} - 850 x^{14} + 1336 x^{13} - 999 x^{12} - 350 x^{11} + 1777 x^{10} - 1950 x^{9} + 722 x^{8} + 652 x^{7} - 988 x^{6} + 420 x^{5} + 100 x^{4} - 172 x^{3} + 35 x^{2} + 22 x - 1$ |
$20$ |
[12,4] |
$61^{6}\cdot 397^{6}$ |
$2$ |
$20.6650329709$ |
$155.6181223379848$ |
|
|
? |
$C_2^5:S_5$ (as 20T281) |
trivial |
$2$ |
$15$ |
$721497.359346$ |
| 20.12.217...625.1 |
$x^{20} - 5 x^{19} + 35 x^{17} - 45 x^{16} - 66 x^{15} + 175 x^{14} + 5 x^{13} - 280 x^{12} + 75 x^{11} + 297 x^{10} - 75 x^{9} - 280 x^{8} - 5 x^{7} + 175 x^{6} + 66 x^{5} - 45 x^{4} - 35 x^{3} + 5 x + 1$ |
$20$ |
[12,4] |
$3^{4}\cdot 5^{16}\cdot 23^{4}\cdot 89^{4}$ |
$4$ |
$20.7407197322$ |
$342.6431489636176$ |
|
|
? |
$C_2\wr S_5$ (as 20T279) |
trivial |
$2$ |
$15$ |
$798245.370635$ |
| 20.12.303...136.1 |
$x^{20} - 5 x^{18} + 6 x^{16} + 2 x^{14} - 9 x^{10} + 2 x^{6} + 6 x^{4} - 5 x^{2} + 1$ |
$20$ |
[12,4] |
$2^{20}\cdot 29^{2}\cdot 61^{4}\cdot 397^{4}$ |
$4$ |
$21.0908393574$ |
|
|
|
✓ |
$C_3^5.D_6$ (as 20T669) |
trivial |
$2$ |
$15$ |
$854162.511057$ |
| 20.12.328...241.1 |
$x^{20} - 7 x^{19} + 12 x^{18} + 6 x^{17} - 32 x^{16} + 51 x^{15} - 12 x^{14} - 151 x^{13} + 57 x^{12} + 203 x^{11} - 53 x^{10} - 203 x^{9} + 57 x^{8} + 151 x^{7} - 12 x^{6} - 51 x^{5} - 32 x^{4} - 6 x^{3} + 12 x^{2} + 7 x + 1$ |
$20$ |
[12,4] |
$7^{8}\cdot 53^{4}\cdot 139^{6}$ |
$3$ |
$21.1738011421$ |
$779.7368423473802$ |
|
|
? |
$C_3^5.D_6$ (as 20T669) |
trivial |
$2$ |
$15$ |
$842197.454232$ |
| 20.12.333...421.1 |
$x^{20} - 2 x^{19} - 16 x^{18} + 24 x^{17} + 96 x^{16} - 30 x^{15} - 360 x^{14} - 336 x^{13} + 617 x^{12} + 1473 x^{11} + 174 x^{10} - 2098 x^{9} - 1732 x^{8} + 763 x^{7} + 1463 x^{6} + 152 x^{5} - 412 x^{4} - 67 x^{3} + 49 x^{2} + x - 1$ |
$20$ |
[12,4] |
$7^{4}\cdot 137^{4}\cdot 163^{4}\cdot 179\cdot 3119$ |
$5$ |
$21.1906687453$ |
$295418.24151023576$ |
|
|
? |
$C_2^9.C_2^5.S_5$ (as 20T992) |
trivial |
$2$ |
$15$ |
$878454.370763$ |
| 20.12.336...656.1 |
$x^{20} - 8 x^{18} + 9 x^{16} + 49 x^{14} - 84 x^{12} - 43 x^{10} + 124 x^{8} - 35 x^{6} - 17 x^{4} + 4 x^{2} + 1$ |
$20$ |
[12,4] |
$2^{10}\cdot 3^{10}\cdot 11^{18}$ |
$3$ |
$21.1996671299$ |
$54.98513375885044$ |
|
|
? |
$C_2^8:C_{10}$ (as 20T262) |
trivial |
$2$ |
$15$ |
$968784.175157$ |
| 20.12.336...656.2 |
$x^{20} - 5 x^{18} - 8 x^{16} + 73 x^{14} - 68 x^{12} - 166 x^{10} + 324 x^{8} - 146 x^{6} - 18 x^{4} + 13 x^{2} + 1$ |
$20$ |
[12,4] |
$2^{10}\cdot 3^{10}\cdot 11^{18}$ |
$3$ |
$21.1996671299$ |
$54.98513375885044$ |
|
|
? |
$C_2^9.C_{10}$ (as 20T340) |
trivial |
$2$ |
$15$ |
$822820.442678$ |
| 20.12.336...656.3 |
$x^{20} - 4 x^{18} - 17 x^{16} + 68 x^{14} + 69 x^{12} - 298 x^{10} + 26 x^{8} + 358 x^{6} - 211 x^{4} + 8 x^{2} + 1$ |
$20$ |
[12,4] |
$2^{10}\cdot 3^{10}\cdot 11^{18}$ |
$3$ |
$21.1996671299$ |
$54.98513375885044$ |
|
|
? |
$C_2^9.C_{10}$ (as 20T340) |
trivial |
$2$ |
$15$ |
$845490.475327$ |
| 20.12.343...901.1 |
$x^{20} - 10 x^{19} + 34 x^{18} - 21 x^{17} - 134 x^{16} + 256 x^{15} + 140 x^{14} - 666 x^{13} + 58 x^{12} + 952 x^{11} - 245 x^{10} - 915 x^{9} + 220 x^{8} + 606 x^{7} - 73 x^{6} - 260 x^{5} - 5 x^{4} + 66 x^{3} + 4 x^{2} - 8 x + 1$ |
$20$ |
[12,4] |
$101\cdot 277^{2}\cdot 6761\cdot 81019273^{2}$ |
$4$ |
$21.2238137865$ |
$123794175.11771174$ |
|
|
✓ |
$C_2^{10}.S_{10}$ (as 20T1110) |
trivial |
$2$ |
$15$ |
$865253.471502$ |
| 20.12.346...984.1 |
$x^{20} - 12 x^{18} + 63 x^{16} - 179 x^{14} + 278 x^{12} - 205 x^{10} + 27 x^{8} + 29 x^{6} + 6 x^{4} - 8 x^{2} + 1$ |
$20$ |
[12,4] |
$2^{20}\cdot 13^{4}\cdot 19^{2}\cdot 47^{2}\cdot 347^{4}$ |
$5$ |
$21.2309636604$ |
|
|
|
? |
$C_2^9.C_2^5.S_5$ (as 20T994) |
trivial |
$2$ |
$15$ |
$896884.192486$ |
| 20.12.357...000.1 |
$x^{20} - 10 x^{18} + 35 x^{16} - 65 x^{14} + 115 x^{12} - 235 x^{10} + 370 x^{8} - 415 x^{6} + 290 x^{4} - 75 x^{2} + 5$ |
$20$ |
[12,4] |
$2^{20}\cdot 5^{23}\cdot 13^{4}$ |
$3$ |
$21.263471583$ |
$45.900474678379865$ |
|
|
? |
$C_4\times S_5$ (as 20T123) |
trivial |
$2$ |
$15$ |
$1074400.99491$ |
| 20.12.369...904.1 |
$x^{20} - 6 x^{19} - 2 x^{18} + 62 x^{17} - 34 x^{16} - 272 x^{15} + 218 x^{14} + 626 x^{13} - 771 x^{12} - 286 x^{11} + 812 x^{10} - 262 x^{9} - 424 x^{8} + 446 x^{7} + 76 x^{6} - 306 x^{5} + 88 x^{4} + 72 x^{3} - 44 x^{2} + 4 x + 1$ |
$20$ |
[12,4] |
$2^{30}\cdot 61^{4}\cdot 397^{4}$ |
$3$ |
$21.2994829934$ |
|
|
|
? |
$C_3^5.D_6$ (as 20T669) |
trivial |
$2$ |
$15$ |
$940381.711684$ |
| 20.12.382...496.1 |
$x^{20} - 2 x^{19} - 14 x^{18} + 46 x^{17} + 17 x^{16} - 286 x^{15} + 274 x^{14} + 468 x^{13} - 1028 x^{12} - 272 x^{11} + 1318 x^{10} - 358 x^{9} - 1127 x^{8} + 510 x^{7} + 776 x^{6} - 88 x^{5} - 257 x^{4} - 42 x^{3} + 26 x^{2} + 10 x + 1$ |
$20$ |
[12,4] |
$2^{30}\cdot 3^{10}\cdot 1567^{4}$ |
$3$ |
$21.3363152794$ |
|
|
|
? |
$C_2\wr S_5$ (as 20T279) |
trivial |
$2$ |
$15$ |
$1754686.02975$ |
| 20.12.390...104.1 |
$x^{20} - 4 x^{18} - 5 x^{16} + 23 x^{14} + 7 x^{12} - 44 x^{10} - x^{8} + 31 x^{6} - 3 x^{4} - 5 x^{2} + 1$ |
$20$ |
[12,4] |
$2^{10}\cdot 11^{16}\cdot 43^{2}\cdot 67^{2}$ |
$4$ |
$21.359125709$ |
$1340.6549595691627$ |
|
|
? |
$C_2^5.C_2^8:C_{10}$ (as 20T751) |
trivial |
$2$ |
$15$ |
$975231.819394$ |
| 20.12.390...125.1 |
$x^{20} - x^{19} - 8 x^{18} + 16 x^{17} + x^{16} - 86 x^{15} + 175 x^{14} + 169 x^{13} - 704 x^{12} + 71 x^{11} + 1178 x^{10} - 773 x^{9} - 770 x^{8} + 1039 x^{7} - 86 x^{6} - 417 x^{5} + 224 x^{4} - 7 x^{3} - 30 x^{2} + 10 x - 1$ |
$20$ |
[12,4] |
$3^{6}\cdot 5^{15}\cdot 23^{4}\cdot 89^{4}$ |
$4$ |
$21.3593212747$ |
$450.9437440672269$ |
|
|
? |
$C_4\times C_2^4:S_5$ (as 20T369) |
trivial |
$2$ |
$15$ |
$1185515.34399$ |
| 20.12.392...624.1 |
$x^{20} - 5 x^{18} + 8 x^{16} - 7 x^{14} + 10 x^{12} - 47 x^{10} + 175 x^{8} - 261 x^{6} + 165 x^{4} - 39 x^{2} + 1$ |
$20$ |
[12,4] |
$2^{20}\cdot 13^{2}\cdot 38569^{4}$ |
$3$ |
$21.3634804045$ |
|
|
|
? |
$C_2^{10}.S_5$ (as 20T799) |
trivial |
$2$ |
$15$ |
$926733.479139$ |
| 20.12.397...312.1 |
$x^{20} - 6 x^{19} + 16 x^{18} - 38 x^{17} + 39 x^{16} + 174 x^{15} - 462 x^{14} + 4 x^{13} + 742 x^{12} - 320 x^{11} - 110 x^{10} - 298 x^{9} - 79 x^{8} + 782 x^{7} - 620 x^{6} - 144 x^{5} + 551 x^{4} - 146 x^{3} - 106 x^{2} + 18 x + 1$ |
$20$ |
[12,4] |
$2^{30}\cdot 13^{4}\cdot 19\cdot 47\cdot 347^{4}$ |
$5$ |
$21.3767723291$ |
|
|
|
? |
$C_2^9.C_2^5.S_5$ (as 20T992) |
trivial |
$2$ |
$15$ |
$976310.162479$ |
| 20.12.423...561.1 |
$x^{20} - x^{19} - 19 x^{18} + 9 x^{17} + 159 x^{16} + 7 x^{15} - 733 x^{14} - 382 x^{13} + 1886 x^{12} + 1875 x^{11} - 2270 x^{10} - 3913 x^{9} - 146 x^{8} + 3180 x^{7} + 2873 x^{6} + 300 x^{5} - 1549 x^{4} - 1071 x^{3} - 220 x^{2} - 4 x + 1$ |
$20$ |
[12,4] |
$3^{10}\cdot 17^{6}\cdot 4153^{4}$ |
$3$ |
$21.4470562089$ |
$934.497801400676$ |
|
|
? |
$C_3^5.D_6$ (as 20T669) |
trivial |
$2$ |
$15$ |
$1160830.70337$ |
| 20.12.455...416.1 |
$x^{20} - 10 x^{18} + 36 x^{16} - 48 x^{14} - 16 x^{12} + 96 x^{10} - 55 x^{8} - 36 x^{6} + 42 x^{4} - 12 x^{2} + 1$ |
$20$ |
[12,4] |
$2^{40}\cdot 13^{4}\cdot 347^{4}$ |
$3$ |
$21.5235823733$ |
|
|
|
✓ |
$C_2\wr S_5$ (as 20T279) |
trivial |
$2$ |
$15$ |
$1007824.80372$ |
| 20.12.455...416.2 |
$x^{20} - 10 x^{18} + 39 x^{16} - 72 x^{14} + 82 x^{12} - 156 x^{10} + 337 x^{8} - 372 x^{6} + 179 x^{4} - 30 x^{2} + 1$ |
$20$ |
[12,4] |
$2^{40}\cdot 13^{4}\cdot 347^{4}$ |
$3$ |
$21.5235823733$ |
|
|
|
? |
$C_4^4:S_5$ (as 20T568) |
trivial |
$2$ |
$15$ |
$973138.252641$ |
| 20.12.455...416.3 |
$x^{20} - 10 x^{18} + 46 x^{16} - 128 x^{14} + 264 x^{12} - 464 x^{10} + 629 x^{8} - 532 x^{6} + 232 x^{4} - 40 x^{2} + 1$ |
$20$ |
[12,4] |
$2^{40}\cdot 13^{4}\cdot 347^{4}$ |
$3$ |
$21.5235823733$ |
|
|
|
? |
$C_2\times C_4^4:S_5$ (as 20T673) |
trivial |
$2$ |
$15$ |
$1111929.25344$ |
| 20.12.493...024.1 |
$x^{20} - 12 x^{18} + 64 x^{16} - 195 x^{14} + 395 x^{12} - 605 x^{10} + 686 x^{8} - 496 x^{6} + 195 x^{4} - 33 x^{2} + 1$ |
$20$ |
[12,4] |
$2^{20}\cdot 37^{2}\cdot 61^{4}\cdot 397^{4}$ |
$4$ |
$21.610968804$ |
|
|
|
? |
$C_3^5.D_6$ (as 20T669) |
trivial |
$2$ |
$15$ |
$1076208.47549$ |
| 20.12.518...984.1 |
$x^{20} - 4 x^{19} + 20 x^{17} - 47 x^{16} + 66 x^{15} + 15 x^{14} - 236 x^{13} + 407 x^{12} - 470 x^{11} + 54 x^{10} + 664 x^{9} + 209 x^{8} - 1098 x^{7} - 349 x^{6} + 858 x^{5} + 29 x^{4} - 160 x^{3} - 11 x^{2} + 8 x + 1$ |
$20$ |
[12,4] |
$2^{20}\cdot 11^{18}\cdot 89$ |
$3$ |
$21.6647116272$ |
$163.2970787472248$ |
|
|
? |
$C_2^{10}.C_{10}$ (as 20T409) |
trivial |
$2$ |
$15$ |
$1135849.69447$ |
| 20.12.572...416.1 |
$x^{20} - 13 x^{18} + 73 x^{16} - 235 x^{14} + 481 x^{12} - 649 x^{10} + 578 x^{8} - 335 x^{6} + 120 x^{4} - 21 x^{2} + 1$ |
$20$ |
[12,4] |
$2^{20}\cdot 11^{16}\cdot 109^{2}$ |
$3$ |
$21.7714218838$ |
|
|
|
? |
$C_2^8:C_{10}$ (as 20T263) |
trivial |
$2$ |
$15$ |
$1129079.57261$ |
| 20.12.572...416.2 |
$x^{20} - 9 x^{18} + 42 x^{16} - 149 x^{14} + 377 x^{12} - 590 x^{10} + 543 x^{8} - 293 x^{6} + 91 x^{4} - 15 x^{2} + 1$ |
$20$ |
[12,4] |
$2^{20}\cdot 11^{16}\cdot 109^{2}$ |
$3$ |
$21.7714218838$ |
|
|
|
? |
$C_2^{10}:C_5$ (as 20T341) |
trivial |
$2$ |
$15$ |
$1180707.59174$ |
| 20.12.572...416.3 |
$x^{20} - 3 x^{18} + 12 x^{16} - 32 x^{14} - 2 x^{12} + 70 x^{10} - 17 x^{8} - 68 x^{6} + 49 x^{4} - 12 x^{2} + 1$ |
$20$ |
[12,4] |
$2^{20}\cdot 11^{16}\cdot 109^{2}$ |
$3$ |
$21.7714218838$ |
|
|
|
? |
$C_2^{10}:C_5$ (as 20T341) |
trivial |
$2$ |
$15$ |
$1172527.05476$ |
| 20.12.601...593.1 |
$x^{20} - 15 x^{18} - 7 x^{17} + 90 x^{16} + 70 x^{15} - 283 x^{14} - 261 x^{13} + 470 x^{12} + 366 x^{11} - 373 x^{10} + 42 x^{9} + 178 x^{8} - 404 x^{7} - 116 x^{6} + 100 x^{5} - 55 x^{4} + 8 x^{3} + 18 x^{2} - x - 1$ |
$20$ |
[12,4] |
$307^{5}\cdot 739^{5}$ |
$2$ |
$21.824570388$ |
$3213.1983264494756$ |
|
|
? |
$C_2^{10}.A_{10}$ (as 20T1106) |
trivial |
$2$ |
$15$ |
$1200075.62946$ |
| 20.12.626...696.1 |
$x^{20} - 9 x^{18} + 19 x^{16} + 29 x^{14} - 101 x^{12} - 52 x^{10} + 254 x^{8} - 165 x^{6} + 31 x^{4} - 7 x^{2} + 1$ |
$20$ |
[12,4] |
$2^{20}\cdot 7^{4}\cdot 137^{4}\cdot 163^{4}$ |
$4$ |
$21.8691164919$ |
|
|
|
? |
$C_2^8.S_5$ (as 20T567) |
trivial |
$2$ |
$15$ |
$1219708.76669$ |
| 20.12.626...696.2 |
$x^{20} - 7 x^{18} + 15 x^{16} - x^{14} - 34 x^{12} + 31 x^{10} + 18 x^{8} - 46 x^{6} + 33 x^{4} - 10 x^{2} + 1$ |
$20$ |
[12,4] |
$2^{20}\cdot 7^{4}\cdot 137^{4}\cdot 163^{4}$ |
$4$ |
$21.8691164919$ |
|
|
|
✓ |
$C_2^9.C_2^4:S_5$ (as 20T964) |
trivial |
$2$ |
$15$ |
$1259029.38413$ |
| 20.12.635...056.1 |
$x^{20} - 2 x^{18} - 10 x^{16} - 2 x^{14} + 164 x^{12} - 358 x^{10} + 255 x^{8} - 18 x^{6} - 30 x^{4} + 1$ |
$20$ |
[12,4] |
$2^{40}\cdot 4903^{4}$ |
$2$ |
$21.8852932349$ |
|
|
|
? |
$C_2\times C_4^4:S_5$ (as 20T673) |
trivial |
$2$ |
$15$ |
$1252950.20449$ |
| 20.12.677...952.1 |
$x^{20} - 2 x^{19} - 17 x^{18} + 32 x^{17} + 114 x^{16} - 206 x^{15} - 396 x^{14} + 696 x^{13} + 819 x^{12} - 1374 x^{11} - 1096 x^{10} + 1702 x^{9} + 864 x^{8} - 1276 x^{7} - 313 x^{6} + 516 x^{5} + 15 x^{4} - 94 x^{3} + 9 x^{2} + 6 x - 1$ |
$20$ |
[12,4] |
$2^{20}\cdot 11^{16}\cdot 14057$ |
$3$ |
$21.955269682639564$ |
|
|
|
? |
$C_2^5.C_2^8:C_{10}$ (as 20T749) |
trivial |
$2$ |
$15$ |
$1449416.5256711214$ |
| 20.12.677...952.2 |
$x^{20} - 8 x^{19} + 20 x^{18} + 16 x^{17} - 202 x^{16} + 424 x^{15} - 22 x^{14} - 1502 x^{13} + 2613 x^{12} - 352 x^{11} - 4475 x^{10} + 5694 x^{9} - 389 x^{8} - 5148 x^{7} + 4516 x^{6} - 338 x^{5} - 1720 x^{4} + 1138 x^{3} - 288 x^{2} + 22 x + 1$ |
$20$ |
[12,4] |
$2^{20}\cdot 11^{16}\cdot 14057$ |
$3$ |
$21.955269682639564$ |
$3092.4742147584775$ |
|
|
? |
$C_2^{10}.C_2\wr C_5$ (as 20T846) |
trivial |
$2$ |
$15$ |
$1315916.404639807$ |
| 20.12.705...929.1 |
$x^{20} - x^{19} - 3 x^{18} + 8 x^{17} - 32 x^{16} - 25 x^{15} + 185 x^{14} + x^{13} - 381 x^{12} + 111 x^{11} + 282 x^{10} + 3 x^{9} + 171 x^{8} - 385 x^{7} - 362 x^{6} + 397 x^{5} + 177 x^{4} - 133 x^{3} - 25 x^{2} + 13 x - 1$ |
$20$ |
[12,4] |
$11^{16}\cdot 43^{4}\cdot 67^{2}$ |
$3$ |
$21.9996271022$ |
$365.49865006155005$ |
|
|
? |
$C_2^8:C_{10}$ (as 20T263) |
trivial |
$2$ |
$15$ |
$1373195.02964$ |
| 20.12.705...929.2 |
$x^{20} - 9 x^{19} + 25 x^{18} + 10 x^{17} - 199 x^{16} + 408 x^{15} - 111 x^{14} - 1001 x^{13} + 2216 x^{12} - 1966 x^{11} - 689 x^{10} + 4104 x^{9} - 4679 x^{8} + 1453 x^{7} + 1806 x^{6} - 1917 x^{5} + 494 x^{4} + 52 x^{3} + 3 x^{2} - x - 1$ |
$20$ |
[12,4] |
$11^{16}\cdot 43^{4}\cdot 67^{2}$ |
$3$ |
$21.9996271022405$ |
$365.49865006155005$ |
|
|
? |
$C_2^8:C_{10}$ (as 20T263) |
trivial |
$2$ |
$15$ |
$1379024.9312377952$ |
| 20.12.743...056.1 |
$x^{20} - 5 x^{19} + 55 x^{17} - 145 x^{16} + 56 x^{15} + 374 x^{14} - 646 x^{13} - 88 x^{12} + 1224 x^{11} - 568 x^{10} - 1182 x^{9} + 657 x^{8} + 701 x^{7} - 242 x^{6} - 211 x^{5} + 32 x^{4} + 13 x^{3} - 20 x^{2} - 9 x - 1$ |
$20$ |
[12,4] |
$2^{24}\cdot 83^{4}\cdot 983^{4}$ |
$3$ |
$22.0578062076$ |
|
|
|
|
$C_2^8.S_5$ (as 20T567) |
trivial |
$2$ |
$15$ |
$2071480.64978$ |
| 20.12.743...056.2 |
$x^{20} - 5 x^{19} + 41 x^{17} - 67 x^{16} - 72 x^{15} + 292 x^{14} - 136 x^{13} - 435 x^{12} + 527 x^{11} + 318 x^{10} - 801 x^{9} + 11 x^{8} + 624 x^{7} - 250 x^{6} - 174 x^{5} + 171 x^{4} - 21 x^{3} - 30 x^{2} + 11 x - 1$ |
$20$ |
[12,4] |
$2^{24}\cdot 83^{4}\cdot 983^{4}$ |
$3$ |
$22.0578062076$ |
|
|
|
|
$C_2^8.S_5$ (as 20T567) |
trivial |
$2$ |
$15$ |
$2098566.90596$ |
| 20.12.743...056.3 |
$x^{20} - 5 x^{18} - 14 x^{16} + 97 x^{14} - 84 x^{12} - 147 x^{10} + 168 x^{8} + 37 x^{6} - 46 x^{4} - 9 x^{2} + 1$ |
$20$ |
[12,4] |
$2^{24}\cdot 83^{4}\cdot 983^{4}$ |
$3$ |
$22.0578062076$ |
|
|
|
? |
$C_2^9.C_2^4:S_5$ (as 20T964) |
trivial |
$2$ |
$15$ |
$1392627.71135$ |
| 20.12.743...056.4 |
$x^{20} - 5 x^{19} + 5 x^{18} + 11 x^{17} - 23 x^{16} + 30 x^{15} - 122 x^{14} + 264 x^{13} - 230 x^{12} - 56 x^{11} + 516 x^{10} - 688 x^{9} - x^{8} + 653 x^{7} - 279 x^{6} - 193 x^{5} + 128 x^{4} + 9 x^{3} - 23 x^{2} + x + 1$ |
$20$ |
[12,4] |
$2^{24}\cdot 83^{4}\cdot 983^{4}$ |
$3$ |
$22.0578062076$ |
|
|
|
? |
$C_2^9.C_2^4:S_5$ (as 20T964) |
trivial |
$2$ |
$15$ |
$1363290.65055$ |
| 20.12.772...625.1 |
$x^{20} - x^{19} - 9 x^{18} + 19 x^{17} - 12 x^{16} - 31 x^{15} + 93 x^{14} - 138 x^{13} + 121 x^{12} - 8 x^{11} - 126 x^{10} + 216 x^{9} - 151 x^{8} - 26 x^{7} + 158 x^{6} - 93 x^{5} - 68 x^{4} + 38 x^{3} + 16 x^{2} - 3 x - 1$ |
$20$ |
[12,4] |
$3^{4}\cdot 5^{14}\cdot 23^{4}\cdot 89^{5}$ |
$4$ |
$22.100206051$ |
$920.3267683406258$ |
|
|
? |
$C_2^8.(D_4\times S_5)$ (as 20T887) |
trivial |
$2$ |
$15$ |
$1857639.96504$ |
| 20.12.775...629.1 |
$x^{20} - 10 x^{19} + 30 x^{18} + 15 x^{17} - 234 x^{16} + 240 x^{15} + 665 x^{14} - 1205 x^{13} - 949 x^{12} + 2665 x^{11} + 766 x^{10} - 3440 x^{9} - 433 x^{8} + 2761 x^{7} + 251 x^{6} - 1320 x^{5} - 119 x^{4} + 322 x^{3} + 21 x^{2} - 27 x + 1$ |
$20$ |
[12,4] |
$461^{2}\cdot 5783^{4}\cdot 3260669$ |
$3$ |
$22.1037554352$ |
$2948359.358905729$ |
|
|
✓ |
$C_2^{10}.C_2\wr S_5$ (as 20T1015) |
trivial |
$2$ |
$15$ |
$1392825.39591$ |
| 20.12.823...609.1 |
$x^{20} - x^{19} - 16 x^{18} + 22 x^{17} + 96 x^{16} - 184 x^{15} - 293 x^{14} + 814 x^{13} + 493 x^{12} - 2154 x^{11} - 276 x^{10} + 3939 x^{9} - 402 x^{8} - 5522 x^{7} - 162 x^{6} + 4485 x^{5} + 909 x^{4} - 1760 x^{3} - 537 x^{2} + 262 x + 89$ |
$20$ |
[12,4] |
$11^{18}\cdot 23^{6}$ |
$2$ |
$22.1703100866$ |
$41.50661671665305$ |
|
|
? |
$C_2^5:C_{10}$ (as 20T74) |
trivial |
$2$ |
$15$ |
$1478677.49853$ |
| 20.12.823...609.2 |
$x^{20} - 7 x^{19} + 9 x^{18} + 30 x^{17} - 53 x^{16} - 48 x^{15} - 52 x^{14} + 227 x^{13} + 645 x^{12} - 780 x^{11} - 1508 x^{10} + 1074 x^{9} + 1740 x^{8} - 558 x^{7} - 981 x^{6} + 92 x^{5} + 261 x^{4} + 4 x^{3} - 29 x^{2} - x + 1$ |
$20$ |
[12,4] |
$11^{18}\cdot 23^{6}$ |
$2$ |
$22.1703100866$ |
$41.50661671665305$ |
|
|
? |
$C_2^5:C_{10}$ (as 20T74) |
trivial |
$2$ |
$15$ |
$1478677.49853$ |
