| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Narrow class group |
Unit group torsion |
Unit group rank |
Regulator |
Unit signature rank |
| 20.0.661...037.1 |
$x^{20} - 2 x^{19} + 16 x^{17} - 46 x^{16} - 88 x^{15} + 270 x^{14} - 322 x^{13} + 491 x^{12} + 33 x^{11} + 325 x^{10} - 1159 x^{9} + 5856 x^{8} - 10579 x^{7} + 5165 x^{6} - 13069 x^{5} + 13317 x^{4} + 7840 x^{3} + 32779 x^{2} + 1658 x + 5671$ |
$20$ |
(0, 10) |
$3^{10}\cdot 7^{15}\cdot 11^{9}$ |
$3$ |
$21.9285979822$ |
$64.51156445742586$ |
|
|
? |
$C_{10}\wr C_2$ (as 20T53) |
$[2]$ |
$[2]$ |
$2$ |
$9$ |
$69540.12284114186$ |
$0$ |
| 20.8.153...125.1 |
$x^{20} - 5 x^{19} + 5 x^{18} + 5 x^{17} - 5 x^{16} + 39 x^{15} - 95 x^{14} - 5 x^{13} - 65 x^{12} + 95 x^{11} + 541 x^{10} - 270 x^{9} + 405 x^{8} - 935 x^{7} - 720 x^{6} + 959 x^{5} - 130 x^{4} + 140 x^{3} + 60 x^{2} - 20 x + 1$ |
$20$ |
(8, 6) |
$3^{10}\cdot 5^{27}\cdot 59^{2}$ |
$3$ |
$22.8694296859$ |
|
|
|
? |
$D_5\wr C_4$ (as 20T614) |
trivial |
$[2]$ |
$2$ |
$13$ |
$1204766.77776$ |
$7$ |
| 20.4.176...625.1 |
$x^{20} - 4 x^{17} - 3 x^{15} + 6 x^{14} + 9 x^{12} - 4 x^{11} - x^{10} - 9 x^{9} + x^{8} + 2 x^{7} + 3 x^{6} + 3 x^{5} - x^{4} - 3 x^{2} + 1$ |
$20$ |
(4, 8) |
$3^{10}\cdot 5^{15}\cdot 359\cdot 27264287819$ |
$4$ |
$25.8417880964$ |
$18118925.270604704$ |
|
|
✓ |
$A_5^4.C_2\wr C_4$ (as 20T1095) |
trivial |
$[2]$ |
$2$ |
$11$ |
$1535371.36793$ |
$3$ |
| 20.4.345...125.1 |
$x^{20} - 4 x^{18} + 6 x^{16} - x^{15} - 4 x^{14} + 3 x^{13} + x^{12} - 3 x^{11} - 4 x^{10} + x^{9} + 8 x^{8} - 4 x^{6} + 4 x^{5} - 4 x^{3} + 1$ |
$20$ |
(4, 8) |
$3^{10}\cdot 5^{15}\cdot 61\cdot 243839\cdot 1290299$ |
$5$ |
$26.7266359969$ |
$25371714.323911626$ |
|
|
✓ |
$A_5^4.C_2\wr C_4$ (as 20T1095) |
trivial |
$[2]$ |
$2$ |
$11$ |
$2645417.48183$ |
$3$ |
| 20.20.171...125.1 |
$x^{20} - 20 x^{18} + 170 x^{16} - x^{15} - 800 x^{14} + 15 x^{13} + 2275 x^{12} - 90 x^{11} - 4004 x^{10} + 275 x^{9} + 4290 x^{8} - 450 x^{7} - 2640 x^{6} + 379 x^{5} + 825 x^{4} - 145 x^{3} - 100 x^{2} + 20 x + 1$ |
$20$ |
(20, 0) |
$3^{10}\cdot 5^{35}$ |
$2$ |
$28.9573046322$ |
$28.957304632206725$ |
|
✓ |
✓ |
$C_{20}$ (as 20T1) |
trivial |
$[2]$ |
$2$ |
$19$ |
$122630529.842$ |
$19$ |
| 20.0.180...125.1 |
$x^{20} - 5 x^{17} - 16 x^{15} + 45 x^{14} + 180 x^{12} - 125 x^{11} + 224 x^{10} - 600 x^{9} + 625 x^{8} - 800 x^{7} + 5000 x^{6} - 320 x^{5} + 14000 x^{4} + 16000 x^{2} + 6400$ |
$20$ |
(0, 10) |
$3^{10}\cdot 5^{26}\cdot 29^{5}$ |
$3$ |
$32.5702530278$ |
$263.10093126562055$ |
|
|
|
$D_5\wr C_4$ (as 20T617) |
$[2]$ |
$[2]$ |
$2$ |
$9$ |
$9468886.70932$ |
$0$ |
| 20.0.967...717.1 |
$x^{20} - 2 x^{19} + 54 x^{18} - 97 x^{17} + 1454 x^{16} - 2178 x^{15} + 24203 x^{14} - 29499 x^{13} + 271844 x^{12} - 266297 x^{11} + 2138211 x^{10} - 1737644 x^{9} + 11918963 x^{8} - 8666349 x^{7} + 46563112 x^{6} - 30553298 x^{5} + 119110990 x^{4} - 62702972 x^{3} + 173029525 x^{2} - 53651341 x + 103856419$ |
$20$ |
(0, 10) |
$3^{10}\cdot 7^{15}\cdot 11^{13}$ |
$3$ |
$35.4233314463$ |
$64.51156445742586$ |
|
|
? |
$C_{10}\wr C_2$ (as 20T53) |
$[2]$ |
$[2]$ |
$2$ |
$9$ |
$7036306.946137199$ |
$0$ |
| 20.20.828...125.1 |
$x^{20} - x^{19} - 39 x^{18} + 43 x^{17} + 579 x^{16} - 664 x^{15} - 4199 x^{14} + 4764 x^{13} + 16062 x^{12} - 17268 x^{11} - 32674 x^{10} + 31502 x^{9} + 34487 x^{8} - 26929 x^{7} - 18180 x^{6} + 9222 x^{5} + 4671 x^{4} - 978 x^{3} - 468 x^{2} - 21 x + 1$ |
$20$ |
(20, 0) |
$3^{10}\cdot 5^{15}\cdot 11^{16}$ |
$3$ |
$39.4368554623$ |
$39.436855462307015$ |
|
✓ |
? |
$C_{20}$ (as 20T1) |
trivial |
$[2]$ |
$2$ |
$19$ |
$2427056473.64$ |
$19$ |
| 20.2.314...375.1 |
$x^{20} - 10 x^{19} + 45 x^{18} - 110 x^{17} + 150 x^{16} - 182 x^{15} + 565 x^{14} - 1480 x^{13} + 1740 x^{12} - 340 x^{11} - 266 x^{10} - 2080 x^{9} + 3645 x^{8} - 2750 x^{7} + 2965 x^{6} - 2728 x^{5} + 975 x^{4} - 1880 x^{3} + 1760 x^{2} + 490 x + 781$ |
$20$ |
(2, 9) |
$-\,3^{10}\cdot 5^{27}\cdot 59^{5}$ |
$3$ |
$42.1583044796$ |
|
|
|
|
$D_5\wr C_4$ (as 20T617) |
$[4]$ |
$[2, 4]$ |
$2$ |
$10$ |
$84949287.8085$ |
$1$ |
| 20.20.619...125.1 |
$x^{20} - 3 x^{19} - 36 x^{18} + 92 x^{17} + 519 x^{16} - 1110 x^{15} - 3841 x^{14} + 6814 x^{13} + 15654 x^{12} - 23105 x^{11} - 35526 x^{10} + 44358 x^{9} + 44365 x^{8} - 47573 x^{7} - 29261 x^{6} + 27081 x^{5} + 9352 x^{4} - 7316 x^{3} - 1317 x^{2} + 732 x + 61$ |
$20$ |
(20, 0) |
$3^{10}\cdot 5^{15}\cdot 61^{4}\cdot 397^{4}$ |
$4$ |
$43.612622164$ |
$901.256274966608$ |
|
|
? |
$C_4\times S_5$ (as 20T123) |
trivial |
$[2, 2, 2, 2]$ |
$2$ |
$19$ |
$10094804779.9$ |
$16$ |
| 20.12.639...125.1 |
$x^{20} - 20 x^{18} + 170 x^{16} - 5 x^{15} - 800 x^{14} + 75 x^{13} + 2275 x^{12} - 450 x^{11} - 3995 x^{10} + 1375 x^{9} + 4200 x^{8} - 2250 x^{7} - 2325 x^{6} + 1880 x^{5} + 375 x^{4} - 650 x^{3} + 125 x^{2} + 25 x - 5$ |
$20$ |
(12, 4) |
$3^{10}\cdot 5^{35}\cdot 61^{2}$ |
$3$ |
$43.6808537809$ |
|
|
|
✓ |
$D_5\wr C_4$ (as 20T614) |
trivial |
$[2]$ |
$2$ |
$15$ |
$1810322979.21$ |
$11$ |
| 20.0.693...312.1 |
$x^{20} + 2646 x^{14} + 31752 x^{12} - 166698 x^{10} + 2750517 x^{8} + 346565142 x^{4} + 10916801973$ |
$20$ |
(0, 10) |
$2^{20}\cdot 3^{10}\cdot 7^{15}\cdot 11^{9}$ |
$4$ |
$43.8571959644$ |
$129.02312891485172$ |
|
|
? |
$C_{10}\wr C_2$ (as 20T53) |
$[2, 2, 2]$ |
$[2, 2, 2]$ |
$2$ |
$9$ |
$15627805.568647645$ |
$0$ |
| 20.0.211...841.1 |
$x^{20} - x^{19} - 10 x^{18} - 2 x^{17} + 170 x^{16} + 545 x^{15} + 379 x^{14} + 69 x^{13} + 7629 x^{12} + 23760 x^{11} + 2312 x^{10} - 113524 x^{9} - 155820 x^{8} + 270476 x^{7} + 1530472 x^{6} + 4025380 x^{5} + 8730182 x^{4} + 12840750 x^{3} + 13160320 x^{2} + 12555242 x + 11688877$ |
$20$ |
(0, 10) |
$3^{10}\cdot 11^{9}\cdot 19^{15}$ |
$3$ |
$46.3716486249$ |
$136.42037679267568$ |
|
|
? |
$C_{10}\wr C_2$ (as 20T53) |
$[2]$ |
$[2]$ |
$2$ |
$9$ |
$122053287.89335619$ |
$0$ |
| 20.12.361...125.1 |
$x^{20} - 20 x^{18} + 170 x^{16} - 2 x^{15} - 800 x^{14} + 30 x^{13} + 2275 x^{12} - 180 x^{11} - 4016 x^{10} + 550 x^{9} + 4410 x^{8} - 900 x^{7} - 3060 x^{6} + 752 x^{5} + 1425 x^{4} - 260 x^{3} - 400 x^{2} + 10 x + 31$ |
$20$ |
(12, 4) |
$3^{10}\cdot 5^{37}\cdot 29^{2}$ |
$3$ |
$47.6315742224$ |
|
|
|
|
$D_5\wr C_4$ (as 20T614) |
trivial |
$[2]$ |
$2$ |
$15$ |
$5523950157.29$ |
$11$ |
| 20.0.645...125.1 |
$x^{20} - 2 x^{19} + 58 x^{17} - 193 x^{16} - 2188 x^{15} - 465 x^{14} - 7861 x^{13} + 91673 x^{12} - 34407 x^{11} + 607603 x^{10} + 3012761 x^{9} + 12205932 x^{8} - 10310764 x^{7} + 30457244 x^{6} - 323709400 x^{5} + 3839375256 x^{4} - 3757533269 x^{3} + 15771143512 x^{2} - 45579456448 x + 87786948061$ |
$20$ |
(0, 10) |
$3^{10}\cdot 5^{10}\cdot 7^{15}\cdot 11^{9}$ |
$4$ |
$49.0338357394$ |
$144.25224346166357$ |
|
|
? |
$C_{10}\wr C_2$ (as 20T53) |
not computed |
not computed |
$2$ |
$9$ |
|
|
| 20.20.900...125.1 |
$x^{20} - 55 x^{18} - 40 x^{17} + 1080 x^{16} + 1392 x^{15} - 8915 x^{14} - 15470 x^{13} + 28185 x^{12} + 61780 x^{11} - 31726 x^{10} - 103100 x^{9} + 7140 x^{8} + 80300 x^{7} + 6950 x^{6} - 29667 x^{5} - 3720 x^{4} + 4405 x^{3} + 535 x^{2} - 125 x + 1$ |
$20$ |
(20, 0) |
$3^{10}\cdot 5^{23}\cdot 31^{4}\cdot 61^{4}$ |
$4$ |
$49.8556563496$ |
$4610.30179232261$ |
|
|
? |
$C_5\wr C_4$ (as 20T237) |
trivial |
$[2]$ |
$2$ |
$19$ |
$41142344883.6$ |
$19$ |
| 20.0.100...125.1 |
$x^{20} - x^{19} + 35 x^{18} - 36 x^{17} + 500 x^{16} - 536 x^{15} + 3874 x^{14} - 4410 x^{13} + 18734 x^{12} - 23144 x^{11} + 64285 x^{10} - 88253 x^{9} + 181094 x^{8} - 254178 x^{7} + 456689 x^{6} - 492583 x^{5} + 958226 x^{4} - 411001 x^{3} + 1371042 x^{2} + 173262 x + 1197901$ |
$20$ |
(0, 10) |
$3^{10}\cdot 5^{15}\cdot 11^{18}$ |
$3$ |
$50.1235182543$ |
$50.12351825429183$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
$[2, 2, 842]$ |
$[2, 2, 842]$ |
$2$ |
$9$ |
$140644.599182$ |
$0$ |
| 20.12.112...000.1 |
$x^{20} - 20 x^{18} + 170 x^{16} - 10 x^{15} - 800 x^{14} + 150 x^{13} + 2275 x^{12} - 900 x^{11} - 3980 x^{10} + 2750 x^{9} + 4050 x^{8} - 4500 x^{7} - 1800 x^{6} + 3790 x^{5} - 375 x^{4} - 1450 x^{3} + 500 x^{2} + 200 x - 80$ |
$20$ |
(12, 4) |
$2^{16}\cdot 3^{10}\cdot 5^{35}$ |
$3$ |
$50.4175957182$ |
|
|
|
? |
$C_5^4:(C_2^3:C_4)$ (as 20T489) |
trivial |
$[2]$ |
$2$ |
$15$ |
$9570122971.31$ |
$11$ |
| 20.0.180...000.1 |
$x^{20} + 60 x^{18} + 1530 x^{16} + 21600 x^{14} + 184275 x^{12} + 973215 x^{10} + 3134700 x^{8} + 5850225 x^{6} + 5740875 x^{4} + 2460375 x^{2} + 295245$ |
$20$ |
(0, 10) |
$2^{20}\cdot 3^{10}\cdot 5^{35}$ |
$3$ |
$57.9146092644$ |
$57.91460926441345$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
$[2, 4322]$ |
$[2, 4322]$ |
$2$ |
$9$ |
$161406.837641$ |
$0$ |
| 20.20.337...125.1 |
$x^{20} - 70 x^{18} - 15 x^{17} + 1710 x^{16} + 1140 x^{15} - 18660 x^{14} - 20360 x^{13} + 89540 x^{12} + 123760 x^{11} - 169905 x^{10} - 275075 x^{9} + 94830 x^{8} + 197705 x^{7} - 27225 x^{6} - 51195 x^{5} + 11020 x^{4} + 3700 x^{3} - 1425 x^{2} + 150 x - 5$ |
$20$ |
(20, 0) |
$3^{10}\cdot 5^{23}\cdot 31^{4}\cdot 151^{4}$ |
$4$ |
$59.7645784528$ |
$9520.22133198581$ |
|
|
? |
$C_5\wr C_4$ (as 20T237) |
trivial |
$[2]$ |
$2$ |
$19$ |
$259644642289$ |
$19$ |
| 20.0.704...125.1 |
$x^{20} - 35 x^{17} - 5 x^{16} + 77 x^{15} + 650 x^{14} + 400 x^{13} - 1560 x^{12} - 5655 x^{11} - 6544 x^{10} + 8125 x^{9} + 29000 x^{8} + 52825 x^{7} + 13550 x^{6} - 114415 x^{5} - 183000 x^{4} - 224375 x^{3} + 27875 x^{2} + 598500 x + 472525$ |
$20$ |
(0, 10) |
$3^{10}\cdot 5^{34}\cdot 29^{5}$ |
$3$ |
$62.0024904613$ |
$279.8741795606824$ |
|
|
? |
$D_5\wr C_4$ (as 20T617) |
$[2]$ |
$[2]$ |
$2$ |
$9$ |
$3763671112.97$ |
$0$ |
| 20.0.709...488.1 |
$x^{20} + 21168 x^{14} + 508032 x^{12} - 5334336 x^{10} + 176033088 x^{8} + 88720676352 x^{4} + 11178805220352$ |
$20$ |
(0, 10) |
$2^{30}\cdot 3^{10}\cdot 7^{15}\cdot 11^{9}$ |
$4$ |
$62.0234413404$ |
$182.46625877119556$ |
|
|
? |
$C_{10}\wr C_2$ (as 20T53) |
not computed |
not computed |
$2$ |
$9$ |
|
|
| 20.0.709...488.2 |
$x^{20} - 21168 x^{14} + 508032 x^{12} + 5334336 x^{10} + 176033088 x^{8} + 88720676352 x^{4} + 11178805220352$ |
$20$ |
(0, 10) |
$2^{30}\cdot 3^{10}\cdot 7^{15}\cdot 11^{9}$ |
$4$ |
$62.0234413404$ |
$182.46625877119556$ |
|
|
? |
$C_{10}\wr C_2$ (as 20T53) |
not computed |
not computed |
$2$ |
$9$ |
|
|
| 20.0.309...081.1 |
$x^{20} - 7 x^{19} + 97 x^{18} - 474 x^{17} + 4007 x^{16} - 15753 x^{15} + 101314 x^{14} - 328342 x^{13} + 1723760 x^{12} - 4540445 x^{11} + 20398857 x^{10} - 42014253 x^{9} + 171356427 x^{8} - 255706810 x^{7} + 1027027774 x^{6} - 925191743 x^{5} + 4322984339 x^{4} - 1470423622 x^{3} + 11553773609 x^{2} + 714284858 x + 15173012827$ |
$20$ |
(0, 10) |
$3^{10}\cdot 11^{13}\cdot 19^{15}$ |
$3$ |
$74.908495303$ |
$136.42037679267568$ |
|
|
|
$C_{10}\wr C_2$ (as 20T53) |
$[2]$ |
$[2]$ |
$2$ |
$9$ |
$45078583218.11364$ |
$0$ |
| 20.0.485...125.1 |
$x^{20} + 100 x^{18} + 4250 x^{16} - 151 x^{15} + 100000 x^{14} - 11325 x^{13} + 1421875 x^{12} - 339750 x^{11} + 12538426 x^{10} - 5190625 x^{9} + 68327550 x^{8} - 42468750 x^{7} + 228935250 x^{6} - 182755451 x^{5} + 484303125 x^{4} - 439980025 x^{3} + 600406250 x^{2} - 725290750 x + 924979351$ |
$20$ |
(0, 10) |
$3^{10}\cdot 5^{35}\cdot 7^{10}$ |
$3$ |
$76.6138266956$ |
$76.61382669555769$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
$[2, 2, 2, 2, 122, 122]$ |
$[2, 2, 2, 2, 122, 122]$ |
$2$ |
$9$ |
$161406.837641$ |
$0$ |
| 20.0.868...000.3 |
$x^{20} - 4 x^{19} + 65 x^{18} - 214 x^{17} + 2035 x^{16} - 5724 x^{15} + 39824 x^{14} - 96080 x^{13} + 534824 x^{12} - 1102236 x^{11} + 5168310 x^{10} - 9006872 x^{9} + 36960084 x^{8} - 53466672 x^{7} + 196375269 x^{6} - 224863132 x^{5} + 733497061 x^{4} - 597365054 x^{3} + 1764047967 x^{2} - 786154512 x + 2065660201$ |
$20$ |
(0, 10) |
$2^{20}\cdot 3^{10}\cdot 5^{15}\cdot 11^{16}$ |
$4$ |
$78.8737109246$ |
$78.87371092461403$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
$[10, 31810]$ |
$[10, 31810]$ |
$2$ |
$9$ |
$140644.599182$ |
$0$ |
| 20.0.911...413.1 |
$x^{20} - 2 x^{19} + 142 x^{17} - 487 x^{16} - 14704 x^{15} - 62037 x^{14} - 104965 x^{13} + 3721019 x^{12} - 3700335 x^{11} + 66521017 x^{10} + 438041117 x^{9} + 3146739432 x^{8} + 3010863560 x^{7} + 3800693924 x^{6} - 102591175456 x^{5} + 5820446848506 x^{4} - 8509114342925 x^{3} + 35158758524902 x^{2} - 277481574966688 x + 1360636406100091$ |
$20$ |
(0, 10) |
$3^{10}\cdot 7^{15}\cdot 11^{9}\cdot 13^{10}$ |
$4$ |
$79.0646844238$ |
$232.59975351164917$ |
|
|
? |
$C_{10}\wr C_2$ (as 20T53) |
not computed |
not computed |
$2$ |
$9$ |
|
|
| 20.20.977...552.1 |
$x^{20} - 4 x^{19} - 70 x^{18} + 272 x^{17} + 1927 x^{16} - 7236 x^{15} - 27190 x^{14} + 97888 x^{13} + 215144 x^{12} - 732552 x^{11} - 977916 x^{10} + 3078868 x^{9} + 2504547 x^{8} - 7029912 x^{7} - 3351642 x^{6} + 7942856 x^{5} + 1920559 x^{4} - 3602816 x^{3} - 111054 x^{2} + 391236 x + 6247$ |
$20$ |
(20, 0) |
$2^{55}\cdot 3^{10}\cdot 11^{16}$ |
$3$ |
$79.3427526718$ |
$79.34275267180627$ |
|
✓ |
? |
$C_{20}$ (as 20T1) |
trivial |
$[2]$ |
$2$ |
$19$ |
$2842376749290$ |
$19$ |
| 20.0.977...552.1 |
$x^{20} - 4 x^{19} + 50 x^{18} - 160 x^{17} + 1183 x^{16} - 3204 x^{15} + 16682 x^{14} - 38000 x^{13} + 149216 x^{12} - 282888 x^{11} + 886308 x^{10} - 1402508 x^{9} + 4088499 x^{8} - 5786136 x^{7} + 17951094 x^{6} - 21370648 x^{5} + 47163703 x^{4} - 38829056 x^{3} + 95586810 x^{2} - 47685756 x + 95829823$ |
$20$ |
(0, 10) |
$2^{55}\cdot 3^{10}\cdot 11^{16}$ |
$3$ |
$79.3427526718$ |
$79.34275267180627$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
$[131042]$ |
$[131042]$ |
$2$ |
$9$ |
$530208.250733$ |
$0$ |
| 20.0.116...000.1 |
$x^{20} - 20 x^{18} + 170 x^{16} - 88 x^{15} - 800 x^{14} + 1320 x^{13} + 2275 x^{12} - 7920 x^{11} - 1832 x^{10} + 24200 x^{9} - 17430 x^{8} - 39600 x^{7} + 73380 x^{6} + 25864 x^{5} - 107775 x^{4} + 24680 x^{3} + 54200 x^{2} - 35680 x + 7312$ |
$20$ |
(0, 10) |
$2^{48}\cdot 3^{10}\cdot 5^{21}\cdot 11^{4}$ |
$4$ |
$80.0257325872$ |
|
|
|
? |
$C_5:D_5^3.D_4$ (as 20T591) |
$[2]$ |
$[2]$ |
$4$ |
$9$ |
$237451987619$ |
$0$ |
| 20.0.184...000.1 |
$x^{20} + 120 x^{18} + 6120 x^{16} + 172800 x^{14} + 2948400 x^{12} + 31142880 x^{10} + 200620800 x^{8} + 748828800 x^{6} + 1469664000 x^{4} + 1259712000 x^{2} + 302330880$ |
$20$ |
(0, 10) |
$2^{30}\cdot 3^{10}\cdot 5^{35}$ |
$3$ |
$81.9036258813$ |
$81.903625881272$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
$[2, 152842]$ |
$[2, 152842]$ |
$2$ |
$9$ |
$161406.837641$ |
$0$ |
| 20.20.184...000.1 |
$x^{20} - 120 x^{18} + 6120 x^{16} - 172800 x^{14} + 2948400 x^{12} - 31142880 x^{10} + 200620800 x^{8} - 748828800 x^{6} + 1469664000 x^{4} - 1259712000 x^{2} + 302330880$ |
$20$ |
(20, 0) |
$2^{30}\cdot 3^{10}\cdot 5^{35}$ |
$3$ |
$81.9036258813$ |
$81.903625881272$ |
|
✓ |
? |
$C_{20}$ (as 20T1) |
$[2]$ |
$[2, 2]$ |
$2$ |
$19$ |
$2584911672430$ |
$19$ |
| 20.0.442...713.1 |
$x^{20} - 2 x^{18} - x^{17} - 31 x^{16} + 1254 x^{15} + 3623 x^{14} + 18500 x^{13} + 183167 x^{12} + 658122 x^{11} + 1787544 x^{10} + 5313132 x^{9} + 12782506 x^{8} + 18439839 x^{7} - 86460055 x^{6} - 166679788 x^{5} + 319083237 x^{4} - 1584395736 x^{3} - 3896978657 x^{2} + 5708282481 x + 10584256111$ |
$20$ |
(0, 10) |
$3^{10}\cdot 11^{9}\cdot 43^{15}$ |
$3$ |
$85.5635268259$ |
$251.71864523755065$ |
|
|
? |
$C_{10}\wr C_2$ (as 20T53) |
$[2]$ |
$[2]$ |
$2$ |
$9$ |
$279376417776.6134$ |
$0$ |
| 20.20.131...125.1 |
$x^{20} - x^{19} - 71 x^{18} + 19 x^{17} + 1925 x^{16} + 634 x^{15} - 24953 x^{14} - 18668 x^{13} + 165468 x^{12} + 169492 x^{11} - 571208 x^{10} - 710592 x^{9} + 966689 x^{8} + 1476993 x^{7} - 603922 x^{6} - 1425462 x^{5} - 116069 x^{4} + 498410 x^{3} + 156880 x^{2} - 24485 x - 9305$ |
$20$ |
(20, 0) |
$3^{10}\cdot 5^{15}\cdot 31^{16}$ |
$3$ |
$90.3394590476$ |
$90.33945904762285$ |
|
✓ |
? |
$C_{20}$ (as 20T1) |
trivial |
$[2, 2, 2, 2, 2]$ |
$2$ |
$19$ |
$40452422642700$ |
$15$ |
| 20.0.133...613.1 |
$x^{20} - 2 x^{19} + 184 x^{17} - 634 x^{16} - 25120 x^{15} - 154626 x^{14} - 226282 x^{13} + 10736027 x^{12} - 11872359 x^{11} + 249706453 x^{10} + 1717214789 x^{9} + 15675666360 x^{8} + 19294765565 x^{7} + 14626683497 x^{6} - 514531832689 x^{5} + 46810722484977 x^{4} - 73184262364724 x^{3} + 303631003542151 x^{2} - 3149047845503386 x + 20156487037106239$ |
$20$ |
(0, 10) |
$3^{10}\cdot 7^{15}\cdot 11^{9}\cdot 17^{10}$ |
$4$ |
$90.4139257022$ |
$265.9879943318089$ |
|
|
? |
$C_{10}\wr C_2$ (as 20T53) |
not computed |
not computed |
$2$ |
$9$ |
|
|
| 20.0.221...416.1 |
$x^{20} + 57 x^{18} + 1368 x^{16} + 38988 x^{14} + 2046870 x^{12} + 35001477 x^{10} + 495020889 x^{8} + 84648572019 x^{4} + 536107622787 x^{2} + 1608322868361$ |
$20$ |
(0, 10) |
$2^{20}\cdot 3^{10}\cdot 11^{9}\cdot 19^{15}$ |
$4$ |
$92.7432972498$ |
$272.84075358535137$ |
|
|
|
$C_{10}\wr C_2$ (as 20T53) |
$[2, 22]$ |
$[2, 22]$ |
$2$ |
$9$ |
$23875425813.093094$ |
$0$ |
| 20.0.405...637.1 |
$x^{20} - 2 x^{19} - 194 x^{17} + 689 x^{16} - 31168 x^{15} + 338475 x^{14} + 262283 x^{13} + 15826931 x^{12} - 29878767 x^{11} - 365384975 x^{10} - 3419682739 x^{9} + 34405291176 x^{8} + 84268890536 x^{7} - 26394328780 x^{6} - 1016302488544 x^{5} + 67406307545202 x^{4} - 178444854232925 x^{3} + 785827214610814 x^{2} + 9284287140719408 x + 66042689440116691$ |
$20$ |
(0, 10) |
$3^{10}\cdot 7^{15}\cdot 11^{9}\cdot 19^{10}$ |
$4$ |
$95.5845425778$ |
$281.1993901596297$ |
|
|
? |
$C_{10}\wr C_2$ (as 20T53) |
not computed |
not computed |
$2$ |
$9$ |
|
|
| 20.0.445...125.1 |
$x^{20} + 160 x^{18} + 10880 x^{16} - 361 x^{15} + 409600 x^{14} - 43320 x^{13} + 9318400 x^{12} - 2079360 x^{11} + 131366161 x^{10} - 50828800 x^{9} + 1137644880 x^{8} - 665395200 x^{7} + 5901800640 x^{6} - 4542160121 x^{5} + 18016281600 x^{4} - 16076932840 x^{3} + 30122086400 x^{2} - 33981478720 x + 43704064801$ |
$20$ |
(0, 10) |
$3^{10}\cdot 5^{35}\cdot 11^{10}$ |
$3$ |
$96.0405144051$ |
$96.04051440505009$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
$[2, 2, 341722]$ |
$[2, 2, 341722]$ |
$2$ |
$9$ |
$161406.837641$ |
$0$ |
| 20.0.676...000.1 |
$x^{20} + 330750 x^{14} + 19845000 x^{12} - 520931250 x^{10} + 42976828125 x^{8} + 135377008593750 x^{4} + 106609394267578125$ |
$20$ |
(0, 10) |
$2^{20}\cdot 3^{10}\cdot 5^{10}\cdot 7^{15}\cdot 11^{9}$ |
$5$ |
$98.0676714788$ |
$288.50448692332714$ |
|
|
? |
$C_{10}\wr C_2$ (as 20T53) |
not computed |
not computed |
$2$ |
$9$ |
|
|
| 20.0.776...977.1 |
$x^{20} - x^{19} + 36 x^{18} - 2 x^{17} + 858 x^{16} + 428 x^{15} + 15919 x^{14} + 12234 x^{13} + 230244 x^{12} + 213645 x^{11} + 2589686 x^{10} + 2500745 x^{9} + 22436528 x^{8} + 19427921 x^{7} + 143319432 x^{6} + 96231189 x^{5} + 629332635 x^{4} + 277057353 x^{3} + 1716995280 x^{2} + 348376851 x + 2203583227$ |
$20$ |
(0, 10) |
$3^{10}\cdot 11^{16}\cdot 17^{15}$ |
$3$ |
$98.7441706469$ |
$98.74417064689038$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
$[104050]$ |
$[104050]$ |
$2$ |
$9$ |
$3338983.62101$ |
$0$ |
| 20.20.105...000.1 |
$x^{20} - 165 x^{18} + 11385 x^{16} - 430650 x^{14} + 9845550 x^{12} - 141334875 x^{10} + 1279030500 x^{8} - 7111850625 x^{6} + 22824078750 x^{4} - 37213171875 x^{2} + 22327903125$ |
$20$ |
(20, 0) |
$2^{20}\cdot 3^{10}\cdot 5^{15}\cdot 11^{18}$ |
$4$ |
$100.247036509$ |
$100.24703650858366$ |
|
✓ |
? |
$C_{20}$ (as 20T1) |
$[2, 2]$ |
$[2, 2, 2, 2]$ |
$2$ |
$19$ |
$9804848600224.398$ |
$18$ |
| 20.0.118...792.1 |
$x^{20} + 132 x^{18} + 6930 x^{16} + 187704 x^{14} + 2879712 x^{12} + 26174016 x^{10} + 143251416 x^{8} + 465743520 x^{6} + 851040432 x^{4} + 762125760 x^{2} + 228637728$ |
$20$ |
(0, 10) |
$2^{55}\cdot 3^{10}\cdot 11^{18}$ |
$3$ |
$100.843179946$ |
$100.84317994603103$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
$[2, 308050]$ |
$[2, 308050]$ |
$2$ |
$9$ |
$530208.2507325789$ |
$0$ |
| 20.20.118...792.1 |
$x^{20} - 132 x^{18} + 6930 x^{16} - 187704 x^{14} + 2879712 x^{12} - 26174016 x^{10} + 143251416 x^{8} - 465743520 x^{6} + 851040432 x^{4} - 762125760 x^{2} + 228637728$ |
$20$ |
(20, 0) |
$2^{55}\cdot 3^{10}\cdot 11^{18}$ |
$3$ |
$100.843179946$ |
$100.84317994603103$ |
|
✓ |
? |
$C_{20}$ (as 20T1) |
$[2]$ |
$[2, 2]$ |
$2$ |
$19$ |
$31890919379863.914$ |
$19$ |
| 20.0.206...625.1 |
$x^{20} - x^{19} - 67 x^{18} - 2 x^{17} + 2507 x^{16} + 11090 x^{15} - 56108 x^{14} - 39660 x^{13} + 5076924 x^{12} + 15419289 x^{11} - 83477551 x^{10} - 357550606 x^{9} + 1302656985 x^{8} + 9580362848 x^{7} + 25185791680 x^{6} + 80262916876 x^{5} + 763433993087 x^{4} + 1979985628593 x^{3} + 183404344549 x^{2} + 7753870520858 x + 26838574955059$ |
$20$ |
(0, 10) |
$3^{10}\cdot 5^{10}\cdot 11^{9}\cdot 19^{15}$ |
$4$ |
$103.690158554$ |
$305.04523602455754$ |
|
|
|
$C_{10}\wr C_2$ (as 20T53) |
not computed |
not computed |
$2$ |
$9$ |
|
|
| 20.0.233...125.1 |
$x^{20} - x^{19} + 111 x^{18} - 167 x^{17} + 5949 x^{16} - 11044 x^{15} + 200941 x^{14} - 406236 x^{13} + 4703832 x^{12} - 9377568 x^{11} + 78907466 x^{10} - 142439068 x^{9} + 948074777 x^{8} - 1434111949 x^{7} + 7982392620 x^{6} - 9291183528 x^{5} + 45302317311 x^{4} - 35276815488 x^{3} + 157681514772 x^{2} - 60274636071 x + 258891665341$ |
$20$ |
(0, 10) |
$3^{10}\cdot 5^{15}\cdot 7^{10}\cdot 11^{16}$ |
$4$ |
$104.340112044$ |
$104.34011204366355$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
$[2, 1558442]$ |
$[2, 1558442]$ |
$2$ |
$9$ |
$140644.5991815038$ |
$0$ |
| 20.20.236...125.1 |
$x^{20} - 200 x^{18} + 17000 x^{16} - 451 x^{15} - 800000 x^{14} + 67650 x^{13} + 22750000 x^{12} - 4059000 x^{11} - 400296599 x^{10} + 124025000 x^{9} + 4279659900 x^{8} - 2029500000 x^{7} - 26038096500 x^{6} + 17046266149 x^{5} + 77329950000 x^{4} - 63063307450 x^{3} - 74149750000 x^{2} + 66883074500 x - 10328533199$ |
$20$ |
(20, 0) |
$3^{10}\cdot 5^{35}\cdot 13^{10}$ |
$3$ |
$104.407046651$ |
$104.40704665065225$ |
|
✓ |
? |
$C_{20}$ (as 20T1) |
$[2]$ |
$[2, 2]$ |
$2$ |
$19$ |
$19484063075260.734$ |
$19$ |
| 20.0.273...013.1 |
$x^{20} - 2 x^{19} - 236 x^{17} + 836 x^{16} - 45700 x^{15} + 584154 x^{14} + 470918 x^{13} + 34084247 x^{12} - 61979619 x^{11} - 968517827 x^{10} - 8802796741 x^{9} + 106311643260 x^{8} + 254034949145 x^{7} - 68438589913 x^{6} - 3195394128199 x^{5} + 328992895342527 x^{4} - 824538530624354 x^{3} + 3605218271933941 x^{2} + 51515431316557004 x + 443668900413495079$ |
$20$ |
(0, 10) |
$3^{10}\cdot 7^{15}\cdot 11^{9}\cdot 23^{10}$ |
$4$ |
$105.165861465$ |
$309.3865944431434$ |
|
|
? |
$C_{10}\wr C_2$ (as 20T53) |
not computed |
not computed |
$2$ |
$9$ |
|
|
| 20.4.484...125.1 |
$x^{20} + 40 x^{18} - 10 x^{17} + 590 x^{16} - 303 x^{15} + 3675 x^{14} - 2890 x^{13} + 6485 x^{12} - 6615 x^{11} - 13451 x^{10} + 19800 x^{9} - 8945 x^{8} - 2470 x^{7} - 8895 x^{6} + 13508 x^{5} - 9050 x^{4} + 10505 x^{3} - 5670 x^{2} + 905 x + 3571$ |
$20$ |
(4, 8) |
$3^{10}\cdot 5^{34}\cdot 269^{5}$ |
$3$ |
$108.205093522$ |
$852.3931962118999$ |
|
|
? |
$D_5\wr C_4$ (as 20T617) |
trivial |
$[2]$ |
$2$ |
$11$ |
$4377434867810$ |
$3$ |
| 20.0.889...000.1 |
$x^{20} - 4 x^{19} + 140 x^{18} - 484 x^{17} + 8995 x^{16} - 26964 x^{15} + 347234 x^{14} - 897860 x^{13} + 8892914 x^{12} - 19607256 x^{11} + 158159580 x^{10} - 291931652 x^{9} + 1992948639 x^{8} - 2991975192 x^{7} + 17755674714 x^{6} - 20587092232 x^{5} + 107656174381 x^{4} - 86695117664 x^{3} + 403679657832 x^{2} - 171720168132 x + 713941020451$ |
$20$ |
(0, 10) |
$2^{30}\cdot 3^{10}\cdot 5^{15}\cdot 11^{16}$ |
$4$ |
$111.544271704$ |
$111.54427170428411$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
not computed |
not computed |
$2$ |
$9$ |
|
|
| 20.20.889...000.1 |
$x^{20} - 4 x^{19} - 160 x^{18} + 596 x^{17} + 10855 x^{16} - 37044 x^{15} - 410446 x^{14} + 1256260 x^{13} + 9550214 x^{12} - 25487736 x^{11} - 142170420 x^{10} + 318380188 x^{9} + 1360120959 x^{8} - 2419997592 x^{7} - 8144811726 x^{6} + 10588403048 x^{5} + 28534156681 x^{4} - 23381756864 x^{3} - 50583618588 x^{2} + 18481726428 x + 31950384751$ |
$20$ |
(20, 0) |
$2^{30}\cdot 3^{10}\cdot 5^{15}\cdot 11^{16}$ |
$4$ |
$111.544271704$ |
$111.54427170428411$ |
|
✓ |
? |
$C_{20}$ (as 20T1) |
$[2]$ |
$[2, 2]$ |
$2$ |
$19$ |
$71481799140222.92$ |
$19$ |
