| 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 |
| 20.0.291...125.1 |
$x^{20} - x^{15} + x^{10} - x^{5} + 1$ |
$20$ |
[0,10] |
$5^{35}$ |
$1$ |
$16.7185076244$ |
$16.71850762441055$ |
✓ |
✓ |
✓ |
$C_{20}$ (as 20T1) |
trivial |
$50$ |
$9$ |
$161406.837641$ |
| 20.0.140...125.1 |
$x^{20} - x^{19} + 5 x^{18} - 6 x^{17} + 20 x^{16} - 11 x^{15} + 59 x^{14} - 30 x^{13} + 179 x^{12} - 109 x^{11} + 260 x^{10} - 128 x^{9} + 334 x^{8} + 82 x^{7} + 199 x^{6} + 22 x^{5} + 146 x^{4} - 41 x^{3} + 12 x^{2} - 3 x + 1$ |
$20$ |
[0,10] |
$5^{15}\cdot 11^{16}$ |
$2$ |
$22.7688791172$ |
$22.76887911715532$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
$[5]$ |
$10$ |
$9$ |
$140644.599182$ |
| 20.20.169...125.1 |
$x^{20} - x^{19} - 20 x^{18} + 19 x^{17} + 170 x^{16} - 151 x^{15} - 801 x^{14} + 650 x^{13} + 2289 x^{12} - 1639 x^{11} - 4080 x^{10} + 2442 x^{9} + 4489 x^{8} - 2058 x^{7} - 2891 x^{6} + 877 x^{5} + 951 x^{4} - 151 x^{3} - 108 x^{2} + 12 x + 1$ |
$20$ |
[20,0] |
$5^{15}\cdot 11^{18}$ |
$2$ |
$28.9388267568$ |
$28.93882675684651$ |
|
✓ |
✓ |
$C_{20}$ (as 20T1) |
trivial |
$2$ |
$19$ |
$115949178.41$ |
| 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 |
$2$ |
$19$ |
$122630529.842$ |
| 20.20.305...000.1 |
$x^{20} - 20 x^{18} + 170 x^{16} - 800 x^{14} + 2275 x^{12} - 4005 x^{10} + 4300 x^{8} - 2675 x^{6} + 875 x^{4} - 125 x^{2} + 5$ |
$20$ |
[20,0] |
$2^{20}\cdot 5^{35}$ |
$2$ |
$33.4370152488$ |
$33.4370152488211$ |
|
✓ |
✓ |
$C_{20}$ (as 20T1) |
trivial |
$2$ |
$19$ |
$550507572.449$ |
| 20.20.439...361.1 |
$x^{20} - x^{19} - 19 x^{18} + 18 x^{17} + 153 x^{16} - 136 x^{15} - 680 x^{14} + 560 x^{13} + 1820 x^{12} - 1365 x^{11} - 3003 x^{10} + 2002 x^{9} + 3003 x^{8} - 1716 x^{7} - 1716 x^{6} + 792 x^{5} + 495 x^{4} - 165 x^{3} - 55 x^{2} + 10 x + 1$ |
$20$ |
[20,0] |
$41^{19}$ |
$1$ |
$34.0521598863$ |
$34.052159886341$ |
|
✓ |
✓ |
$C_{20}$ (as 20T1) |
trivial |
$2$ |
$19$ |
$592074817.62$ |
| 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 |
$2$ |
$19$ |
$2427056473.64$ |
| 20.20.822...125.1 |
$x^{20} - 40 x^{18} + 680 x^{16} - 11 x^{15} - 6400 x^{14} + 330 x^{13} + 36400 x^{12} - 3960 x^{11} - 128039 x^{10} + 24200 x^{9} + 272780 x^{8} - 79200 x^{7} - 325460 x^{6} + 132429 x^{5} + 175600 x^{4} - 92290 x^{3} - 15600 x^{2} + 8580 x + 401$ |
$20$ |
[20,0] |
$5^{35}\cdot 7^{10}$ |
$2$ |
$44.2330134663$ |
$44.23301346632757$ |
|
✓ |
? |
$C_{20}$ (as 20T1) |
trivial |
$2$ |
$19$ |
$9489514790.4$ |
| 20.20.147...000.1 |
$x^{20} - 4 x^{19} - 35 x^{18} + 146 x^{17} + 455 x^{16} - 2044 x^{15} - 2696 x^{14} + 13960 x^{13} + 6764 x^{12} - 48836 x^{11} - 2270 x^{10} + 84688 x^{9} - 15516 x^{8} - 65992 x^{7} + 17949 x^{6} + 20748 x^{5} - 6419 x^{4} - 1814 x^{3} + 787 x^{2} - 72 x + 1$ |
$20$ |
[20,0] |
$2^{20}\cdot 5^{15}\cdot 11^{16}$ |
$3$ |
$45.5377582343$ |
$45.53775823431064$ |
|
✓ |
? |
$C_{20}$ (as 20T1) |
trivial |
$2$ |
$19$ |
$8953413920.01$ |
| 20.0.165...848.1 |
$x^{20} + 36 x^{18} + 498 x^{16} + 3416 x^{14} + 12736 x^{12} + 26944 x^{10} + 32408 x^{8} + 21280 x^{6} + 6960 x^{4} + 960 x^{2} + 32$ |
$20$ |
[0,10] |
$2^{55}\cdot 11^{16}$ |
$2$ |
$45.8085596133$ |
$45.80855961331325$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
$[521]$ |
$2$ |
$9$ |
$530208.250733$ |
| 20.20.165...848.1 |
$x^{20} - 36 x^{18} + 498 x^{16} - 3416 x^{14} + 12736 x^{12} - 26944 x^{10} + 32408 x^{8} - 21280 x^{6} + 6960 x^{4} - 960 x^{2} + 32$ |
$20$ |
[20,0] |
$2^{55}\cdot 11^{16}$ |
$2$ |
$45.8085596133$ |
$45.80855961331325$ |
|
✓ |
? |
$C_{20}$ (as 20T1) |
trivial |
$2$ |
$19$ |
$8594581552.27$ |
| 20.0.235...877.1 |
$x^{20} - x^{19} - 9 x^{18} + 31 x^{17} + 55 x^{16} - 48 x^{15} + 189 x^{14} + 352 x^{13} + 1680 x^{12} + 4302 x^{11} + 4614 x^{10} + 17042 x^{9} + 24675 x^{8} + 19061 x^{7} + 33622 x^{6} - 55350 x^{5} - 15945 x^{4} + 101736 x^{3} + 82138 x^{2} - 16471 x + 40283$ |
$20$ |
[0,10] |
$11^{16}\cdot 13^{15}$ |
$2$ |
$46.6199348592$ |
$46.61993485918934$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
$[61]$ |
$2$ |
$9$ |
$2015201.7242$ |
| 20.0.312...000.1 |
$x^{20} + 40 x^{18} + 680 x^{16} + 6400 x^{14} + 36400 x^{12} + 128160 x^{10} + 275200 x^{8} + 342400 x^{6} + 224000 x^{4} + 64000 x^{2} + 5120$ |
$20$ |
[0,10] |
$2^{30}\cdot 5^{35}$ |
$2$ |
$47.2870804502$ |
$47.28708045015879$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
$[1202]$ |
$2$ |
$9$ |
$161406.837641$ |
| 20.20.312...000.1 |
$x^{20} - 40 x^{18} + 680 x^{16} - 6400 x^{14} + 36400 x^{12} - 128160 x^{10} + 275200 x^{8} - 342400 x^{6} + 224000 x^{4} - 64000 x^{2} + 5120$ |
$20$ |
[20,0] |
$2^{30}\cdot 5^{35}$ |
$2$ |
$47.2870804502$ |
$47.28708045015879$ |
|
✓ |
? |
$C_{20}$ (as 20T1) |
trivial |
$2$ |
$19$ |
$17989238529.3$ |
| 20.0.834...741.1 |
$x^{20} - x^{19} + 2 x^{18} + 36 x^{17} - 29 x^{16} + 51 x^{15} + 413 x^{14} - 267 x^{13} + 414 x^{12} + 1778 x^{11} - 745 x^{10} + 691 x^{9} + 3278 x^{8} - 541 x^{7} - 1330 x^{6} + 1820 x^{5} - 261 x^{4} - 439 x^{3} + 2983 x^{2} - 522 x + 611$ |
$20$ |
[0,10] |
$61^{19}$ |
$1$ |
$49.6664756335$ |
$49.6664756335031$ |
✓ |
✓ |
|
$C_{20}$ (as 20T1) |
$[41]$ |
$2$ |
$9$ |
$36549838.4715$ |
| 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) |
$[2, 2, 842]$ |
$2$ |
$9$ |
$140644.599182$ |
| 20.0.221...125.2 |
$x^{20} - x^{19} + 13 x^{18} - 4 x^{17} + 138 x^{16} - 481 x^{15} + 2045 x^{14} - 4980 x^{13} + 19301 x^{12} - 36325 x^{11} + 68890 x^{10} - 104714 x^{9} + 174168 x^{8} - 44226 x^{7} + 47983 x^{6} - 14164 x^{5} + 10616 x^{4} + 445 x^{3} + 2650 x^{2} - 125 x + 625$ |
$20$ |
[0,10] |
$5^{15}\cdot 31^{16}$ |
$2$ |
$52.1575109996$ |
$52.15751099959023$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
$[2, 2, 10, 10]$ |
$10$ |
$9$ |
$24173706.8324$ |
| 20.20.754...125.1 |
$x^{20} - 60 x^{18} + 1530 x^{16} - 31 x^{15} - 21600 x^{14} + 1395 x^{13} + 184275 x^{12} - 25110 x^{11} - 972254 x^{10} + 230175 x^{9} + 3105870 x^{8} - 1129950 x^{7} - 5547510 x^{6} + 2832749 x^{5} + 4443525 x^{4} - 2942985 x^{3} - 514350 x^{2} + 354330 x + 51151$ |
$20$ |
[20,0] |
$5^{35}\cdot 11^{10}$ |
$2$ |
$55.4490168449$ |
$55.449016844865795$ |
|
✓ |
? |
$C_{20}$ (as 20T1) |
trivial |
$2$ |
$19$ |
$73895548051.9$ |
| 20.20.131...673.1 |
$x^{20} - x^{19} - 49 x^{18} + 32 x^{17} + 926 x^{16} - 354 x^{15} - 8765 x^{14} + 1660 x^{13} + 45828 x^{12} - 2629 x^{11} - 137522 x^{10} - 4409 x^{9} + 237299 x^{8} + 22455 x^{7} - 226443 x^{6} - 31515 x^{5} + 107725 x^{4} + 17397 x^{3} - 20309 x^{2} - 2449 x + 1033$ |
$20$ |
[20,0] |
$11^{16}\cdot 17^{15}$ |
$2$ |
$57.0099735039$ |
$57.00997350388851$ |
|
✓ |
? |
$C_{20}$ (as 20T1) |
trivial |
$2$ |
$19$ |
$124763101953$ |
| 20.0.177...000.1 |
$x^{20} + 55 x^{18} + 1265 x^{16} + 15950 x^{14} + 121550 x^{12} + 581625 x^{10} + 1754500 x^{8} + 3251875 x^{6} + 3478750 x^{4} + 1890625 x^{2} + 378125$ |
$20$ |
[0,10] |
$2^{20}\cdot 5^{15}\cdot 11^{18}$ |
$3$ |
$57.8776535137$ |
$57.87765351369302$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
$[2, 2, 2762]$ |
$2$ |
$9$ |
$140644.599182$ |
| 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) |
$[2, 4322]$ |
$2$ |
$9$ |
$161406.837641$ |
| 20.0.200...608.1 |
$x^{20} + 44 x^{18} + 770 x^{16} + 6952 x^{14} + 35552 x^{12} + 107712 x^{10} + 196504 x^{8} + 212960 x^{6} + 129712 x^{4} + 38720 x^{2} + 3872$ |
$20$ |
[0,10] |
$2^{55}\cdot 11^{18}$ |
$2$ |
$58.2218370878$ |
$58.22183708777889$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
$[2050]$ |
$2$ |
$9$ |
$530208.250733$ |
| 20.20.200...608.1 |
$x^{20} - 44 x^{18} + 770 x^{16} - 6952 x^{14} + 35552 x^{12} - 107712 x^{10} + 196504 x^{8} - 212960 x^{6} + 129712 x^{4} - 38720 x^{2} + 3872$ |
$20$ |
[20,0] |
$2^{55}\cdot 11^{18}$ |
$2$ |
$58.2218370878$ |
$58.22183708777889$ |
|
✓ |
? |
$C_{20}$ (as 20T1) |
trivial |
$2$ |
$19$ |
$228779211109$ |
| 20.0.259...689.1 |
$x^{20} - x^{19} + 22 x^{18} - 23 x^{17} + 153 x^{16} - 177 x^{15} + 304 x^{14} - 506 x^{13} - 476 x^{12} + 316 x^{11} - 1773 x^{10} + 5692 x^{9} - 8231 x^{8} + 16816 x^{7} + 2671 x^{6} + 10386 x^{5} + 74910 x^{4} - 82739 x^{3} + 50170 x^{2} + 37115 x + 51907$ |
$20$ |
[0,10] |
$3^{10}\cdot 41^{19}$ |
$2$ |
$58.9800710306$ |
$58.98007103060146$ |
✓ |
✓ |
|
$C_{20}$ (as 20T1) |
$[2, 2, 2, 2, 34]$ |
$2$ |
$9$ |
$5104264.63655$ |
| 20.20.284...117.1 |
$x^{20} - x^{19} - 51 x^{18} + 48 x^{17} + 998 x^{16} - 854 x^{15} - 9572 x^{14} + 7010 x^{13} + 48842 x^{12} - 27812 x^{11} - 139547 x^{10} + 54957 x^{9} + 224814 x^{8} - 51088 x^{7} - 194675 x^{6} + 16639 x^{5} + 78872 x^{4} + 1845 x^{3} - 10254 x^{2} - 1316 x - 43$ |
$20$ |
[20,0] |
$11^{18}\cdot 13^{15}$ |
$2$ |
$59.2530801083$ |
$59.253080108324006$ |
|
✓ |
? |
$C_{20}$ (as 20T1) |
trivial |
$2$ |
$19$ |
$168224843913$ |
| 20.20.396...125.1 |
$x^{20} - x^{19} - 64 x^{18} + 78 x^{17} + 1609 x^{16} - 2224 x^{15} - 20399 x^{14} + 30774 x^{13} + 139797 x^{12} - 228288 x^{11} - 510719 x^{10} + 929822 x^{9} + 878982 x^{8} - 2003579 x^{7} - 355510 x^{6} + 2013497 x^{5} - 574064 x^{4} - 658628 x^{3} + 441152 x^{2} - 86946 x + 4621$ |
$20$ |
[20,0] |
$5^{15}\cdot 7^{10}\cdot 11^{16}$ |
$3$ |
$60.2407917757$ |
$60.24079177568486$ |
|
✓ |
? |
$C_{20}$ (as 20T1) |
trivial |
$2$ |
$19$ |
$249459949124$ |
| 20.0.401...125.1 |
$x^{20} + 60 x^{18} + 1530 x^{16} - 61 x^{15} + 21600 x^{14} - 2745 x^{13} + 184275 x^{12} - 49410 x^{11} + 976936 x^{10} - 452925 x^{9} + 3246330 x^{8} - 2223450 x^{7} + 7022340 x^{6} - 5859721 x^{5} + 10764225 x^{4} - 10075065 x^{3} + 9995400 x^{2} - 13549320 x + 18662101$ |
$20$ |
[0,10] |
$5^{35}\cdot 13^{10}$ |
$2$ |
$60.279436489$ |
$60.27943648904789$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
$[15362]$ |
$2$ |
$9$ |
$161406.837641$ |
| 20.0.150...000.1 |
$x^{20} - 4 x^{19} + 40 x^{18} - 124 x^{17} + 815 x^{16} - 2164 x^{15} + 10834 x^{14} - 24620 x^{13} + 101774 x^{12} - 198776 x^{11} + 710860 x^{10} - 1188452 x^{9} + 3826719 x^{8} - 5429272 x^{7} + 15991074 x^{6} - 18262392 x^{5} + 47151361 x^{4} - 38741504 x^{3} + 92992732 x^{2} - 43101732 x + 90594151$ |
$20$ |
[0,10] |
$2^{30}\cdot 5^{15}\cdot 11^{16}$ |
$3$ |
$64.400115295$ |
$64.4001152950292$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
$[22082]$ |
$2$ |
$9$ |
$140644.599182$ |
| 20.20.150...000.2 |
$x^{20} - 4 x^{19} - 60 x^{18} + 236 x^{17} + 1435 x^{16} - 5524 x^{15} - 17726 x^{14} + 66220 x^{13} + 122474 x^{12} - 437336 x^{11} - 480740 x^{10} + 1596028 x^{9} + 1047359 x^{8} - 3070872 x^{7} - 1203606 x^{6} + 2823768 x^{5} + 614261 x^{4} - 1007904 x^{3} - 118608 x^{2} + 70588 x + 1451$ |
$20$ |
[20,0] |
$2^{30}\cdot 5^{15}\cdot 11^{16}$ |
$3$ |
$64.400115295$ |
$64.4001152950292$ |
|
✓ |
? |
$C_{20}$ (as 20T1) |
$[5]$ |
$2$ |
$19$ |
$107373870215$ |
| 20.0.194...125.1 |
$x^{20} - x^{19} + 17 x^{18} - 38 x^{17} + 294 x^{16} + 679 x^{15} + 3849 x^{14} + 6496 x^{13} + 45177 x^{12} + 27901 x^{11} + 73952 x^{10} + 44804 x^{9} + 108670 x^{8} + 59106 x^{7} + 153711 x^{6} + 82674 x^{5} + 202338 x^{4} + 88695 x^{3} + 39366 x^{2} + 15309 x + 6561$ |
$20$ |
[0,10] |
$5^{15}\cdot 41^{16}$ |
$2$ |
$65.2310829497$ |
$65.23108294968821$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
$[505]$ |
$10$ |
$9$ |
$41023218.2567$ |
| 20.0.460...936.1 |
$x^{20} + 41 x^{18} + 656 x^{16} + 5289 x^{14} + 23165 x^{12} + 55801 x^{10} + 71545 x^{8} + 45141 x^{6} + 13120 x^{4} + 1517 x^{2} + 41$ |
$20$ |
[0,10] |
$2^{20}\cdot 41^{19}$ |
$2$ |
$68.1043197727$ |
$68.104319772682$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
$[2, 482]$ |
$2$ |
$9$ |
$5104264.63655$ |
| 20.0.586...125.1 |
$x^{20} + 80 x^{18} + 2720 x^{16} - 101 x^{15} + 51200 x^{14} - 6060 x^{13} + 582400 x^{12} - 145440 x^{11} + 4111321 x^{10} - 1777600 x^{9} + 18020840 x^{8} - 11635200 x^{7} + 49539760 x^{6} - 40331421 x^{5} + 89987200 x^{4} - 82660420 x^{3} + 98054400 x^{2} - 123793680 x + 161532401$ |
$20$ |
[0,10] |
$5^{35}\cdot 17^{10}$ |
$2$ |
$68.9321728381$ |
$68.9321728381389$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
$[11, 5302]$ |
$2$ |
$9$ |
$161406.837641$ |
| 20.0.159...433.1 |
$x^{20} - x^{19} + 27 x^{18} - 31 x^{17} + 348 x^{16} - 472 x^{15} + 2986 x^{14} - 4874 x^{13} + 20558 x^{12} - 40054 x^{11} + 130294 x^{10} - 168519 x^{9} + 700706 x^{8} - 32881 x^{7} + 2845143 x^{6} + 2390937 x^{5} + 8994354 x^{4} + 9962701 x^{3} + 26015925 x^{2} + 20544384 x + 83519437$ |
$20$ |
[0,10] |
$11^{18}\cdot 17^{15}$ |
$2$ |
$72.4586282071$ |
$72.45862820705953$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
$[8194]$ |
$2$ |
$9$ |
$3338983.62101$ |
| 20.20.178...125.1 |
$x^{20} - 100 x^{18} + 4250 x^{16} - 101 x^{15} - 100000 x^{14} + 7575 x^{13} + 1421875 x^{12} - 227250 x^{11} - 12505424 x^{10} + 3471875 x^{9} + 66677450 x^{8} - 28406250 x^{7} - 200058500 x^{6} + 118907199 x^{5} + 278040625 x^{4} - 210961225 x^{3} - 84750000 x^{2} + 68478000 x - 6502099$ |
$20$ |
[20,0] |
$5^{35}\cdot 19^{10}$ |
$2$ |
$72.8742852216$ |
$72.87428522161984$ |
|
✓ |
? |
$C_{20}$ (as 20T1) |
trivial |
$2$ |
$19$ |
$1261324189610$ |
| 20.20.213...125.1 |
$x^{20} - x^{19} - 57 x^{18} + 66 x^{17} + 1198 x^{16} - 1526 x^{15} - 12200 x^{14} + 17240 x^{13} + 64636 x^{12} - 104480 x^{11} - 174550 x^{10} + 341431 x^{9} + 205983 x^{8} - 586336 x^{7} - 12337 x^{6} + 478381 x^{5} - 146594 x^{4} - 137680 x^{3} + 63070 x^{2} + 8405 x - 4645$ |
$20$ |
[20,0] |
$5^{15}\cdot 31^{18}$ |
$2$ |
$73.5280464922$ |
$73.52804649223957$ |
|
✓ |
? |
$C_{20}$ (as 20T1) |
trivial |
$2$ |
$19$ |
$3696529687160$ |
| 20.20.429...625.1 |
$x^{20} - x^{19} - 60 x^{18} + 59 x^{17} + 1465 x^{16} - 1407 x^{15} - 18966 x^{14} + 17616 x^{13} + 142122 x^{12} - 125226 x^{11} - 630959 x^{10} + 509336 x^{9} + 1631687 x^{8} - 1138974 x^{7} - 2320717 x^{6} + 1291062 x^{5} + 1584530 x^{4} - 656657 x^{3} - 352368 x^{2} + 129857 x - 4099$ |
$20$ |
[20,0] |
$5^{10}\cdot 41^{19}$ |
$2$ |
$76.1429442865$ |
$76.14294428654999$ |
|
✓ |
? |
$C_{20}$ (as 20T1) |
$[2]$ |
$2$ |
$19$ |
$1163330087490$ |
| 20.0.479...125.1 |
$x^{20} - x^{19} + 90 x^{18} - 91 x^{17} + 3360 x^{16} - 3451 x^{15} + 68499 x^{14} - 71950 x^{13} + 849729 x^{12} - 921679 x^{11} + 6805360 x^{10} - 7799638 x^{9} + 36820719 x^{8} - 45394658 x^{7} + 141833529 x^{6} - 176867903 x^{5} + 410339451 x^{4} - 382542201 x^{3} + 863744092 x^{2} - 219225038 x + 1102456301$ |
$20$ |
[0,10] |
$5^{15}\cdot 7^{10}\cdot 11^{18}$ |
$3$ |
$76.5649388326$ |
$76.5649388325977$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
$[2, 2, 64564]$ |
$2$ |
$9$ |
$140644.599182$ |
| 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) |
$[2, 2, 2, 2, 122, 122]$ |
$2$ |
$9$ |
$161406.837641$ |
| 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) |
$[10, 31810]$ |
$2$ |
$9$ |
$140644.599182$ |
| 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) |
$[131042]$ |
$2$ |
$9$ |
$530208.250733$ |
| 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 |
$2$ |
$19$ |
$2842376749290$ |
| 20.20.120...125.1 |
$x^{20} - 120 x^{18} + 6120 x^{16} - 151 x^{15} - 172800 x^{14} + 13590 x^{13} + 2948400 x^{12} - 489240 x^{11} - 31120079 x^{10} + 8969400 x^{9} + 199252740 x^{8} - 88063200 x^{7} - 720099540 x^{6} + 442743929 x^{5} + 1223413200 x^{4} - 953469870 x^{3} - 520959600 x^{2} + 437027220 x - 64286399$ |
$20$ |
[20,0] |
$5^{35}\cdot 23^{10}$ |
$2$ |
$80.1791458879$ |
$80.17914588789216$ |
|
✓ |
? |
$C_{20}$ (as 20T1) |
trivial |
$2$ |
$19$ |
$3975952893490$ |
| 20.0.120...901.1 |
$x^{20} - x^{19} + 3 x^{18} - 11 x^{17} + 44 x^{16} + 300 x^{15} + 316 x^{14} - 1991 x^{13} - 80 x^{12} + 1958 x^{11} + 24000 x^{10} + 7237 x^{9} - 31618 x^{8} - 6930 x^{7} + 112662 x^{6} + 144019 x^{5} - 16152 x^{4} - 21866 x^{3} + 125333 x^{2} + 197892 x + 120577$ |
$20$ |
[0,10] |
$101^{19}$ |
$1$ |
$80.1872472994$ |
$80.18724729938236$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
$[5, 25]$ |
$2$ |
$9$ |
$224544554.426$ |
| 20.20.138...973.1 |
$x^{20} - x^{19} - 74 x^{18} - 8 x^{17} + 2161 x^{16} + 2188 x^{15} - 30387 x^{14} - 53182 x^{13} + 205169 x^{12} + 517750 x^{11} - 537473 x^{10} - 2291342 x^{9} - 343368 x^{8} + 4213355 x^{7} + 3433304 x^{6} - 1687071 x^{5} - 3020232 x^{4} - 1007476 x^{3} + 2500 x^{2} + 17940 x + 529$ |
$20$ |
[20,0] |
$3^{10}\cdot 11^{16}\cdot 13^{15}$ |
$3$ |
$80.7480958217$ |
$80.74809582166735$ |
|
✓ |
? |
$C_{20}$ (as 20T1) |
trivial |
$2$ |
$19$ |
$5124246016990$ |
| 20.0.182...000.1 |
$x^{20} + 110 x^{18} + 5060 x^{16} + 127600 x^{14} + 1944800 x^{12} + 18612000 x^{10} + 112288000 x^{8} + 416240000 x^{6} + 890560000 x^{4} + 968000000 x^{2} + 387200000$ |
$20$ |
[0,10] |
$2^{30}\cdot 5^{15}\cdot 11^{18}$ |
$3$ |
$81.8513625574$ |
$81.85136255739549$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
$[2, 2, 62564]$ |
$2$ |
$9$ |
$140644.599182$ |
| 20.20.182...000.1 |
$x^{20} - 110 x^{18} + 5060 x^{16} - 127600 x^{14} + 1944800 x^{12} - 18612000 x^{10} + 112288000 x^{8} - 416240000 x^{6} + 890560000 x^{4} - 968000000 x^{2} + 387200000$ |
$20$ |
[20,0] |
$2^{30}\cdot 5^{15}\cdot 11^{18}$ |
$3$ |
$81.8513625574$ |
$81.85136255739549$ |
|
✓ |
? |
$C_{20}$ (as 20T1) |
$[2]$ |
$2$ |
$19$ |
$1855680090430$ |
| 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) |
$[2, 152842]$ |
$2$ |
$9$ |
$161406.837641$ |
| 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) |
$[2]$ |
$2$ |
$19$ |
$2584911672430$ |
| 20.0.193...125.1 |
$x^{20} - x^{19} + 61 x^{18} - 97 x^{17} + 1959 x^{16} - 3824 x^{15} + 42001 x^{14} - 86676 x^{13} + 651922 x^{12} - 1272388 x^{11} + 7455206 x^{10} - 12647278 x^{9} + 61958107 x^{8} - 85243529 x^{7} + 364805340 x^{6} - 374838878 x^{5} + 1487095911 x^{4} - 973042478 x^{3} + 3808215652 x^{2} - 1149290321 x + 4751163121$ |
$20$ |
[0,10] |
$5^{15}\cdot 11^{16}\cdot 13^{10}$ |
$3$ |
$82.0943611417$ |
$82.09436114174476$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
$[331922]$ |
$2$ |
$9$ |
$140644.599182$ |
| 20.0.396...789.1 |
$x^{20} - x^{19} + x^{18} - 93 x^{17} + 209 x^{16} - 800 x^{15} + 4981 x^{14} - 12556 x^{13} + 52672 x^{12} - 186410 x^{11} + 461402 x^{10} - 1486634 x^{9} + 3730667 x^{8} - 7453323 x^{7} + 16223240 x^{6} - 23433182 x^{5} + 16658019 x^{4} - 7158636 x^{3} + 5906450 x^{2} - 2576267 x + 1575113$ |
$20$ |
[0,10] |
$11^{16}\cdot 29^{15}$ |
$2$ |
$85.0966858577$ |
$85.09668585773373$ |
✓ |
✓ |
? |
$C_{20}$ (as 20T1) |
$[8221]$ |
$2$ |
$9$ |
$15197121.6751$ |
