| 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 |
| 20.4.187...873.1 |
$x^{20} - 2 x^{19} + 3 x^{17} - 9 x^{16} + 20 x^{15} - 26 x^{14} + 19 x^{13} - 5 x^{12} - 8 x^{11} + 42 x^{10} - 89 x^{9} + 94 x^{8} - 76 x^{7} + 75 x^{6} - 64 x^{5} + 33 x^{4} - 14 x^{3} + 6 x^{2} - 1$ |
$20$ |
[4,8] |
$3^{8}\cdot 17^{15}$ |
$2$ |
$12.992274655$ |
$14.500978825806921$ |
|
|
? |
$C_2\times F_5$ (as 20T9) |
trivial |
$2$ |
$11$ |
$1051.52404478$ |
| 20.0.107...125.1 |
$x^{20} - 5 x^{19} + 12 x^{18} - 20 x^{17} + 28 x^{16} - 35 x^{15} + 34 x^{14} - 25 x^{13} + 30 x^{12} - 70 x^{11} + 119 x^{10} - 140 x^{9} + 208 x^{8} - 325 x^{7} + 292 x^{6} - 85 x^{5} - 14 x^{4} - 70 x^{3} + 40 x^{2} + 25 x + 25$ |
$20$ |
[0,10] |
$5^{15}\cdot 37^{8}$ |
$2$ |
$14.1745145113$ |
$20.33894234805392$ |
|
|
|
$C_2\times F_5$ (as 20T9) |
trivial |
$10$ |
$9$ |
$9032.09324455$ |
| 20.0.200...000.1 |
$x^{20} - 5 x^{19} + 10 x^{18} - 10 x^{17} + 10 x^{16} - 25 x^{15} + 40 x^{14} - 25 x^{13} + 40 x^{12} - 200 x^{11} + 515 x^{10} - 850 x^{9} + 1050 x^{8} - 1075 x^{7} + 1000 x^{6} - 875 x^{5} + 700 x^{4} - 500 x^{3} + 300 x^{2} - 125 x + 25$ |
$20$ |
[0,10] |
$2^{24}\cdot 5^{23}$ |
$2$ |
$14.6235057356$ |
$18.00364738986388$ |
|
|
? |
$C_2\times F_5$ (as 20T9) |
trivial |
$10$ |
$9$ |
$13801.9175678$ |
| 20.4.774...000.1 |
$x^{20} - 2 x^{18} - 3 x^{17} - 9 x^{16} - 12 x^{15} - 12 x^{14} + 18 x^{13} + 84 x^{12} + 132 x^{11} + 174 x^{10} + 198 x^{9} + 177 x^{8} + 120 x^{7} + 42 x^{6} + 27 x^{5} + 48 x^{4} + 12 x^{3} - 8 x^{2} + 3 x + 1$ |
$20$ |
[4,8] |
$2^{16}\cdot 3^{18}\cdot 5^{15}$ |
$3$ |
$15.6480645526$ |
$15.648064552551654$ |
|
|
? |
$C_2\times F_5$ (as 20T9) |
trivial |
$2$ |
$11$ |
$10430.7192804$ |
| 20.4.274...125.2 |
$x^{20} - 48 x^{15} + 449 x^{10} + 1548 x^{5} + 1$ |
$20$ |
[4,8] |
$3^{10}\cdot 5^{31}$ |
$2$ |
$20.9876655123$ |
$20.987665512343366$ |
|
|
|
$C_2\times F_5$ (as 20T9) |
trivial |
$2$ |
$11$ |
$254461.23805804938$ |
| 20.0.450...000.1 |
$x^{20} + 10 x^{18} - 5 x^{17} + 15 x^{16} - 46 x^{15} - 60 x^{14} - 100 x^{13} - 30 x^{12} + 290 x^{11} + 356 x^{10} + 470 x^{9} + 335 x^{8} - 2190 x^{7} + 490 x^{6} - 2261 x^{5} + 3950 x^{4} - 1800 x^{3} + 1630 x^{2} - 1305 x + 311$ |
$20$ |
[0,10] |
$2^{16}\cdot 5^{23}\cdot 7^{8}$ |
$3$ |
$24.1367458504$ |
$29.321657836504627$ |
✓ |
|
? |
$C_2\times F_5$ (as 20T9) |
trivial |
$10$ |
$9$ |
$1633832.53547$ |
| 20.4.488...000.1 |
$x^{20} - 5 x^{18} + 15 x^{16} - 30 x^{14} + 135 x^{12} - 270 x^{10} + 50 x^{8} + 300 x^{6} - 175 x^{4} - 100 x^{2} + 80$ |
$20$ |
[4,8] |
$2^{20}\cdot 5^{31}$ |
$2$ |
$24.2344686664$ |
$24.234468666426533$ |
|
|
? |
$C_2\times F_5$ (as 20T9) |
trivial |
$2$ |
$11$ |
$1219166.1361908035$ |
| 20.0.233...000.1 |
$x^{20} - 5 x^{19} + 18 x^{18} - 48 x^{17} + 134 x^{16} - 233 x^{15} + 416 x^{14} - 476 x^{13} + 897 x^{12} - 786 x^{11} + 2316 x^{10} - 854 x^{9} + 4296 x^{8} - 870 x^{7} + 3820 x^{6} + 110 x^{5} + 565 x^{4} - 125 x^{3} + 50 x^{2} + 50 x + 25$ |
$20$ |
[0,10] |
$2^{16}\cdot 5^{15}\cdot 43^{8}$ |
$3$ |
$26.2083018492$ |
$38.17558734657697$ |
✓ |
|
? |
$C_2\times F_5$ (as 20T9) |
trivial |
$10$ |
$9$ |
$3323311.71225$ |
| 20.4.169...125.1 |
$x^{20} - 8 x^{19} + 20 x^{18} + 5 x^{17} - 139 x^{16} + 320 x^{15} - 74 x^{14} - 1080 x^{13} + 2051 x^{12} - 150 x^{11} - 4520 x^{10} + 5643 x^{9} + 946 x^{8} - 9460 x^{7} + 7095 x^{6} + 4345 x^{5} - 8140 x^{4} + 1375 x^{3} + 3025 x^{2} + 275 x + 275$ |
$20$ |
[4,8] |
$5^{15}\cdot 11^{18}$ |
$2$ |
$28.9388267568$ |
$28.93882675684651$ |
|
|
|
$C_2\times F_5$ (as 20T9) |
$[5]$ |
$2$ |
$11$ |
$3624334.381450157$ |
| 20.4.131...125.1 |
$x^{20} - 144 x^{15} - 10889 x^{10} + 259506 x^{5} + 161051$ |
$20$ |
[4,8] |
$5^{31}\cdot 7^{10}$ |
$2$ |
$32.0591886236$ |
$32.05918862357587$ |
|
|
|
$C_2\times F_5$ (as 20T9) |
trivial |
$2$ |
$11$ |
$19025685.222571$ |
| 20.4.500...000.1 |
$x^{20} - 10 x^{18} + 60 x^{16} - 240 x^{14} + 2160 x^{12} - 8640 x^{10} + 3200 x^{8} + 38400 x^{6} - 44800 x^{4} - 51200 x^{2} + 81920$ |
$20$ |
[4,8] |
$2^{30}\cdot 5^{31}$ |
$2$ |
$34.272714265$ |
$34.27271426496622$ |
|
|
? |
$C_2\times F_5$ (as 20T9) |
trivial |
$2$ |
$11$ |
$36992598.74215467$ |
| 20.0.500...000.4 |
$x^{20} + 10 x^{18} + 60 x^{16} + 240 x^{14} + 2160 x^{12} + 8640 x^{10} + 3200 x^{8} - 38400 x^{6} - 44800 x^{4} + 51200 x^{2} + 81920$ |
$20$ |
[0,10] |
$2^{30}\cdot 5^{31}$ |
$2$ |
$34.272714265$ |
$34.27271426496622$ |
|
|
? |
$C_2\times F_5$ (as 20T9) |
$[2]$ |
$2$ |
$9$ |
$9073975.914877787$ |
| 20.20.100...353.1 |
$x^{20} - x^{19} - 33 x^{18} + 48 x^{17} + 398 x^{16} - 758 x^{15} - 2109 x^{14} + 5370 x^{13} + 4019 x^{12} - 18033 x^{11} + 3882 x^{10} + 25627 x^{9} - 20370 x^{8} - 8176 x^{7} + 14111 x^{6} - 2752 x^{5} - 1888 x^{4} + 657 x^{3} + 22 x^{2} - 17 x + 1$ |
$20$ |
[20,0] |
$17^{15}\cdot 37^{8}$ |
$2$ |
$35.4909300788$ |
$50.9257639953836$ |
|
|
? |
$C_2\times F_5$ (as 20T9) |
trivial |
$2$ |
$19$ |
$1110509306.59$ |
| 20.20.184...000.1 |
$x^{20} - 40 x^{18} + 660 x^{16} - 5800 x^{14} + 29320 x^{12} - 86420 x^{10} + 145120 x^{8} - 130160 x^{6} + 55120 x^{4} - 8800 x^{2} + 80$ |
$20$ |
[20,0] |
$2^{28}\cdot 5^{23}\cdot 7^{8}$ |
$3$ |
$36.5844655471$ |
$44.4433225403395$ |
|
|
? |
$C_2\times F_5$ (as 20T9) |
trivial |
$2$ |
$19$ |
$1931821970.59$ |
| 20.4.828...125.1 |
$x^{20} - 2 x^{19} - 6 x^{18} - 40 x^{17} + 42 x^{16} + 148 x^{15} + 358 x^{14} - 294 x^{13} + 2428 x^{12} + 12630 x^{11} + 20819 x^{10} - 35474 x^{9} - 210554 x^{8} - 467528 x^{7} - 574374 x^{6} - 350538 x^{5} - 101396 x^{4} + 9920 x^{3} + 46712 x^{2} + 22468 x + 991$ |
$20$ |
[4,8] |
$3^{10}\cdot 5^{15}\cdot 11^{16}$ |
$3$ |
$39.4368554623$ |
$39.436855462307015$ |
|
|
|
$C_2\times F_5$ (as 20T9) |
$[5]$ |
$2$ |
$11$ |
$32045543.871448386$ |
| 20.4.120...125.1 |
$x^{20} - 294 x^{15} - 64864 x^{10} + 5348406 x^{5} + 28629151$ |
$20$ |
[4,8] |
$5^{31}\cdot 11^{10}$ |
$2$ |
$40.1883197801$ |
$40.188319780080704$ |
|
|
|
$C_2\times F_5$ (as 20T9) |
trivial |
$2$ |
$11$ |
$184304774.0008127$ |
| 20.0.288...000.2 |
$x^{20} + 15 x^{18} + 135 x^{16} + 810 x^{14} + 10935 x^{12} + 65610 x^{10} + 36450 x^{8} - 656100 x^{6} - 1148175 x^{4} + 1968300 x^{2} + 4723920$ |
$20$ |
[0,10] |
$2^{20}\cdot 3^{10}\cdot 5^{31}$ |
$3$ |
$41.9753310247$ |
$41.97533102468673$ |
|
|
? |
$C_2\times F_5$ (as 20T9) |
$[2, 2]$ |
$2$ |
$9$ |
$33378319.401772223$ |
| 20.0.641...125.2 |
$x^{20} - 144 x^{15} + 9986 x^{10} - 6429744 x^{5} + 844596301$ |
$20$ |
[0,10] |
$5^{31}\cdot 13^{10}$ |
$2$ |
$43.6893097052$ |
$43.68930970521314$ |
|
|
|
$C_2\times F_5$ (as 20T9) |
$[2]$ |
$2$ |
$9$ |
$85038813.71090905$ |
| 20.4.147...000.2 |
$x^{20} - 5 x^{18} - 129 x^{16} - 620 x^{14} - 1509 x^{12} - 2355 x^{10} - 864 x^{8} - 410 x^{6} + 1401 x^{4} + 2290 x^{2} + 1805$ |
$20$ |
[4,8] |
$2^{20}\cdot 5^{15}\cdot 11^{16}$ |
$3$ |
$45.5377582343$ |
$45.53775823431064$ |
|
|
? |
$C_2\times F_5$ (as 20T9) |
$[5]$ |
$2$ |
$11$ |
$354914655.78466165$ |
| 20.4.317...125.1 |
$x^{20} - 2 x^{19} - 10 x^{18} - 20 x^{17} - 14 x^{16} + 380 x^{15} + 116 x^{14} + 2555 x^{13} - 5209 x^{12} + 7230 x^{11} - 29195 x^{10} + 50437 x^{9} - 54804 x^{8} + 151255 x^{7} - 200155 x^{6} + 184205 x^{5} - 249815 x^{4} + 320775 x^{3} + 21600 x^{2} - 35775 x - 119475$ |
$20$ |
[4,8] |
$5^{15}\cdot 19^{18}$ |
$2$ |
$47.3266478133$ |
$47.32664781325231$ |
|
|
|
$C_2\times F_5$ (as 20T9) |
trivial |
$2$ |
$11$ |
$2565467606.734227$ |
| 20.0.938...125.2 |
$x^{20} - 5 x^{19} + 25 x^{18} - 35 x^{17} + 270 x^{16} - 919 x^{15} + 4850 x^{14} + 24400 x^{13} + 158005 x^{12} + 323200 x^{11} + 240476 x^{10} - 2451535 x^{9} - 9806600 x^{8} - 22103305 x^{7} - 18499285 x^{6} + 36486691 x^{5} + 184536915 x^{4} + 378693200 x^{3} + 498508960 x^{2} + 402067640 x + 168988496$ |
$20$ |
[0,10] |
$5^{31}\cdot 17^{10}$ |
$2$ |
$49.9606370462$ |
$49.96063704619908$ |
|
|
|
$C_2\times F_5$ (as 20T9) |
$[2]$ |
$2$ |
$9$ |
$265705502.8157561$ |
| 20.0.100...125.2 |
$x^{20} - 8 x^{19} + 42 x^{18} - 204 x^{17} + 928 x^{16} - 3530 x^{15} + 12796 x^{14} - 40207 x^{13} + 115483 x^{12} - 299394 x^{11} + 694684 x^{10} - 1456697 x^{9} + 2707188 x^{8} - 4255273 x^{7} + 5598538 x^{6} - 6354447 x^{5} + 6400086 x^{4} - 5497910 x^{3} + 3643915 x^{2} - 1608255 x + 377245$ |
$20$ |
[0,10] |
$3^{10}\cdot 5^{15}\cdot 11^{18}$ |
$3$ |
$50.1235182543$ |
$50.12351825429183$ |
|
|
|
$C_2\times F_5$ (as 20T9) |
$[2, 2, 10]$ |
$2$ |
$9$ |
$26826674.447924238$ |
| 20.4.285...125.1 |
$x^{20} - 5 x^{19} - 10 x^{18} + 225 x^{17} - 835 x^{16} + 623 x^{15} + 9665 x^{14} - 65095 x^{13} + 212270 x^{12} - 167595 x^{11} - 1654471 x^{10} + 6783670 x^{9} - 12617985 x^{8} - 6471845 x^{7} + 95240190 x^{6} - 35696808 x^{5} - 334401910 x^{4} + 81011030 x^{3} + 520007480 x^{2} - 283432920 x + 293849141$ |
$20$ |
[4,8] |
$5^{31}\cdot 19^{10}$ |
$2$ |
$52.8177999337$ |
$52.81779993367809$ |
|
|
|
$C_2\times F_5$ (as 20T9) |
trivial |
$2$ |
$11$ |
$2616130963.265845$ |
| 20.0.776...125.2 |
$x^{20} - 5 x^{19} + 30 x^{18} - 50 x^{17} + 430 x^{16} - 1319 x^{15} + 7885 x^{14} + 40785 x^{13} + 317315 x^{12} + 799150 x^{11} + 1072566 x^{10} - 5300355 x^{9} - 28263385 x^{8} - 79891605 x^{7} - 100137290 x^{6} + 71914741 x^{5} + 734798300 x^{4} + 1874737995 x^{3} + 2942848715 x^{2} + 2827663210 x + 1410941641$ |
$20$ |
[0,10] |
$3^{10}\cdot 5^{31}\cdot 7^{10}$ |
$3$ |
$55.5281435455$ |
$55.52814354546755$ |
|
|
|
$C_2\times F_5$ (as 20T9) |
not computed |
$2$ |
$9$ |
|
| 20.0.177...000.2 |
$x^{20} + 66 x^{16} + 440 x^{14} - 1749 x^{12} + 10340 x^{10} - 11374 x^{8} - 21780 x^{6} + 246961 x^{4} - 350900 x^{2} + 242000$ |
$20$ |
[0,10] |
$2^{20}\cdot 5^{15}\cdot 11^{18}$ |
$3$ |
$57.8776535137$ |
$57.87765351369302$ |
|
|
? |
$C_2\times F_5$ (as 20T9) |
$[2, 2, 10]$ |
$2$ |
$9$ |
$196738506.401326$ |
| 20.4.192...125.1 |
$x^{20} - 5 x^{19} - 15 x^{18} + 280 x^{17} - 945 x^{16} + 198 x^{15} + 14180 x^{14} - 97645 x^{13} + 351970 x^{12} - 255555 x^{11} - 3611196 x^{10} + 14891330 x^{9} - 27752675 x^{8} - 29312330 x^{7} + 303998195 x^{6} - 85381863 x^{5} - 1286617875 x^{4} + 298330310 x^{3} + 2109281000 x^{2} - 1225863600 x + 2214298096$ |
$20$ |
[4,8] |
$5^{31}\cdot 23^{10}$ |
$2$ |
$58.1122143906$ |
$58.11221439059137$ |
|
|
|
$C_2\times F_5$ (as 20T9) |
not computed |
$2$ |
$11$ |
|
| 20.4.295...000.1 |
$x^{20} - 30 x^{18} + 540 x^{16} - 6480 x^{14} + 174960 x^{12} - 2099520 x^{10} + 2332800 x^{8} + 83980800 x^{6} - 293932800 x^{4} - 1007769600 x^{2} + 4837294080$ |
$20$ |
[4,8] |
$2^{30}\cdot 3^{10}\cdot 5^{31}$ |
$3$ |
$59.3620824202$ |
$59.36208242021212$ |
|
|
? |
$C_2\times F_5$ (as 20T9) |
not computed |
$2$ |
$11$ |
|
| 20.0.295...000.2 |
$x^{20} + 30 x^{18} + 540 x^{16} + 6480 x^{14} + 174960 x^{12} + 2099520 x^{10} + 2332800 x^{8} - 83980800 x^{6} - 293932800 x^{4} + 1007769600 x^{2} + 4837294080$ |
$20$ |
[0,10] |
$2^{30}\cdot 3^{10}\cdot 5^{31}$ |
$3$ |
$59.3620824202$ |
$59.36208242021212$ |
|
|
? |
$C_2\times F_5$ (as 20T9) |
not computed |
$2$ |
$9$ |
|
| 20.4.396...125.1 |
$x^{20} - 3 x^{19} - 25 x^{18} + 85 x^{17} + 390 x^{16} - 619 x^{15} - 3918 x^{14} + 385 x^{13} + 34925 x^{12} + 29720 x^{11} - 270083 x^{10} - 443136 x^{9} + 1143615 x^{8} + 3870405 x^{7} + 873000 x^{6} - 14910222 x^{5} - 18671249 x^{4} + 17902740 x^{3} + 5924040 x^{2} - 41740760 x + 18411920$ |
$20$ |
[4,8] |
$5^{15}\cdot 7^{10}\cdot 11^{16}$ |
$3$ |
$60.2407917757$ |
$60.24079177568486$ |
|
|
|
$C_2\times F_5$ (as 20T9) |
$[5]$ |
$2$ |
$11$ |
$3188661065.882411$ |
| 20.4.519...125.1 |
$x^{20} - x^{19} + 9 x^{18} - 41 x^{17} + 154 x^{16} - 773 x^{15} + 2026 x^{14} - 4929 x^{13} + 12491 x^{12} - 11134 x^{11} - 15441 x^{10} + 91658 x^{9} - 228717 x^{8} - 233197 x^{7} + 1624938 x^{6} - 1158742 x^{5} - 2192037 x^{4} + 3529578 x^{3} - 2820992 x^{2} + 2354928 x - 261584$ |
$20$ |
[4,8] |
$3^{10}\cdot 5^{15}\cdot 19^{16}$ |
$3$ |
$61.0648101718$ |
$61.064810171787656$ |
|
|
|
$C_2\times F_5$ (as 20T9) |
$[4, 4]$ |
$2$ |
$11$ |
$689582360.0767176$ |
| 20.0.137...000.2 |
$x^{20} + 35 x^{18} + 735 x^{16} + 10290 x^{14} + 324135 x^{12} + 4537890 x^{10} + 5882450 x^{8} - 247062900 x^{6} - 1008840175 x^{4} + 4035360700 x^{2} + 22598019920$ |
$20$ |
[0,10] |
$2^{20}\cdot 5^{31}\cdot 7^{10}$ |
$3$ |
$64.1183772472$ |
$64.11837724715174$ |
|
|
? |
$C_2\times F_5$ (as 20T9) |
not computed |
$2$ |
$9$ |
|
| 20.4.150...000.1 |
$x^{20} - 10 x^{18} - 516 x^{16} - 4960 x^{14} - 24144 x^{12} - 75360 x^{10} - 55296 x^{8} - 52480 x^{6} + 358656 x^{4} + 1172480 x^{2} + 1848320$ |
$20$ |
[4,8] |
$2^{30}\cdot 5^{15}\cdot 11^{16}$ |
$3$ |
$64.400115295$ |
$64.4001152950292$ |
|
|
? |
$C_2\times F_5$ (as 20T9) |
$[5, 5]$ |
$2$ |
$11$ |
$1045681850.2312742$ |
| 20.0.150...000.2 |
$x^{20} + 10 x^{18} - 516 x^{16} + 4960 x^{14} - 24144 x^{12} + 75360 x^{10} - 55296 x^{8} + 52480 x^{6} + 358656 x^{4} - 1172480 x^{2} + 1848320$ |
$20$ |
[0,10] |
$2^{30}\cdot 5^{15}\cdot 11^{16}$ |
$3$ |
$64.400115295$ |
$64.4001152950292$ |
|
|
? |
$C_2\times F_5$ (as 20T9) |
$[10]$ |
$2$ |
$9$ |
$1102575145.3799999$ |
| 20.0.195...125.2 |
$x^{20} - 5 x^{19} + 40 x^{18} - 80 x^{17} + 840 x^{16} - 2329 x^{15} + 17495 x^{14} + 92155 x^{13} + 934495 x^{12} + 3023350 x^{11} + 6716306 x^{10} - 16162825 x^{9} - 138381605 x^{8} - 538651975 x^{7} - 1008503770 x^{6} - 270425399 x^{5} + 5808953160 x^{4} + 21092371985 x^{3} + 43037450335 x^{2} + 53878854080 x + 35445196901$ |
$20$ |
[0,10] |
$5^{31}\cdot 29^{10}$ |
$2$ |
$65.253303891$ |
$65.25330389102201$ |
|
|
|
$C_2\times F_5$ (as 20T9) |
not computed |
$2$ |
$9$ |
|
| 20.4.381...125.1 |
$x^{20} - 5 x^{19} - 25 x^{18} + 390 x^{17} - 1075 x^{16} - 1282 x^{15} + 24500 x^{14} - 185365 x^{13} + 839990 x^{12} - 575235 x^{11} - 12799606 x^{10} + 53786260 x^{9} - 99979485 x^{8} - 217085270 x^{7} + 1894042635 x^{6} - 255897903 x^{5} - 10721050195 x^{4} + 2198708690 x^{3} + 18277709420 x^{2} - 12345750840 x + 49350856976$ |
$20$ |
[4,8] |
$5^{31}\cdot 31^{10}$ |
$2$ |
$67.4659054965$ |
$67.46590549652524$ |
|
|
|
$C_2\times F_5$ (as 20T9) |
not computed |
$2$ |
$11$ |
|
| 20.0.642...125.1 |
$x^{20} - 9 x^{19} + 34 x^{18} - 44 x^{17} - 265 x^{16} + 1286 x^{15} - 773 x^{14} - 3682 x^{13} + 13368 x^{12} + 20263 x^{11} - 34508 x^{10} - 44433 x^{9} + 246404 x^{8} + 66122 x^{7} - 138042 x^{6} - 33663 x^{5} + 299206 x^{4} + 241895 x^{3} + 108785 x^{2} + 43805 x + 8705$ |
$20$ |
[0,10] |
$5^{15}\cdot 29^{18}$ |
$2$ |
$69.2445665982$ |
$69.24456659819765$ |
|
|
|
$C_2\times F_5$ (as 20T9) |
$[2, 2]$ |
$2$ |
$9$ |
$10016717916.562931$ |
| 20.0.713...125.2 |
$x^{20} - 5 x^{19} + 45 x^{18} - 95 x^{17} + 1090 x^{16} - 2939 x^{15} + 24430 x^{14} + 128940 x^{13} + 1449605 x^{12} + 5100880 x^{11} + 13220076 x^{10} - 24508695 x^{9} - 259823140 x^{8} - 1145438325 x^{7} - 2438250905 x^{6} - 1385834729 x^{5} + 13088961695 x^{4} + 55400347980 x^{3} + 125265538040 x^{2} + 174097207960 x + 128412299536$ |
$20$ |
[0,10] |
$3^{10}\cdot 5^{31}\cdot 11^{10}$ |
$3$ |
$69.6082117299$ |
$69.60821172992507$ |
|
|
|
$C_2\times F_5$ (as 20T9) |
not computed |
$2$ |
$9$ |
|
| 20.4.923...000.1 |
$x^{20} - x^{18} - 109 x^{16} + 149 x^{14} - 2014 x^{12} - 36365 x^{10} + 127585 x^{8} - 1005950 x^{6} + 733025 x^{4} + 67500 x^{2} + 50000$ |
$20$ |
[4,8] |
$2^{20}\cdot 5^{15}\cdot 19^{16}$ |
$3$ |
$70.5115691814$ |
$70.51156918139$ |
|
|
? |
$C_2\times F_5$ (as 20T9) |
trivial |
$2$ |
$11$ |
$218846902353.9545$ |
| 20.4.213...125.1 |
$x^{20} - 7 x^{19} + 2 x^{18} + 85 x^{17} - 89 x^{16} - 485 x^{15} - 502 x^{14} + 7124 x^{13} - 3389 x^{12} - 37645 x^{11} + 1825 x^{10} + 232525 x^{9} + 94360 x^{8} - 986175 x^{7} - 1307700 x^{6} + 1275150 x^{5} + 3604650 x^{4} + 1354000 x^{3} - 3259625 x^{2} - 3537500 x - 968125$ |
$20$ |
[4,8] |
$5^{15}\cdot 31^{18}$ |
$2$ |
$73.5280464922$ |
$73.52804649223957$ |
|
|
|
$C_2\times F_5$ (as 20T9) |
$[5]$ |
$2$ |
$11$ |
$46639726240.276184$ |
| 20.0.223...125.1 |
$x^{20} - 5 x^{19} + 50 x^{18} - 110 x^{17} + 1370 x^{16} - 3619 x^{15} + 33025 x^{14} + 174325 x^{13} + 2145955 x^{12} + 8083750 x^{11} + 23745326 x^{10} - 34682135 x^{9} - 452982025 x^{8} - 2228991105 x^{7} - 5269012810 x^{6} - 4302198659 x^{5} + 26632021340 x^{4} + 130244452175 x^{3} + 322173998635 x^{2} + 490733138390 x + 401120497321$ |
$20$ |
[0,10] |
$5^{31}\cdot 37^{10}$ |
$2$ |
$73.7062589729$ |
$73.70625897291279$ |
|
|
|
$C_2\times F_5$ (as 20T9) |
not computed |
$2$ |
$9$ |
|
| 20.4.379...125.1 |
$x^{20} - 5 x^{19} - 35 x^{18} + 500 x^{17} - 1085 x^{16} - 3602 x^{15} + 35340 x^{14} - 305645 x^{13} + 1752770 x^{12} - 1234795 x^{11} - 35238496 x^{10} + 150274870 x^{9} - 275565135 x^{8} - 919172770 x^{7} + 7876207515 x^{6} - 176450583 x^{5} - 55565363835 x^{4} + 9898849230 x^{3} + 91075080080 x^{2} - 73949086720 x + 521177724016$ |
$20$ |
[4,8] |
$3^{10}\cdot 5^{31}\cdot 13^{10}$ |
$3$ |
$75.672104157$ |
$75.6721041570412$ |
|
|
|
$C_2\times F_5$ (as 20T9) |
not computed |
$2$ |
$11$ |
|
| 20.0.479...125.2 |
$x^{20} - 6 x^{19} + 10 x^{18} + 30 x^{17} - 231 x^{16} - 846 x^{15} + 14657 x^{14} - 96020 x^{13} + 424696 x^{12} - 1471866 x^{11} + 4600432 x^{10} - 13640902 x^{9} + 41055054 x^{8} - 108630102 x^{7} + 263443921 x^{6} - 515816388 x^{5} + 871193851 x^{4} - 1118784220 x^{3} + 1251134700 x^{2} - 767760000 x + 778286125$ |
$20$ |
[0,10] |
$5^{15}\cdot 7^{10}\cdot 11^{18}$ |
$3$ |
$76.5649388326$ |
$76.5649388325977$ |
|
|
|
$C_2\times F_5$ (as 20T9) |
$[2, 2, 20]$ |
$2$ |
$9$ |
$818536127.5632833$ |
| 20.0.625...125.2 |
$x^{20} - 5 x^{19} + 55 x^{18} - 125 x^{17} + 1680 x^{16} - 4369 x^{15} + 43460 x^{14} + 229210 x^{13} + 3060265 x^{12} + 12199900 x^{11} + 39844916 x^{10} - 46253755 x^{9} - 744886310 x^{8} - 4046349655 x^{7} - 10452282415 x^{6} - 10776463559 x^{5} + 49933574625 x^{4} + 280542235970 x^{3} + 751545978640 x^{2} + 1241779064960 x + 1114173964016$ |
$20$ |
[0,10] |
$5^{31}\cdot 41^{10}$ |
$2$ |
$77.5881568497$ |
$77.58815684965134$ |
|
|
|
$C_2\times F_5$ (as 20T9) |
not computed |
$2$ |
$9$ |
|
| 20.0.868...000.4 |
$x^{20} + 15 x^{18} - 1161 x^{16} + 16740 x^{14} - 122229 x^{12} + 572265 x^{10} - 629856 x^{8} + 896670 x^{6} + 9191961 x^{4} - 45074070 x^{2} + 106583445$ |
$20$ |
[0,10] |
$2^{20}\cdot 3^{10}\cdot 5^{15}\cdot 11^{16}$ |
$4$ |
$78.8737109246$ |
$78.87371092461403$ |
|
|
? |
$C_2\times F_5$ (as 20T9) |
$[5, 10, 10]$ |
$2$ |
$9$ |
$212425982.34586897$ |
| 20.4.100...125.1 |
$x^{20} - 5 x^{19} - 40 x^{18} + 555 x^{17} - 1045 x^{16} - 5077 x^{15} + 40505 x^{14} - 378895 x^{13} + 2435570 x^{12} - 1764255 x^{11} - 54740221 x^{10} + 234681130 x^{9} - 425930625 x^{8} - 1679254355 x^{7} + 14514361470 x^{6} + 372998712 x^{5} - 112341446200 x^{4} + 18580850960 x^{3} + 175486910000 x^{2} - 158789506050 x + 1412257296521$ |
$20$ |
[4,8] |
$5^{31}\cdot 43^{10}$ |
$2$ |
$79.4580192246$ |
$79.45801922460754$ |
|
|
|
$C_2\times F_5$ (as 20T9) |
not computed |
$2$ |
$11$ |
|
| 20.0.126...000.2 |
$x^{20} + 55 x^{18} + 1815 x^{16} + 39930 x^{14} + 1976535 x^{12} + 43483770 x^{10} + 88578050 x^{8} - 5846151300 x^{6} - 37512804175 x^{4} + 235794769100 x^{2} + 2074993968080$ |
$20$ |
[0,10] |
$2^{20}\cdot 5^{31}\cdot 11^{10}$ |
$3$ |
$80.3766395602$ |
$80.37663956016141$ |
|
|
? |
$C_2\times F_5$ (as 20T9) |
not computed |
$2$ |
$9$ |
|
| 20.4.182...000.1 |
$x^{20} + 264 x^{16} - 3520 x^{14} - 27984 x^{12} - 330880 x^{10} - 727936 x^{8} + 2787840 x^{6} + 63222016 x^{4} + 179660800 x^{2} + 247808000$ |
$20$ |
[4,8] |
$2^{30}\cdot 5^{15}\cdot 11^{18}$ |
$3$ |
$81.8513625574$ |
$81.85136255739549$ |
|
|
? |
$C_2\times F_5$ (as 20T9) |
$[10]$ |
$2$ |
$11$ |
$26924583700.72881$ |
| 20.0.182...000.2 |
$x^{20} + 264 x^{16} + 3520 x^{14} - 27984 x^{12} + 330880 x^{10} - 727936 x^{8} - 2787840 x^{6} + 63222016 x^{4} - 179660800 x^{2} + 247808000$ |
$20$ |
[0,10] |
$2^{30}\cdot 5^{15}\cdot 11^{18}$ |
$3$ |
$81.8513625574$ |
$81.85136255739549$ |
|
|
? |
$C_2\times F_5$ (as 20T9) |
$[2, 2, 20]$ |
$2$ |
$9$ |
$1640482329.2124414$ |
| 20.0.187...125.1 |
$x^{20} - 3 x^{19} + 26 x^{18} + 97 x^{17} - 294 x^{16} - 440 x^{15} + 1705 x^{14} - 8469 x^{13} - 25967 x^{12} - 57053 x^{11} - 45091 x^{10} + 433083 x^{9} + 1796869 x^{8} + 4440981 x^{7} + 17183403 x^{6} + 35686946 x^{5} + 51034338 x^{4} + 54483025 x^{3} + 40765960 x^{2} + 24180423 x + 8509591$ |
$20$ |
[0,10] |
$3^{10}\cdot 5^{15}\cdot 19^{18}$ |
$3$ |
$81.9721585645$ |
$81.9721585644715$ |
|
|
|
$C_2\times F_5$ (as 20T9) |
$[2, 2, 2, 2, 2]$ |
$2$ |
$9$ |
$3932635547.52714$ |
| 20.0.193...125.2 |
$x^{20} - 3 x^{19} + 100 x^{18} - 190 x^{17} + 3990 x^{16} - 5019 x^{15} + 84557 x^{14} - 80690 x^{13} + 1053075 x^{12} - 972755 x^{11} + 8039592 x^{10} - 8576736 x^{9} + 39544565 x^{8} - 45897320 x^{7} + 141614400 x^{6} - 123999347 x^{5} + 380740776 x^{4} - 184199435 x^{3} + 502243165 x^{2} - 464217385 x + 121715395$ |
$20$ |
[0,10] |
$5^{15}\cdot 11^{16}\cdot 13^{10}$ |
$3$ |
$82.0943611417$ |
$82.09436114174476$ |
|
|
|
$C_2\times F_5$ (as 20T9) |
$[10]$ |
$2$ |
$9$ |
$11176801552.71916$ |
