| 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 |
| 20.2.274...000.1 |
$x^{20} - 2 x^{19} + 11 x^{18} - 24 x^{17} + 65 x^{16} - 152 x^{15} + 296 x^{14} - 552 x^{13} + 819 x^{12} - 1038 x^{11} + 1045 x^{10} - 784 x^{9} + 371 x^{8} + 32 x^{7} - 244 x^{6} + 272 x^{5} - 185 x^{4} + 90 x^{3} - 39 x^{2} + 8 x - 1$ |
$20$ |
[2,9] |
$-\,2^{52}\cdot 5^{14}$ |
$2$ |
$18.7049689565$ |
$29.170658948868436$ |
|
|
|
$D_4\times F_5$ (as 20T42) |
trivial |
$2$ |
$10$ |
$67620.9124596$ |
| 20.0.761...000.1 |
$x^{20} - 12 x^{18} + 39 x^{16} - 12 x^{14} - 30 x^{12} - 12 x^{10} + 6 x^{8} + 12 x^{6} + 45 x^{4} - 24 x^{2} + 3$ |
$20$ |
[0,10] |
$2^{28}\cdot 3^{19}\cdot 5^{12}$ |
$3$ |
$19.6829046449$ |
$30.849184495989267$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
trivial |
$6$ |
$9$ |
$251749.70025$ |
| 20.0.879...000.1 |
$x^{20} - 2 x^{19} + 4 x^{18} - 8 x^{17} + 12 x^{16} + 4 x^{15} - 4 x^{14} + 16 x^{13} - 16 x^{12} + 8 x^{11} - 20 x^{10} + 16 x^{9} + 116 x^{8} + 96 x^{7} - 80 x^{6} - 256 x^{5} - 110 x^{4} + 92 x^{3} + 96 x^{2} + 32 x + 4$ |
$20$ |
[0,10] |
$2^{56}\cdot 5^{13}$ |
$2$ |
$19.825059101$ |
$29.170658948868436$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
trivial |
$4$ |
$9$ |
$547846.080547$ |
| 20.2.109...000.1 |
$x^{20} - 6 x^{19} + 15 x^{18} - 22 x^{17} + 25 x^{16} - 32 x^{15} + 56 x^{14} - 80 x^{13} + 88 x^{12} - 104 x^{11} + 72 x^{10} - 80 x^{9} + 124 x^{8} - 64 x^{7} + 136 x^{6} - 32 x^{5} - 37 x^{4} - 90 x^{3} - 51 x^{2} - 18 x - 1$ |
$20$ |
[2,9] |
$-\,2^{54}\cdot 5^{14}$ |
$2$ |
$20.0474893451$ |
$29.170658948868436$ |
|
|
|
$D_4\times F_5$ (as 20T42) |
trivial |
$2$ |
$10$ |
$187244.399204$ |
| 20.0.158...000.1 |
$x^{20} - 4 x^{19} + 22 x^{18} - 60 x^{17} + 171 x^{16} - 330 x^{15} + 594 x^{14} - 786 x^{13} + 870 x^{12} - 634 x^{11} + 196 x^{10} + 266 x^{9} - 420 x^{8} + 270 x^{7} + 138 x^{6} - 198 x^{5} + 249 x^{4} + 42 x^{3} - 14 x^{2} + 2 x + 1$ |
$20$ |
[0,10] |
$2^{27}\cdot 3^{18}\cdot 5^{15}$ |
$3$ |
$22.91010748062466$ |
$33.54236065495944$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
$[4]$ |
$2$ |
$9$ |
$290906.5724675383$ |
| 20.0.284...000.1 |
$x^{20} + 7$ |
$20$ |
[0,10] |
$2^{10}\cdot 5^{12}\cdot 7^{19}$ |
$3$ |
$23.5906625562$ |
$42.47179703557583$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
trivial |
$2$ |
$9$ |
$866342.344588$ |
| 20.0.660...000.1 |
$x^{20} + 14 x^{10} + 32$ |
$20$ |
[0,10] |
$2^{27}\cdot 5^{12}\cdot 17^{10}$ |
$3$ |
$27.6055851634$ |
$51.452793149040794$ |
|
|
|
$D_4\times F_5$ (as 20T42) |
trivial |
$2$ |
$9$ |
$9169008.40398$ |
| 20.0.101...000.1 |
$x^{20} - x^{18} + 24 x^{16} - 42 x^{14} + 189 x^{12} - 159 x^{10} + 96 x^{8} - 108 x^{6} + 36 x^{4} - 10 x^{2} + 10$ |
$20$ |
[0,10] |
$2^{33}\cdot 3^{18}\cdot 5^{15}$ |
$3$ |
$28.2056508339$ |
$41.29548993075364$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
$[4]$ |
$2$ |
$9$ |
$3425525.895280538$ |
| 20.0.116...000.1 |
$x^{20} - 3 x^{10} + 3$ |
$20$ |
[0,10] |
$2^{20}\cdot 3^{19}\cdot 5^{20}$ |
$3$ |
$28.3965246792$ |
$51.124101742197034$ |
|
|
✓ |
$D_4\times F_5$ (as 20T42) |
trivial |
$6$ |
$9$ |
$11115433.2713$ |
| 20.0.883...832.1 |
$x^{20} + x^{18} + x^{16} - 33 x^{14} + 55 x^{12} + 59 x^{10} + 440 x^{8} - 2112 x^{6} + 512 x^{4} + 4096 x^{2} + 32768$ |
$20$ |
[0,10] |
$2^{27}\cdot 7^{10}\cdot 13^{12}$ |
$3$ |
$31.427188145$ |
$51.23320533148189$ |
|
|
|
$D_4\times F_5$ (as 20T42) |
$[3]$ |
$2$ |
$9$ |
$7649961.18437$ |
| 20.10.100...808.1 |
$x^{20} - 4 x^{19} - 4 x^{18} + 44 x^{17} - 68 x^{16} - 42 x^{15} + 270 x^{14} - 376 x^{13} + 74 x^{12} + 776 x^{11} - 1639 x^{10} + 908 x^{9} + 1790 x^{8} - 3164 x^{7} + 1110 x^{6} + 890 x^{5} - 508 x^{4} - 104 x^{3} + 44 x^{2} + 4 x - 1$ |
$20$ |
[10,5] |
$-\,2^{30}\cdot 7^{9}\cdot 13^{12}$ |
$3$ |
$31.6377159748$ |
$51.23320533148189$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
trivial |
$2$ |
$14$ |
$65056134.1888$ |
| 20.2.108...000.1 |
$x^{20} + 10 x^{18} - 20 x^{17} + 32 x^{16} - 100 x^{15} + 110 x^{14} + 80 x^{13} - 156 x^{12} + 400 x^{11} - 1430 x^{10} + 3000 x^{9} - 3992 x^{8} + 5360 x^{7} - 7360 x^{6} + 10400 x^{5} - 11104 x^{4} + 9600 x^{3} - 5760 x^{2} + 2560 x - 640$ |
$20$ |
[2,9] |
$-\,2^{38}\cdot 3^{17}\cdot 5^{15}$ |
$3$ |
$31.7495490712$ |
$33.54236065495944$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
$[2]$ |
$2$ |
$10$ |
$25639309.554053202$ |
| 20.0.165...000.1 |
$x^{20} - 5 x^{19} + 9 x^{18} + 10 x^{17} - 49 x^{16} - 25 x^{15} + 401 x^{14} - 646 x^{13} - 203 x^{12} + 2129 x^{11} - 2237 x^{10} - 1404 x^{9} + 7072 x^{8} - 6760 x^{7} + 1808 x^{6} + 5360 x^{5} - 1860 x^{4} - 560 x^{3} + 3946 x^{2} - 274 x + 1226$ |
$20$ |
[0,10] |
$2^{27}\cdot 5^{14}\cdot 17^{10}$ |
$3$ |
$32.426043268$ |
$51.452793149040794$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
$[2]$ |
$2$ |
$9$ |
$9169008.40398$ |
| 20.0.361...000.1 |
$x^{20} - 10 x^{10} + 32$ |
$20$ |
[0,10] |
$2^{27}\cdot 5^{20}\cdot 7^{10}$ |
$3$ |
$33.7217045076$ |
$62.85234949347$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
trivial |
$2$ |
$9$ |
$21875168.2325$ |
| 20.4.422...000.1 |
$x^{20} - 14 x^{10} + 32$ |
$20$ |
[4,8] |
$2^{33}\cdot 5^{12}\cdot 17^{10}$ |
$3$ |
$33.9864619511$ |
$63.34581883643315$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
trivial |
$2$ |
$11$ |
$88361003.7586$ |
| 20.4.118...000.1 |
$x^{20} - 14 x^{15} - 435 x^{10} + 958 x^{5} + 1$ |
$20$ |
[4,8] |
$2^{30}\cdot 5^{20}\cdot 41^{5}$ |
$3$ |
$35.7858190836$ |
$115.27959096423206$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
trivial |
$2$ |
$11$ |
$66761437.6852$ |
| 20.2.549...000.1 |
$x^{20} - 2$ |
$20$ |
[2,9] |
$-\,2^{59}\cdot 5^{20}$ |
$2$ |
$38.637453157$ |
$54.57685321285674$ |
|
|
✓ |
$D_4\times F_5$ (as 20T42) |
trivial |
$2$ |
$10$ |
$140727999.65$ |
| 20.0.549...000.2 |
$x^{20} + 2$ |
$20$ |
[0,10] |
$2^{59}\cdot 5^{20}$ |
$2$ |
$38.637453157$ |
$54.57685321285674$ |
|
|
✓ |
$D_4\times F_5$ (as 20T42) |
trivial |
$2$ |
$9$ |
$142005933.58$ |
| 20.10.734...875.1 |
$x^{20} - 2 x^{19} - 14 x^{18} + 25 x^{17} + 113 x^{16} - 268 x^{15} - 556 x^{14} + 1786 x^{13} + 1627 x^{12} - 5838 x^{11} - 3758 x^{10} + 8861 x^{9} + 7388 x^{8} - 5488 x^{7} - 6997 x^{6} + 31 x^{5} + 1642 x^{4} + 269 x^{3} - 7 x^{2} - 9 x - 1$ |
$20$ |
[10,5] |
$-\,5^{10}\cdot 13^{12}\cdot 19^{9}$ |
$3$ |
$39.200367091$ |
$66.72972220231422$ |
|
|
|
$D_4\times F_5$ (as 20T42) |
trivial |
$2$ |
$14$ |
$670449501.541$ |
| 20.0.119...000.1 |
$x^{20} - 96 x^{10} + 3072$ |
$20$ |
[0,10] |
$2^{30}\cdot 3^{19}\cdot 5^{20}$ |
$3$ |
$40.1587503255937$ |
$72.30039804795702$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
trivial |
$6$ |
$9$ |
$418747824.9653931$ |
| 20.0.298...000.1 |
$x^{20} + 7168$ |
$20$ |
[0,10] |
$2^{30}\cdot 5^{12}\cdot 7^{19}$ |
$3$ |
$47.18132511247428$ |
$84.94359407115167$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
$[2]$ |
$2$ |
$9$ |
$738827162.6953382$ |
| 20.2.121...000.1 |
$x^{20} - 3$ |
$20$ |
[2,9] |
$-\,2^{40}\cdot 3^{19}\cdot 5^{20}$ |
$3$ |
$56.7930493584$ |
$72.30039804795702$ |
|
|
✓ |
$D_4\times F_5$ (as 20T42) |
$[2]$ |
$2$ |
$10$ |
$3729139104.85$ |
| 20.20.105...408.1 |
$x^{20} - 34 x^{18} + 491 x^{16} - 3920 x^{14} + 18850 x^{12} - 55698 x^{10} + 98720 x^{8} - 97708 x^{6} + 47009 x^{4} - 8664 x^{2} + 112$ |
$20$ |
[20,0] |
$2^{50}\cdot 7^{9}\cdot 13^{12}$ |
$3$ |
$63.2754319496$ |
$121.85378460918722$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
trivial |
$2$ |
$19$ |
$757195156993$ |
| 20.0.105...408.1 |
$x^{20} + 34 x^{18} + 491 x^{16} + 3920 x^{14} + 18850 x^{12} + 55698 x^{10} + 98720 x^{8} + 97708 x^{6} + 47009 x^{4} + 8664 x^{2} + 112$ |
$20$ |
[0,10] |
$2^{50}\cdot 7^{9}\cdot 13^{12}$ |
$3$ |
$63.2754319496$ |
$121.85378460918722$ |
✓ |
|
? |
$D_4\times F_5$ (as 20T42) |
$[2, 670]$ |
$2$ |
$9$ |
$9631410.14359$ |
| 20.2.305...000.1 |
$x^{20} - 7$ |
$20$ |
[2,9] |
$-\,2^{40}\cdot 5^{12}\cdot 7^{19}$ |
$3$ |
$66.7244698648$ |
$84.94359407115167$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
$[2]$ |
$2$ |
$10$ |
$37273956638.4$ |
| 20.20.151...000.1 |
$x^{20} - 40 x^{18} + 680 x^{16} - 6400 x^{14} + 36400 x^{12} - 128048 x^{10} + 272960 x^{8} - 326720 x^{6} + 179200 x^{4} - 19200 x^{2} + 128$ |
$20$ |
[20,0] |
$2^{49}\cdot 5^{20}\cdot 7^{10}$ |
$3$ |
$72.2840560055$ |
$121.42273546804758$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
trivial |
$2$ |
$19$ |
$5867613660310$ |
| 20.0.151...000.1 |
$x^{20} + 40 x^{18} + 680 x^{16} + 6400 x^{14} + 36400 x^{12} + 128048 x^{10} + 272960 x^{8} + 326720 x^{6} + 179200 x^{4} + 19200 x^{2} + 128$ |
$20$ |
[0,10] |
$2^{49}\cdot 5^{20}\cdot 7^{10}$ |
$3$ |
$72.2840560055$ |
$121.42273546804758$ |
✓ |
|
? |
$D_4\times F_5$ (as 20T42) |
$[2170]$ |
$2$ |
$9$ |
$45772805.4982$ |
| 20.0.545...000.1 |
$x^{20} - 10 x^{19} + 45 x^{18} - 120 x^{17} + 220 x^{16} - 284 x^{15} + 130 x^{14} + 640 x^{13} - 2335 x^{12} - 1890 x^{11} + 29993 x^{10} - 83440 x^{9} + 127410 x^{8} - 98360 x^{7} + 89320 x^{6} - 200888 x^{5} + 312880 x^{4} - 267040 x^{3} + 191840 x^{2} - 162240 x + 71696$ |
$20$ |
[0,10] |
$2^{38}\cdot 3^{17}\cdot 5^{20}\cdot 11^{5}$ |
$4$ |
$86.4625886361$ |
$211.77659853582566$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
$[2]$ |
$2$ |
$9$ |
$455641598745.8738$ |
| 20.0.348...000.1 |
$x^{20} - 156 x^{15} + 200772 x^{10} + 22464 x^{5} + 648$ |
$20$ |
[0,10] |
$2^{44}\cdot 3^{17}\cdot 5^{20}\cdot 11^{5}$ |
$4$ |
$106.44793296268294$ |
$260.72757616457096$ |
|
|
|
$D_4\times F_5$ (as 20T42) |
$[2, 2]$ |
$2$ |
$9$ |
$4373003225221.053$ |
| 20.2.638...000.1 |
$x^{20} - 6$ |
$20$ |
[2,9] |
$-\,2^{59}\cdot 3^{19}\cdot 5^{20}$ |
$3$ |
$109.716939211$ |
$154.9792959172223$ |
|
|
✓ |
$D_4\times F_5$ (as 20T42) |
trivial |
$2$ |
$10$ |
$10716506705700$ |
| 20.2.638...000.2 |
$x^{20} - 6144$ |
$20$ |
[2,9] |
$-\,2^{59}\cdot 3^{19}\cdot 5^{20}$ |
$3$ |
$109.71693921141936$ |
$154.9792959172223$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
trivial |
$2$ |
$10$ |
$7204063400163.169$ |
| 20.0.638...000.1 |
$x^{20} + 6$ |
$20$ |
[0,10] |
$2^{59}\cdot 3^{19}\cdot 5^{20}$ |
$3$ |
$109.716939211$ |
$154.9792959172223$ |
|
|
✓ |
$D_4\times F_5$ (as 20T42) |
$[2]$ |
$2$ |
$9$ |
$3249681118900$ |
| 20.2.823...000.1 |
$x^{20} + 53700 x^{10} - 4608$ |
$20$ |
[2,9] |
$-\,2^{33}\cdot 3^{18}\cdot 5^{20}\cdot 11^{10}$ |
$4$ |
$139.886231004$ |
$260.72757616457096$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
$[2, 2]$ |
$2$ |
$10$ |
$78705759249858.3$ |
| 20.0.118...000.1 |
$x^{20} - 10 x^{19} + 75 x^{18} - 264 x^{17} - 312 x^{16} + 10716 x^{15} - 19644 x^{14} + 118446 x^{13} + 1040871 x^{12} - 2263018 x^{11} + 2579485 x^{10} + 65471640 x^{9} + 46232796 x^{8} - 146915028 x^{7} - 380644878 x^{6} + 280326630 x^{5} + 1833189930 x^{4} - 4763924676 x^{3} + 6350854338 x^{2} - 5069452068 x + 1918665666$ |
$20$ |
[0,10] |
$2^{28}\cdot 3^{18}\cdot 5^{15}\cdot 7^{17}\cdot 11^{5}$ |
$5$ |
$225.818818977$ |
$453.27650131632214$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
$[2, 20]$ |
$2$ |
$9$ |
$742303713446840.1$ |
| 20.4.118...000.1 |
$x^{20} - 10 x^{19} - 31 x^{18} + 516 x^{17} + 930 x^{16} - 11166 x^{15} - 118038 x^{14} + 737754 x^{13} + 2716053 x^{12} - 26686966 x^{11} + 20210059 x^{10} + 241180492 x^{9} - 305684694 x^{8} - 685583514 x^{7} - 8401869924 x^{6} + 45243207786 x^{5} - 12557012244 x^{4} - 286707112440 x^{3} + 464496861710 x^{2} + 275058903196 x - 821370177614$ |
$20$ |
[4,8] |
$2^{28}\cdot 3^{18}\cdot 5^{15}\cdot 7^{17}\cdot 11^{5}$ |
$5$ |
$225.81881897691528$ |
$453.27650131632214$ |
|
|
|
$D_4\times F_5$ (as 20T42) |
$[20]$ |
$2$ |
$11$ |
$4948878552907683.0$ |
| 20.0.118...000.2 |
$x^{20} - 6 x^{18} - 336 x^{17} - 555 x^{16} + 2940 x^{15} + 40032 x^{14} + 128268 x^{13} - 203910 x^{12} - 1893780 x^{11} - 7281204 x^{10} - 24592932 x^{9} + 2658978 x^{8} + 393644916 x^{7} + 1863648288 x^{6} + 4838649732 x^{5} + 7200970677 x^{4} + 5189980068 x^{3} + 2184248826 x^{2} + 1356866532 x + 701304921$ |
$20$ |
[0,10] |
$2^{28}\cdot 3^{18}\cdot 5^{15}\cdot 7^{17}\cdot 11^{5}$ |
$5$ |
$225.81881897691528$ |
$453.27650131632214$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
$[2, 4]$ |
$2$ |
$9$ |
$742303713446840.1$ |
| 20.0.146...000.1 |
$x^{20} - 5 x^{19} + 45 x^{17} - 30 x^{16} - 471 x^{15} - 4620 x^{14} + 10305 x^{13} - 141585 x^{12} + 606760 x^{11} + 609838 x^{10} - 1952580 x^{9} + 28987335 x^{8} - 74225835 x^{7} + 179083080 x^{6} - 244662507 x^{5} + 710403480 x^{4} - 436562865 x^{3} - 5116531050 x^{2} + 2621446065 x + 6872217039$ |
$20$ |
[0,10] |
$2^{22}\cdot 3^{18}\cdot 5^{38}\cdot 19^{5}$ |
$4$ |
$256.019787607$ |
$713.213298041763$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
$[2]$ |
$2$ |
$9$ |
$23307627262679628$ |
| 20.0.146...000.2 |
$x^{20} - 5 x^{19} + 5 x^{18} - 15 x^{17} + 135 x^{16} - 441 x^{15} - 4785 x^{14} + 41985 x^{13} - 244905 x^{12} + 364195 x^{11} + 1678009 x^{10} - 7005175 x^{9} + 33976275 x^{8} - 47498175 x^{7} + 146201325 x^{6} + 72090015 x^{5} + 74152500 x^{4} - 1484055750 x^{3} - 1393848250 x^{2} + 3776471750 x + 7954197850$ |
$20$ |
[0,10] |
$2^{22}\cdot 3^{18}\cdot 5^{38}\cdot 19^{5}$ |
$4$ |
$256.0197876073492$ |
$713.213298041763$ |
|
|
|
$D_4\times F_5$ (as 20T42) |
$[10]$ |
$2$ |
$9$ |
$5442154832171113.0$ |
| 20.4.698...000.1 |
$x^{20} + 65 x^{18} - 2738 x^{16} - 26292 x^{15} - 218240 x^{14} - 2265900 x^{13} - 5195701 x^{12} - 38299128 x^{11} - 90961241 x^{10} + 455452620 x^{9} + 720754398 x^{8} + 4471295556 x^{7} + 25334742324 x^{6} + 52611971412 x^{5} - 122053122444 x^{4} + 47805685956 x^{3} + 795301311816 x^{2} + 466959547656 x - 2101842107004$ |
$20$ |
[4,8] |
$2^{22}\cdot 3^{17}\cdot 5^{15}\cdot 7^{18}\cdot 11^{10}$ |
$5$ |
$348.496277572$ |
$453.27650131632214$ |
|
|
|
$D_4\times F_5$ (as 20T42) |
$[2, 4, 20]$ |
$2$ |
$11$ |
$75775460004876270$ |
| 20.0.158...000.1 |
$x^{20} - 10 x^{19} + 105 x^{18} - 660 x^{17} + 3870 x^{16} - 15852 x^{15} + 59130 x^{14} - 236400 x^{13} + 877605 x^{12} - 1837930 x^{11} + 2750173 x^{10} - 1729980 x^{9} - 56073540 x^{8} + 197617680 x^{7} + 614328480 x^{6} - 2562120432 x^{5} + 2348943840 x^{4} - 11563309440 x^{3} + 25741488960 x^{2} + 36027296640 x + 11462824512$ |
$20$ |
[0,10] |
$2^{38}\cdot 3^{18}\cdot 5^{37}\cdot 29^{5}$ |
$4$ |
$457.151478313$ |
$1246.1107092239415$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
$[2, 20]$ |
$2$ |
$9$ |
$664049058604952300$ |
| 20.4.101...000.1 |
$x^{20} - 130 x^{18} + 7485 x^{16} - 1440 x^{15} - 251160 x^{14} - 93600 x^{13} + 5435730 x^{12} + 6271200 x^{11} - 78473676 x^{10} - 158464800 x^{9} + 906116850 x^{8} + 2131034400 x^{7} + 3736929000 x^{6} - 11867885280 x^{5} + 112416622125 x^{4} - 58691196000 x^{3} + 284318426750 x^{2} + 294181380000 x - 161721068975$ |
$20$ |
[4,8] |
$2^{44}\cdot 3^{18}\cdot 5^{37}\cdot 29^{5}$ |
$4$ |
$562.8194885777191$ |
$1534.142238070327$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
$[2, 4]$ |
$2$ |
$11$ |
$33821894379267130000$ |
| 20.2.154...000.1 |
$x^{20} + 8362440 x^{10} - 498225937500$ |
$20$ |
[2,9] |
$-\,2^{28}\cdot 3^{17}\cdot 5^{37}\cdot 19^{10}$ |
$4$ |
$574.733310706$ |
$713.213298041763$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
$[2, 210]$ |
$2$ |
$10$ |
$512931228173057100$ |
| 20.0.457...000.1 |
$x^{20} - 5 x^{19} + 20 x^{18} + 35 x^{17} - 110 x^{16} - 14471 x^{15} + 58720 x^{14} - 37205 x^{13} + 5614535 x^{12} + 11523240 x^{11} + 26044322 x^{10} - 259765920 x^{9} - 1244384545 x^{8} - 14123682335 x^{7} + 168604014460 x^{6} - 439041788393 x^{5} + 856847774500 x^{4} - 248531078125 x^{3} - 26823631243750 x^{2} + 41896992259375 x + 197430725614375$ |
$20$ |
[0,10] |
$2^{16}\cdot 3^{17}\cdot 5^{37}\cdot 11^{10}\cdot 31^{5}$ |
$5$ |
$680.782427472$ |
$1993.433827495938$ |
|
|
|
$D_4\times F_5$ (as 20T42) |
$[2, 2, 20]$ |
$2$ |
$9$ |
$16621017784297850000$ |
| 20.2.102...000.1 |
$x^{20} - 5 x^{19} - 30 x^{18} - 150 x^{17} + 1365 x^{16} + 6495 x^{15} + 13290 x^{14} - 163440 x^{13} - 1387860 x^{12} - 1430930 x^{11} + 8552986 x^{10} - 18873780 x^{9} - 7336320 x^{8} + 141614280 x^{7} - 1202920740 x^{6} - 4356308556 x^{5} - 2480977080 x^{4} - 24898685040 x^{3} + 20689622640 x^{2} + 83497187880 x + 48728820456$ |
$20$ |
[2,9] |
$-\,2^{16}\cdot 3^{18}\cdot 5^{12}\cdot 7^{17}\cdot 19^{10}\cdot 41^{5}$ |
$6$ |
$708.795949485$ |
$2516.6197113520266$ |
|
|
|
$D_4\times F_5$ (as 20T42) |
not computed |
$2$ |
$10$ |
|
| 20.4.169...000.1 |
$x^{20} - 115 x^{18} + 5770 x^{16} - 1440 x^{15} - 165830 x^{14} - 82800 x^{13} + 3014885 x^{12} + 3272400 x^{11} - 35378423 x^{10} - 79322400 x^{9} + 393756960 x^{8} + 1323298800 x^{7} + 4758606720 x^{6} - 10520047440 x^{5} + 55152558720 x^{4} - 11607321600 x^{3} + 171320650560 x^{2} + 26672716800 x - 189670693824$ |
$20$ |
[4,8] |
$2^{33}\cdot 3^{17}\cdot 5^{38}\cdot 29^{10}$ |
$4$ |
$915.154809715$ |
$1534.142238070327$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
not computed |
$2$ |
$11$ |
|
| 20.2.283...000.1 |
$x^{20} - 15 x^{18} + 68 x^{16} + 783210 x^{14} + 11146009 x^{12} - 1515223395 x^{10} - 20127194318 x^{8} - 88440811800 x^{6} + 24804966751136 x^{4} - 36520551394800 x^{2} - 3143510018924000$ |
$20$ |
[2,9] |
$-\,2^{27}\cdot 3^{16}\cdot 5^{15}\cdot 7^{18}\cdot 11^{5}\cdot 19^{10}$ |
$6$ |
$938.9191759928063$ |
$2503.4728038414896$ |
|
|
|
$D_4\times F_5$ (as 20T42) |
$[3, 6, 60]$ |
$2$ |
$10$ |
$149531292570303900000$ |
| 20.0.187...000.1 |
$x^{20} - 5 x^{18} + 2335 x^{16} - 15000 x^{15} - 9310 x^{14} - 37500 x^{13} + 2176205 x^{12} + 453262500 x^{11} + 77878949 x^{10} - 366112500 x^{9} + 1504122825 x^{8} - 502304662500 x^{7} + 2221690070250 x^{6} + 121316632500 x^{5} + 1738615449375 x^{4} + 51625865812500 x^{3} + 334108569684375 x^{2} + 478599181875000 x + 204323528728125$ |
$20$ |
[0,10] |
$2^{28}\cdot 3^{17}\cdot 5^{37}\cdot 11^{10}\cdot 31^{5}$ |
$5$ |
$1031.8732035082019$ |
$3021.480676577824$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
$[2, 2, 2, 4]$ |
$2$ |
$9$ |
$2472034484027324400000$ |
| 20.2.419...000.1 |
$x^{20} + 25 x^{18} - 5490 x^{16} - 504 x^{15} - 113550 x^{14} + 6300 x^{13} + 12321165 x^{12} - 37702980 x^{11} + 194913981 x^{10} - 152195400 x^{9} - 14147475720 x^{8} - 103823335980 x^{7} - 155832812520 x^{6} - 342412302204 x^{5} + 8327095658280 x^{4} - 27229794641280 x^{3} + 45732471096340 x^{2} - 28848825275760 x - 1993393085504492$ |
$20$ |
[2,9] |
$-\,2^{28}\cdot 3^{18}\cdot 5^{12}\cdot 7^{17}\cdot 19^{10}\cdot 41^{5}$ |
$6$ |
$1074.3337629106172$ |
$3814.482188102883$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
not computed |
$2$ |
$10$ |
|
| 20.0.539...000.1 |
$x^{20} - 120 x^{18} + 7888 x^{16} - 1764 x^{15} - 45000 x^{14} - 6315120 x^{13} + 54010144 x^{12} + 90853056 x^{11} - 3602584704 x^{10} + 14654077200 x^{9} + 112702188032 x^{8} - 1752566231808 x^{7} + 11914781620224 x^{6} - 54255565782264 x^{5} + 184031339300816 x^{4} - 477951506932032 x^{3} + 893163408031104 x^{2} - 1066289337176448 x + 709016550047036$ |
$20$ |
[0,10] |
$2^{38}\cdot 3^{16}\cdot 5^{15}\cdot 7^{17}\cdot 11^{10}\cdot 19^{5}$ |
$6$ |
$1087.92655029$ |
$2503.4728038414896$ |
|
|
? |
$D_4\times F_5$ (as 20T42) |
not computed |
$2$ |
$9$ |
|
| 20.0.622...000.1 |
$x^{20} - 5 x^{19} - 50 x^{18} + 320 x^{17} + 2345 x^{16} - 12181 x^{15} - 73320 x^{14} + 512730 x^{13} + 918540 x^{12} - 51640740 x^{11} + 84666708 x^{10} + 486916920 x^{9} + 757508760 x^{8} + 25534653840 x^{7} - 24954019920 x^{6} - 242263297872 x^{5} + 604206514080 x^{4} - 2304783771840 x^{3} + 3925294084800 x^{2} + 4137580751040 x + 1135110106944$ |
$20$ |
[0,10] |
$2^{27}\cdot 3^{17}\cdot 5^{38}\cdot 11^{5}\cdot 19^{10}$ |
$5$ |
$1095.7501547555275$ |
$3345.26689325073$ |
|
|
|
$D_4\times F_5$ (as 20T42) |
$[2, 8, 16]$ |
$2$ |
$9$ |
$5229517898179829000000$ |
