| 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 |
| 20.0.781...000.1 |
$x^{20} - 5 x^{19} + 5 x^{18} + 15 x^{17} - 30 x^{16} - 21 x^{15} + 75 x^{14} + 15 x^{13} - 120 x^{12} - 5 x^{11} + 141 x^{10} - 5 x^{9} - 120 x^{8} + 15 x^{7} + 75 x^{6} - 21 x^{5} - 30 x^{4} + 15 x^{3} + 5 x^{2} - 5 x + 1$ |
$20$ |
[0,10] |
$2^{16}\cdot 5^{23}$ |
$2$ |
$11.0825449519$ |
$11.08254495193135$ |
|
✓ |
? |
$F_5$ (as 20T5) |
trivial |
$10$ |
$9$ |
$525.931286845$ |
| 20.0.335...752.1 |
$x^{20} - 2 x^{19} + 10 x^{17} - 15 x^{16} + 40 x^{14} - 64 x^{13} + 46 x^{12} + 8 x^{11} - 32 x^{10} + 8 x^{9} + 46 x^{8} - 64 x^{7} + 40 x^{6} - 15 x^{4} + 10 x^{3} - 2 x + 1$ |
$20$ |
[0,10] |
$2^{16}\cdot 13^{15}$ |
$2$ |
$11.9201442437$ |
$11.920144243683046$ |
|
✓ |
? |
$F_5$ (as 20T5) |
trivial |
$2$ |
$9$ |
$238.906276128$ |
| 20.0.465...125.1 |
$x^{20} - 10 x^{19} + 50 x^{18} - 165 x^{17} + 375 x^{16} - 552 x^{15} + 445 x^{14} - 85 x^{13} - 35 x^{12} - 375 x^{11} + 879 x^{10} - 925 x^{9} + 585 x^{8} - 285 x^{7} + 175 x^{6} - 128 x^{5} + 65 x^{4} - 15 x^{3} + 1$ |
$20$ |
[0,10] |
$5^{31}$ |
$1$ |
$12.1172343332$ |
$12.117234333213267$ |
|
✓ |
|
$F_5$ (as 20T5) |
trivial |
$10$ |
$9$ |
$1543.06769005$ |
| 20.0.860...000.1 |
$x^{20} - x^{19} + 4 x^{18} - 4 x^{17} + 2 x^{16} + 9 x^{15} + 2 x^{14} + 46 x^{13} + 69 x^{12} + 84 x^{11} + 62 x^{10} - 6 x^{9} - 6 x^{8} + 26 x^{7} + 62 x^{6} + 54 x^{5} + 17 x^{4} + x^{3} + 4 x^{2} + 4 x + 1$ |
$20$ |
[0,10] |
$2^{16}\cdot 3^{16}\cdot 5^{15}$ |
$3$ |
$14.020015816$ |
$14.020015815993006$ |
|
✓ |
? |
$F_5$ (as 20T5) |
trivial |
$10$ |
$9$ |
$12526.9970149$ |
| 20.0.169...857.1 |
$x^{20} - x^{19} + 2 x^{18} + 3 x^{17} - 6 x^{16} + 23 x^{15} - 13 x^{14} + 7 x^{13} + 34 x^{12} - 50 x^{11} + 81 x^{10} - 50 x^{9} + 34 x^{8} + 7 x^{7} - 13 x^{6} + 23 x^{5} - 6 x^{4} + 3 x^{3} + 2 x^{2} - x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 17^{15}$ |
$2$ |
$14.5009788258$ |
$14.500978825806921$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[2]$ |
$2$ |
$9$ |
$1314.30559263$ |
| 20.0.513...125.1 |
$x^{20} - 5 x^{19} + 20 x^{18} - 60 x^{17} + 140 x^{16} - 281 x^{15} + 460 x^{14} - 645 x^{13} + 770 x^{12} - 780 x^{11} + 711 x^{10} - 560 x^{9} + 420 x^{8} - 155 x^{7} + 60 x^{6} - x^{5} - 20 x^{4} - 20 x^{3} - 30 x^{2} - 25 x + 41$ |
$20$ |
[0,10] |
$3^{16}\cdot 5^{23}$ |
$2$ |
$15.3289535693$ |
$15.328953569291674$ |
|
✓ |
|
$F_5$ (as 20T5) |
trivial |
$10$ |
$9$ |
$21670.1464682$ |
| 20.0.101...125.1 |
$x^{20} - 5 x^{19} + 13 x^{18} - 30 x^{17} + 63 x^{16} - 110 x^{15} + 181 x^{14} - 275 x^{13} + 355 x^{12} - 445 x^{11} + 561 x^{10} - 635 x^{9} + 703 x^{8} - 775 x^{7} + 773 x^{6} - 690 x^{5} + 546 x^{4} - 370 x^{3} + 215 x^{2} - 100 x + 25$ |
$20$ |
[0,10] |
$5^{15}\cdot 7^{16}$ |
$2$ |
$15.8601005109$ |
$15.860100510897633$ |
|
✓ |
|
$F_5$ (as 20T5) |
trivial |
$10$ |
$9$ |
$53376.7417145$ |
| 20.0.155...928.1 |
$x^{20} + 4 x^{18} + 14 x^{16} + 28 x^{14} + 45 x^{12} + 64 x^{10} + 132 x^{8} + 256 x^{6} + 292 x^{4} + 160 x^{2} + 32$ |
$20$ |
[0,10] |
$2^{55}\cdot 3^{16}$ |
$2$ |
$16.2005400398$ |
$16.20054003982431$ |
|
✓ |
|
$F_5$ (as 20T5) |
trivial |
$2$ |
$9$ |
$104319.684091$ |
| 20.0.128...000.1 |
$x^{20} + 5 x^{16} - 4 x^{15} + 30 x^{14} + 20 x^{13} + 25 x^{12} + 60 x^{11} + 46 x^{10} + 60 x^{9} + 25 x^{8} + 20 x^{7} + 30 x^{6} - 4 x^{5} + 5 x^{4} + 1$ |
$20$ |
[0,10] |
$2^{30}\cdot 5^{23}$ |
$2$ |
$18.0036473899$ |
$18.00364738986388$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[2]$ |
$2$ |
$9$ |
$26927.8287731$ |
| 20.0.146...125.1 |
$x^{20} - 4 x^{19} + 11 x^{18} - 14 x^{17} + 27 x^{16} - 4 x^{15} + 76 x^{14} + 26 x^{13} + 242 x^{12} + 186 x^{11} + 1176 x^{10} + 1496 x^{9} + 3207 x^{8} + 3946 x^{7} + 4941 x^{6} + 3726 x^{5} + 4572 x^{4} + 2746 x^{3} + 2191 x^{2} + 686 x + 641$ |
$20$ |
[0,10] |
$5^{15}\cdot 37^{10}$ |
$2$ |
$20.3389423481$ |
$20.33894234805392$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[2]$ |
$2$ |
$9$ |
$72096.60689$ |
| 20.0.275...000.1 |
$x^{20} - 3 x^{19} + 16 x^{18} - 32 x^{17} + 110 x^{16} - 153 x^{15} + 358 x^{14} - 206 x^{13} + 553 x^{12} + 106 x^{11} + 758 x^{10} + 946 x^{9} + 724 x^{8} + 664 x^{7} - 58 x^{6} + 66 x^{5} + 161 x^{4} + 205 x^{3} + 190 x^{2} + 50 x + 25$ |
$20$ |
[0,10] |
$2^{16}\cdot 5^{15}\cdot 13^{10}$ |
$3$ |
$20.9905189563$ |
$20.99051895628543$ |
|
✓ |
? |
$F_5$ (as 20T5) |
$[2]$ |
$2$ |
$9$ |
$72830.9231902$ |
| 20.0.565...664.1 |
$x^{20} - 6 x^{19} + 22 x^{18} - 61 x^{17} + 147 x^{16} - 338 x^{15} + 780 x^{14} - 1782 x^{13} + 3658 x^{12} - 6414 x^{11} + 10114 x^{10} - 15538 x^{9} + 23243 x^{8} - 31374 x^{7} + 35592 x^{6} - 32603 x^{5} + 23544 x^{4} - 13072 x^{3} + 5366 x^{2} - 1501 x + 223$ |
$20$ |
[0,10] |
$2^{16}\cdot 29^{15}$ |
$2$ |
$21.7581764785$ |
$21.758176478524742$ |
|
✓ |
? |
$F_5$ (as 20T5) |
trivial |
$2$ |
$9$ |
$147782.929749$ |
| 20.0.738...000.1 |
$x^{20} + 5 x^{18} - 10 x^{17} + 20 x^{16} - 18 x^{15} - 25 x^{14} + 30 x^{13} + 20 x^{12} + 350 x^{11} - 261 x^{10} - 950 x^{9} + 155 x^{8} + 1010 x^{7} + 730 x^{6} - 172 x^{5} - 980 x^{4} - 880 x^{3} + 160 x^{2} + 640 x + 256$ |
$20$ |
[0,10] |
$2^{20}\cdot 3^{10}\cdot 5^{23}$ |
$3$ |
$22.0498748071$ |
$22.049874807078353$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[2, 2]$ |
$2$ |
$9$ |
$179913.802936$ |
| 20.0.934...768.1 |
$x^{20} - 4 x^{18} + 14 x^{16} + 32 x^{14} - 258 x^{12} + 1432 x^{10} - 824 x^{8} + 384 x^{6} + 313 x^{4} - 308 x^{2} + 242$ |
$20$ |
[0,10] |
$2^{55}\cdot 11^{10}$ |
$2$ |
$22.3115031756$ |
$22.311503175611666$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[2]$ |
$2$ |
$9$ |
$1376572.32836$ |
| 20.0.109...000.1 |
$x^{20} - 8 x^{19} + 40 x^{18} - 136 x^{17} + 352 x^{16} - 728 x^{15} + 1256 x^{14} - 1912 x^{13} + 3125 x^{12} - 6608 x^{11} + 16456 x^{10} - 37920 x^{9} + 71958 x^{8} - 107952 x^{7} + 126216 x^{6} - 112960 x^{5} + 75672 x^{4} - 36736 x^{3} + 12288 x^{2} - 2560 x + 256$ |
$20$ |
[0,10] |
$2^{55}\cdot 5^{15}$ |
$2$ |
$22.4936530076$ |
$22.493653007613965$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[4]$ |
$2$ |
$9$ |
$1993746.99362$ |
| 20.0.140...125.2 |
$x^{20} - 2 x^{19} - 2 x^{18} + 18 x^{17} - 32 x^{16} + 88 x^{15} + 58 x^{14} - 782 x^{13} + 1538 x^{12} + 1348 x^{11} - 466 x^{10} - 894 x^{9} + 346 x^{8} - 114 x^{7} - 424 x^{6} - 88 x^{5} + 214 x^{4} + 54 x^{3} + 14 x^{2} + 4 x + 1$ |
$20$ |
[0,10] |
$5^{15}\cdot 11^{16}$ |
$2$ |
$22.7688791172$ |
$22.76887911715532$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[5]$ |
$10$ |
$9$ |
$643711.144226$ |
| 20.0.141...000.1 |
$x^{20} - 2 x^{19} + 13 x^{18} - 22 x^{17} + 99 x^{16} - 152 x^{15} + 492 x^{14} - 688 x^{13} + 1763 x^{12} - 2238 x^{11} + 4497 x^{10} - 5026 x^{9} + 8525 x^{8} - 7336 x^{7} + 10214 x^{6} - 7176 x^{5} + 6476 x^{4} - 2960 x^{3} + 2160 x^{2} - 960 x + 320$ |
$20$ |
[0,10] |
$2^{30}\cdot 3^{16}\cdot 5^{15}$ |
$3$ |
$22.775582887$ |
$22.775582886985283$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[2]$ |
$2$ |
$9$ |
$639468.319487$ |
| 20.0.164...125.1 |
$x^{20} - 5 x^{19} + 15 x^{18} - 30 x^{17} + 45 x^{16} - 70 x^{15} + 145 x^{14} - 360 x^{13} + 755 x^{12} - 1115 x^{11} + 930 x^{10} - 305 x^{9} + 705 x^{8} - 3530 x^{7} + 8095 x^{6} - 11300 x^{5} + 11445 x^{4} - 9200 x^{3} + 5425 x^{2} - 1925 x + 295$ |
$20$ |
[0,10] |
$5^{23}\cdot 13^{10}$ |
$2$ |
$22.9502373392$ |
$22.950237339189933$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[2]$ |
$2$ |
$9$ |
$117824.99403$ |
| 20.0.181...125.2 |
$x^{20} + 25 x^{10} + 5$ |
$20$ |
[0,10] |
$5^{39}$ |
$1$ |
$23.0670208648$ |
$23.067020864764707$ |
|
✓ |
|
$F_5$ (as 20T5) |
trivial |
$10$ |
$9$ |
$1782067.31277$ |
| 20.0.403...000.1 |
$x^{20} - 5 x^{19} - 3 x^{18} + 51 x^{17} - 36 x^{16} - 221 x^{15} + 399 x^{14} - 153 x^{13} + 262 x^{12} - 677 x^{11} + 169 x^{10} + 203 x^{9} + 236 x^{8} - 335 x^{7} - 335 x^{6} + 325 x^{5} + 990 x^{4} + 1025 x^{3} + 575 x^{2} + 175 x + 25$ |
$20$ |
[0,10] |
$2^{16}\cdot 5^{15}\cdot 17^{10}$ |
$3$ |
$24.0035767574$ |
$24.00357675738704$ |
|
✓ |
? |
$F_5$ (as 20T5) |
$[2]$ |
$2$ |
$9$ |
$246762.21333$ |
| 20.0.496...832.1 |
$x^{20} - 8 x^{19} + 40 x^{18} - 112 x^{17} + 194 x^{16} - 88 x^{15} - 380 x^{14} + 1128 x^{13} - 1232 x^{12} - 32 x^{11} + 2600 x^{10} - 4352 x^{9} + 4326 x^{8} - 2744 x^{7} + 1924 x^{6} - 1304 x^{5} + 1047 x^{4} - 72 x^{3} + 168 x^{2} - 96 x + 16$ |
$20$ |
[0,10] |
$2^{55}\cdot 13^{10}$ |
$2$ |
$24.2551611404$ |
$24.255161140409015$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[2]$ |
$2$ |
$9$ |
$3641112.82209$ |
| 20.0.533...125.1 |
$x^{20} - 4 x^{19} + 10 x^{18} - 5 x^{17} - 19 x^{16} + 50 x^{15} + 54 x^{14} - 40 x^{13} - 199 x^{12} + 840 x^{11} + 620 x^{10} - 1279 x^{9} + 1556 x^{8} + 5430 x^{7} + 3925 x^{6} - 1385 x^{5} + 2240 x^{4} + 2325 x^{3} + 1225 x^{2} + 25 x + 25$ |
$20$ |
[0,10] |
$5^{15}\cdot 53^{10}$ |
$2$ |
$24.3425145381$ |
$24.342514538096598$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[2]$ |
$2$ |
$9$ |
$367558.874812$ |
| 20.0.925...000.1 |
$x^{20} - 6 x^{19} + 21 x^{18} - 54 x^{17} + 162 x^{16} - 494 x^{15} + 1081 x^{14} - 1382 x^{13} + 1059 x^{12} - 1812 x^{11} + 5568 x^{10} - 7980 x^{9} + 1291 x^{8} + 3950 x^{7} + 6055 x^{6} - 2470 x^{5} - 890 x^{4} + 850 x^{3} + 1275 x^{2} + 150 x + 25$ |
$20$ |
[0,10] |
$2^{30}\cdot 5^{15}\cdot 7^{10}$ |
$3$ |
$25.0219710195$ |
$25.021971019484877$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[2, 2]$ |
$2$ |
$9$ |
$905204.455446$ |
| 20.0.207...000.1 |
$x^{20} - 8 x^{19} + 24 x^{18} - 48 x^{17} + 134 x^{16} - 296 x^{15} + 584 x^{14} - 1304 x^{13} + 1717 x^{12} - 2032 x^{11} + 3016 x^{10} - 1352 x^{9} + 4276 x^{8} + 3008 x^{7} - 6232 x^{6} + 9872 x^{5} + 2300 x^{4} - 4992 x^{3} + 1872 x^{2} - 256 x + 16$ |
$20$ |
[0,10] |
$2^{55}\cdot 3^{10}\cdot 5^{10}$ |
$3$ |
$26.0542224973$ |
$26.054222497305222$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[2, 2]$ |
$2$ |
$9$ |
$6532127.80174$ |
| 20.0.218...248.1 |
$x^{20} - 10 x^{19} + 60 x^{18} - 255 x^{17} + 833 x^{16} - 2176 x^{15} + 4622 x^{14} - 8044 x^{13} + 11428 x^{12} - 13058 x^{11} + 11680 x^{10} - 7762 x^{9} + 3457 x^{8} - 830 x^{7} + 1310 x^{6} - 3773 x^{5} + 4070 x^{4} - 1854 x^{3} - 876 x^{2} + 1177 x + 1381$ |
$20$ |
[0,10] |
$2^{16}\cdot 37^{15}$ |
$2$ |
$26.1201273228$ |
$26.12012732284832$ |
|
✓ |
|
$F_5$ (as 20T5) |
trivial |
$2$ |
$9$ |
$1702148.10944$ |
| 20.0.240...125.1 |
$x^{20} - 5 x^{19} + 20 x^{18} - 65 x^{17} + 200 x^{16} - 482 x^{15} + 1015 x^{14} - 2005 x^{13} + 3375 x^{12} - 5715 x^{11} + 8584 x^{10} - 12320 x^{9} + 16915 x^{8} - 25850 x^{7} + 28430 x^{6} - 32983 x^{5} + 54230 x^{4} + 1020 x^{3} + 71185 x^{2} + 31085 x + 14741$ |
$20$ |
[0,10] |
$5^{23}\cdot 17^{10}$ |
$2$ |
$26.2446004655$ |
$26.244600465513358$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[2]$ |
$2$ |
$9$ |
$382451.294806$ |
| 20.0.327...000.1 |
$x^{20} + 12 x^{18} - 7 x^{17} + 41 x^{16} - 58 x^{15} + 102 x^{14} + 272 x^{13} + 568 x^{12} + 538 x^{11} + 664 x^{10} + 362 x^{9} + 3461 x^{8} + 14 x^{7} + 8626 x^{6} + 3161 x^{5} + 5774 x^{4} + 3726 x^{3} + 1980 x^{2} + 351 x + 81$ |
$20$ |
[0,10] |
$2^{16}\cdot 5^{10}\cdot 13^{15}$ |
$3$ |
$26.6542528305$ |
$26.65425283047811$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[2]$ |
$2$ |
$9$ |
$1421636.55011$ |
| 20.0.333...000.1 |
$x^{20} - 5 x^{19} + 27 x^{18} - 81 x^{17} + 204 x^{16} - 379 x^{15} + 509 x^{14} - 707 x^{13} + 1062 x^{12} - 1983 x^{11} + 3759 x^{10} - 2473 x^{9} + 2326 x^{8} - 1065 x^{7} + 6885 x^{6} + 765 x^{5} - 540 x^{4} + 6075 x^{3} + 2025 x^{2} + 2025 x + 2025$ |
$20$ |
[0,10] |
$2^{16}\cdot 3^{10}\cdot 5^{15}\cdot 7^{10}$ |
$4$ |
$26.6784839944$ |
$26.67848399443575$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[2, 2]$ |
$2$ |
$9$ |
$737205.625442$ |
| 20.0.336...000.1 |
$x^{20} - 5 x^{19} - 15 x^{18} + 115 x^{17} - 20 x^{16} - 841 x^{15} + 1115 x^{14} + 1785 x^{13} - 3880 x^{12} - 1055 x^{11} + 5601 x^{10} - 1055 x^{9} - 3880 x^{8} + 1785 x^{7} + 1115 x^{6} - 841 x^{5} - 20 x^{4} + 115 x^{3} - 15 x^{2} - 5 x + 1$ |
$20$ |
[0,10] |
$2^{16}\cdot 3^{16}\cdot 5^{23}$ |
$3$ |
$26.689258329$ |
$26.689258328973995$ |
|
✓ |
? |
$F_5$ (as 20T5) |
$[5]$ |
$10$ |
$9$ |
$1117806.26947$ |
| 20.0.336...000.2 |
$x^{20} - 5 x^{19} + 10 x^{18} - 10 x^{17} + 30 x^{16} - 113 x^{15} - 30 x^{14} + 590 x^{13} + 275 x^{12} - 2640 x^{11} - 2256 x^{10} + 6770 x^{9} + 8900 x^{8} - 9670 x^{7} - 21040 x^{6} + 9408 x^{5} + 56075 x^{4} + 65245 x^{3} + 37290 x^{2} + 10890 x + 1331$ |
$20$ |
[0,10] |
$2^{16}\cdot 3^{16}\cdot 5^{23}$ |
$3$ |
$26.689258329$ |
$26.689258328973995$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[5]$ |
$10$ |
$9$ |
$3774223.93146$ |
| 20.0.336...000.3 |
$x^{20} - 5 x^{19} + 15 x^{18} - 35 x^{17} + 70 x^{16} - 97 x^{15} + 95 x^{14} - 135 x^{13} + 590 x^{12} - 2555 x^{11} + 5169 x^{10} - 6185 x^{9} + 2780 x^{8} + 4905 x^{7} + 1565 x^{6} - 7753 x^{5} + 3460 x^{4} + 595 x^{3} - 2205 x^{2} - 1715 x + 2401$ |
$20$ |
[0,10] |
$2^{16}\cdot 3^{16}\cdot 5^{23}$ |
$3$ |
$26.689258329$ |
$26.689258328973995$ |
|
✓ |
? |
$F_5$ (as 20T5) |
$[5]$ |
$10$ |
$9$ |
$1373081.37212$ |
| 20.0.746...125.1 |
$x^{20} - 2 x^{19} + 7 x^{18} - 2 x^{17} - 37 x^{16} + 28 x^{15} - 245 x^{13} + 266 x^{12} + 395 x^{11} - 660 x^{10} + 1358 x^{9} + 6413 x^{8} + 6698 x^{7} + 4837 x^{6} + 9188 x^{5} + 16636 x^{4} + 20385 x^{3} + 19110 x^{2} + 11925 x + 3555$ |
$20$ |
[0,10] |
$3^{10}\cdot 5^{15}\cdot 23^{10}$ |
$3$ |
$27.7748708771$ |
$27.77487087706129$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[2, 2]$ |
$2$ |
$9$ |
$1412098.09505$ |
| 20.0.873...125.1 |
$x^{20} - 4 x^{19} + 7 x^{18} - x^{17} - 6 x^{16} - 119 x^{15} + 843 x^{14} - 3114 x^{13} + 8298 x^{12} - 17511 x^{11} + 30458 x^{10} - 45048 x^{9} + 57805 x^{8} - 64072 x^{7} + 59806 x^{6} - 45528 x^{5} + 27366 x^{4} - 12495 x^{3} + 4080 x^{2} - 850 x + 85$ |
$20$ |
[0,10] |
$5^{15}\cdot 17^{15}$ |
$2$ |
$27.9939507549$ |
$27.99395075493803$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[4]$ |
$2$ |
$9$ |
$1365722.71668$ |
| 20.0.131...125.1 |
$x^{20} - 2 x^{19} - 17 x^{18} + 48 x^{17} + 94 x^{16} - 402 x^{15} + 137 x^{14} + 1337 x^{13} - 2082 x^{12} - 23 x^{11} + 3747 x^{10} - 5361 x^{9} + 5490 x^{8} - 5271 x^{7} + 5114 x^{6} - 4061 x^{5} + 2436 x^{4} - 1100 x^{3} + 415 x^{2} - 125 x + 25$ |
$20$ |
[0,10] |
$5^{15}\cdot 73^{10}$ |
$2$ |
$28.5685983518$ |
$28.56859835181669$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[2]$ |
$2$ |
$9$ |
$1811157.39147$ |
| 20.0.181...125.1 |
$x^{20} - 3 x^{19} + 13 x^{18} - 18 x^{17} + 74 x^{16} - 63 x^{15} + 202 x^{14} + 3 x^{13} + 828 x^{12} - 357 x^{11} - 578 x^{10} - 2484 x^{9} - 1065 x^{8} - 789 x^{7} + 994 x^{6} + 1896 x^{5} + 2446 x^{4} + 2010 x^{3} + 700 x^{2} + 690 x + 545$ |
$20$ |
[0,10] |
$3^{16}\cdot 5^{15}\cdot 13^{10}$ |
$3$ |
$29.0332853935$ |
$29.033285393546965$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[2]$ |
$2$ |
$9$ |
$2671069.94942$ |
| 20.0.198...125.1 |
$x^{20} - 5 x^{19} + 10 x^{18} - 10 x^{17} + 30 x^{16} - 141 x^{15} + 340 x^{14} - 415 x^{13} + 220 x^{12} + 20 x^{11} - 99 x^{10} + 20 x^{9} + 220 x^{8} - 415 x^{7} + 340 x^{6} - 141 x^{5} + 30 x^{4} - 10 x^{3} + 10 x^{2} - 5 x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 5^{23}\cdot 7^{10}$ |
$3$ |
$29.1692425898$ |
$29.169242589818822$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[2, 2]$ |
$2$ |
$9$ |
$1126766.82054$ |
| 20.20.220...000.1 |
$x^{20} - 10 x^{19} + 20 x^{18} + 105 x^{17} - 465 x^{16} + 48 x^{15} + 2450 x^{14} - 3200 x^{13} - 3700 x^{12} + 9850 x^{11} - 1396 x^{10} - 10230 x^{9} + 6315 x^{8} + 3270 x^{7} - 3620 x^{6} + 17 x^{5} + 680 x^{4} - 100 x^{3} - 40 x^{2} + 5 x + 1$ |
$20$ |
[20,0] |
$2^{16}\cdot 5^{23}\cdot 7^{10}$ |
$3$ |
$29.3216578365$ |
$29.321657836504627$ |
|
✓ |
? |
$F_5$ (as 20T5) |
trivial |
$2$ |
$19$ |
$148023785.442$ |
| 20.0.220...368.1 |
$x^{20} - 4 x^{19} + 14 x^{18} - 20 x^{17} + 63 x^{16} - 16 x^{15} + 220 x^{14} + 264 x^{13} + 1741 x^{12} + 1036 x^{11} + 6254 x^{10} + 11660 x^{9} + 22413 x^{8} + 29992 x^{7} + 50816 x^{6} + 74528 x^{5} + 80510 x^{4} + 81312 x^{3} + 52056 x^{2} + 25888 x + 11576$ |
$20$ |
[0,10] |
$2^{55}\cdot 19^{10}$ |
$2$ |
$29.3230599686$ |
$29.323059968612448$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[2]$ |
$2$ |
$9$ |
$20791866.5937$ |
| 20.0.371...229.1 |
$x^{20} - x^{19} - 2 x^{18} - 11 x^{17} + 54 x^{16} - 28 x^{15} + 63 x^{14} - 158 x^{13} + 317 x^{12} - 264 x^{11} + 852 x^{10} - 323 x^{9} + 986 x^{8} - 413 x^{7} + 2414 x^{6} - 1452 x^{5} + 5813 x^{4} - 2026 x^{3} + 6579 x^{2} - 1020 x + 2075$ |
$20$ |
[0,10] |
$3^{16}\cdot 29^{15}$ |
$2$ |
$30.0950800054$ |
$30.095080005394955$ |
|
✓ |
|
$F_5$ (as 20T5) |
trivial |
$2$ |
$9$ |
$4795512.92142$ |
| 20.0.755...000.1 |
$x^{20} - 25 x^{16} + 60 x^{14} + 165 x^{12} - 270 x^{10} - 2680 x^{8} + 6120 x^{6} + 2080 x^{4} - 2400 x^{2} + 2880$ |
$20$ |
[0,10] |
$2^{30}\cdot 3^{10}\cdot 5^{23}$ |
$3$ |
$31.1832320008$ |
$31.18323200079904$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[2, 2]$ |
$2$ |
$9$ |
$4833940.00984$ |
| 20.0.841...000.1 |
$x^{20} - 6 x^{19} + 15 x^{18} - 36 x^{17} + 115 x^{16} - 242 x^{15} + 466 x^{14} - 1176 x^{13} + 1851 x^{12} - 2716 x^{11} + 6539 x^{10} - 8834 x^{9} + 13461 x^{8} - 34154 x^{7} + 25816 x^{6} + 22302 x^{5} - 11105 x^{4} - 18754 x^{3} - 10375 x^{2} + 2366 x + 18671$ |
$20$ |
[0,10] |
$2^{16}\cdot 5^{15}\cdot 29^{10}$ |
$3$ |
$31.3509350806$ |
$31.350935080608856$ |
|
✓ |
? |
$F_5$ (as 20T5) |
$[2, 2]$ |
$2$ |
$9$ |
$2498106.65213$ |
| 20.0.951...125.1 |
$x^{20} - 2 x^{19} + 23 x^{18} - 52 x^{17} + 194 x^{16} - 482 x^{15} + 1027 x^{14} - 1983 x^{13} + 3618 x^{12} - 5173 x^{11} + 7077 x^{10} - 8941 x^{9} + 9730 x^{8} - 9101 x^{7} + 7784 x^{6} - 5241 x^{5} + 2746 x^{4} - 1190 x^{3} + 415 x^{2} - 75 x + 25$ |
$20$ |
[0,10] |
$5^{15}\cdot 89^{10}$ |
$2$ |
$31.544417097$ |
$31.544417096966722$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[2, 2]$ |
$2$ |
$9$ |
$3392623.57291$ |
| 20.0.116...501.1 |
$x^{20} - 16 x^{18} + 82 x^{16} + 13 x^{14} - 999 x^{12} + 308 x^{10} + 7923 x^{8} + 12402 x^{6} + 4714 x^{4} - 1313 x^{2} + 101$ |
$20$ |
[0,10] |
$101^{15}$ |
$1$ |
$31.859652191$ |
$31.859652191026974$ |
|
✓ |
|
$F_5$ (as 20T5) |
trivial |
$2$ |
$9$ |
$11240237.3489$ |
| 20.0.132...000.1 |
$x^{20} - 10 x^{18} - 10 x^{17} + 11 x^{16} + 80 x^{15} + 290 x^{14} + 20 x^{13} - 1584 x^{12} - 3590 x^{11} + 5160 x^{10} + 15670 x^{9} + 1091 x^{8} - 43440 x^{7} - 32170 x^{6} + 77300 x^{5} + 49621 x^{4} - 55690 x^{3} - 36870 x^{2} - 17700 x + 48220$ |
$20$ |
[0,10] |
$2^{20}\cdot 5^{15}\cdot 23^{10}$ |
$3$ |
$32.0716583552$ |
$32.07165835515686$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[2, 2]$ |
$2$ |
$9$ |
$8895897.14135$ |
| 20.0.149...232.1 |
$x^{20} - 8 x^{19} + 28 x^{18} - 80 x^{17} + 286 x^{16} - 896 x^{15} + 2080 x^{14} - 4136 x^{13} + 9133 x^{12} - 17560 x^{11} + 29132 x^{10} - 49080 x^{9} + 105208 x^{8} - 212512 x^{7} + 339544 x^{6} - 409424 x^{5} + 410364 x^{4} - 340128 x^{3} + 234400 x^{2} - 97920 x + 18496$ |
$20$ |
[0,10] |
$2^{55}\cdot 23^{10}$ |
$2$ |
$32.2623802889$ |
$32.262380288915416$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[2, 2]$ |
$2$ |
$9$ |
$38650073.2246$ |
| 20.0.170...957.1 |
$x^{20} - 7 x^{19} + 29 x^{18} - 90 x^{17} + 210 x^{16} - 345 x^{15} + 260 x^{14} + 206 x^{13} - 62 x^{12} + 1599 x^{11} - 2242 x^{10} - 4550 x^{9} - 1200 x^{8} + 2598 x^{7} + 8307 x^{6} + 10639 x^{5} + 7581 x^{4} + 4455 x^{3} + 2700 x^{2} + 1215 x + 243$ |
$20$ |
[0,10] |
$7^{16}\cdot 13^{15}$ |
$2$ |
$32.4740119561$ |
$32.474011956132756$ |
|
✓ |
|
$F_5$ (as 20T5) |
trivial |
$2$ |
$9$ |
$9407573.54607$ |
| 20.0.264...125.1 |
$x^{20} - 10 x^{19} + 50 x^{18} - 165 x^{17} + 386 x^{16} - 640 x^{15} + 880 x^{14} - 1590 x^{13} + 4691 x^{12} - 13170 x^{11} + 29250 x^{10} - 50875 x^{9} + 78876 x^{8} - 111880 x^{7} + 156405 x^{6} - 191825 x^{5} + 181936 x^{4} - 122455 x^{3} + 29985 x^{2} + 10150 x + 43025$ |
$20$ |
[0,10] |
$3^{16}\cdot 5^{15}\cdot 17^{10}$ |
$3$ |
$33.2008320478$ |
$33.20083204776826$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[2]$ |
$2$ |
$9$ |
$8803149.53857$ |
| 20.0.306...000.1 |
$x^{20} - 10 x^{19} + 64 x^{18} - 291 x^{17} + 1069 x^{16} - 3248 x^{15} + 8514 x^{14} - 19384 x^{13} + 39326 x^{12} - 71194 x^{11} + 118256 x^{10} - 179424 x^{9} + 256621 x^{8} - 336594 x^{7} + 417836 x^{6} - 458653 x^{5} + 468466 x^{4} - 389860 x^{3} + 311630 x^{2} - 163125 x + 96595$ |
$20$ |
[0,10] |
$2^{16}\cdot 3^{10}\cdot 5^{15}\cdot 11^{10}$ |
$4$ |
$33.4432495658$ |
$33.44324956582635$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[2, 2, 2]$ |
$2$ |
$9$ |
$7583540.84842$ |
| 20.0.325...125.1 |
$x^{20} - 9 x^{19} + 51 x^{18} - 231 x^{17} + 833 x^{16} - 2458 x^{15} + 5989 x^{14} - 11695 x^{13} + 20202 x^{12} - 33492 x^{11} + 57953 x^{10} - 92370 x^{9} + 130181 x^{8} - 163476 x^{7} + 201934 x^{6} - 235037 x^{5} + 238937 x^{4} - 173528 x^{3} + 91296 x^{2} - 30696 x + 10256$ |
$20$ |
[0,10] |
$5^{10}\cdot 37^{15}$ |
$2$ |
$33.5456564715$ |
$33.54565647151909$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[2]$ |
$2$ |
$9$ |
$5638854.77787$ |
| 20.0.353...000.1 |
$x^{20} + 15 x^{18} + 75 x^{16} + 30 x^{14} - 385 x^{12} + 815 x^{10} + 1745 x^{8} - 2980 x^{6} + 5420 x^{4} - 8400 x^{2} + 3920$ |
$20$ |
[0,10] |
$2^{20}\cdot 5^{23}\cdot 7^{10}$ |
$3$ |
$33.6817401226$ |
$33.68174012257879$ |
|
✓ |
|
$F_5$ (as 20T5) |
$[2, 2]$ |
$2$ |
$9$ |
$6938252.87449$ |
