| 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 |
| 20.0.333...328.4 |
$x^{20} - 10 x^{18} + 57 x^{16} - 216 x^{14} + 618 x^{12} - 1356 x^{10} + 2274 x^{8} - 2808 x^{6} + 2405 x^{4} - 1274 x^{2} + 325$ |
$20$ |
[0,10] |
$2^{40}\cdot 13^{13}$ |
$2$ |
$21.1896200919$ |
|
|
|
? |
$C_2^9.(C_2\times F_5)$ (as 20T514) |
trivial |
trivial |
$4$ |
$9$ |
$289160.867144$ |
| 20.0.333...328.5 |
$x^{20} - 2 x^{18} - 15 x^{16} + 60 x^{14} + 58 x^{12} - 488 x^{10} + 770 x^{8} - 572 x^{6} + 273 x^{4} - 78 x^{2} + 13$ |
$20$ |
[0,10] |
$2^{40}\cdot 13^{13}$ |
$2$ |
$21.1896200919$ |
|
|
|
? |
$C_2^9.(C_2\times F_5)$ (as 20T514) |
trivial |
trivial |
$4$ |
$9$ |
$752160.226838$ |
| 20.4.513...000.1 |
$x^{20} - 5 x^{18} + 35 x^{16} + 235 x^{14} + 355 x^{12} - 1150 x^{10} + 6145 x^{8} - 50480 x^{6} + 125280 x^{4} - 97600 x^{2} + 11520$ |
$20$ |
[4,8] |
$2^{10}\cdot 5^{23}\cdot 29^{10}$ |
$3$ |
$48.476304162$ |
|
|
|
|
$C_2^9.(C_2\times F_5)$ (as 20T514) |
$[4]$ |
$[2, 4]$ |
$2$ |
$11$ |
$4206423032.7$ |
| 20.4.513...000.2 |
$x^{20} - 5 x^{16} - 185 x^{14} - 1560 x^{12} - 8180 x^{10} - 2445 x^{8} - 19895 x^{6} + 11180 x^{4} - 1575 x^{2} + 20$ |
$20$ |
[4,8] |
$2^{10}\cdot 5^{23}\cdot 29^{10}$ |
$3$ |
$48.476304162$ |
|
|
|
? |
$C_2^9.(C_2\times F_5)$ (as 20T514) |
$[4]$ |
$[2, 4]$ |
$2$ |
$11$ |
$1863737091.17$ |
| 20.0.715...512.1 |
$x^{20} - 8 x^{18} - 3 x^{16} + 96 x^{14} + 1340 x^{12} + 2306 x^{10} + 9695 x^{8} + 11130 x^{6} + 5512 x^{4} + 954 x^{2} + 53$ |
$20$ |
[0,10] |
$2^{38}\cdot 53^{13}$ |
$2$ |
$49.287445176$ |
|
|
|
? |
$C_2^9.(C_2\times F_5)$ (as 20T514) |
trivial |
trivial |
$4$ |
$9$ |
$3197865313.35$ |
| 20.0.715...512.2 |
$x^{20} - 6 x^{18} + 25 x^{16} + 60 x^{14} + 276 x^{12} + 1120 x^{10} - 112 x^{8} - 10176 x^{6} - 3392 x^{4} + 13568 x^{2} + 13568$ |
$20$ |
[0,10] |
$2^{38}\cdot 53^{13}$ |
$2$ |
$49.287445176$ |
|
|
|
? |
$C_2^9.(C_2\times F_5)$ (as 20T514) |
trivial |
trivial |
$4$ |
$9$ |
$2717986108.5$ |
| 20.0.866...552.1 |
$x^{20} - 14 x^{18} + 81 x^{16} - 496 x^{14} + 3674 x^{12} - 4612 x^{10} + 4334 x^{8} - 3456 x^{6} + 8910 x^{4} - 14580 x^{2} + 13122$ |
$20$ |
[0,10] |
$2^{69}\cdot 59^{8}$ |
$2$ |
$55.8334275743336$ |
|
|
|
|
$C_2^9.(C_2\times F_5)$ (as 20T514) |
$[4]$ |
$[4]$ |
$4$ |
$9$ |
$11247636774.983953$ |
| 20.0.866...552.2 |
$x^{20} + 32 x^{16} - 8 x^{14} + 498 x^{12} - 112 x^{10} + 2540 x^{8} - 248 x^{6} + 6706 x^{4} - 10688 x^{2} + 12800$ |
$20$ |
[0,10] |
$2^{69}\cdot 59^{8}$ |
$2$ |
$55.8334275743336$ |
|
|
|
|
$C_2^9.(C_2\times F_5)$ (as 20T514) |
$[4]$ |
$[4]$ |
$4$ |
$9$ |
$9426852324.645239$ |
| 20.0.210...000.2 |
$x^{20} + 110 x^{16} + 220 x^{14} + 2410 x^{12} + 6403 x^{10} - 700 x^{8} - 11380 x^{6} - 4350 x^{4} + 4940 x^{2} + 2645$ |
$20$ |
[0,10] |
$2^{20}\cdot 5^{21}\cdot 29^{10}$ |
$3$ |
$58.3643293027$ |
|
|
|
? |
$C_2^9.(C_2\times F_5)$ (as 20T514) |
$[2]$ |
$[2]$ |
$2$ |
$9$ |
$3420646893.7$ |
| 20.0.210...000.3 |
$x^{20} - 5 x^{18} - 15 x^{16} + 10 x^{14} - 495 x^{12} - 177 x^{10} + 13020 x^{8} + 70510 x^{6} + 199285 x^{4} + 220140 x^{2} + 405$ |
$20$ |
[0,10] |
$2^{20}\cdot 5^{21}\cdot 29^{10}$ |
$3$ |
$58.3643293027$ |
|
|
|
? |
$C_2^9.(C_2\times F_5)$ (as 20T514) |
$[2]$ |
$[2]$ |
$2$ |
$9$ |
$2234987565.71$ |
| 20.8.373...048.1 |
$x^{20} - 8 x^{19} + 14 x^{18} + 2 x^{17} - 21 x^{16} + 150 x^{15} - 17 x^{14} + 740 x^{13} - 313 x^{12} - 734 x^{11} - 2624 x^{10} - 19890 x^{9} - 46542 x^{8} - 150718 x^{7} - 289649 x^{6} - 560672 x^{5} - 1049270 x^{4} - 1489378 x^{3} - 1570892 x^{2} - 568452 x + 101457$ |
$20$ |
[8,6] |
$2^{30}\cdot 17^{13}\cdot 37^{8}$ |
$3$ |
$75.616658507$ |
$144.0398122329659$ |
|
|
? |
$C_2^9.(C_2\times F_5)$ (as 20T514) |
$[2]$ |
$[2, 2, 4]$ |
$2$ |
$13$ |
$156656643998$ |
| 20.8.373...048.2 |
$x^{20} + 2 x^{18} - 55 x^{16} - 86 x^{14} + 948 x^{12} + 1172 x^{10} - 5389 x^{8} - 6110 x^{6} + 6155 x^{4} + 5026 x^{2} + 17$ |
$20$ |
[8,6] |
$2^{30}\cdot 17^{13}\cdot 37^{8}$ |
$3$ |
$75.616658507$ |
$144.0398122329659$ |
|
|
? |
$C_2^9.(C_2\times F_5)$ (as 20T514) |
$[2]$ |
$[2, 2, 4]$ |
$2$ |
$13$ |
$169966877653$ |
| 20.12.382...152.5 |
$x^{20} - 64 x^{18} + 1244 x^{16} - 6262 x^{14} - 20928 x^{12} + 216742 x^{10} - 261295 x^{8} - 616048 x^{6} + 352190 x^{4} + 96316 x^{2} + 4913$ |
$20$ |
[12,4] |
$2^{40}\cdot 17^{13}\cdot 37^{8}$ |
$3$ |
$106.938104002$ |
|
|
|
? |
$C_2^9.(C_2\times F_5)$ (as 20T514) |
$[2]$ |
$[2, 2, 2]$ |
$2$ |
$15$ |
$12316530469600$ |
| 20.12.382...152.6 |
$x^{20} - 2 x^{18} - 55 x^{16} + 86 x^{14} + 948 x^{12} - 1172 x^{10} - 5389 x^{8} + 6110 x^{6} + 6155 x^{4} - 5026 x^{2} + 17$ |
$20$ |
[12,4] |
$2^{40}\cdot 17^{13}\cdot 37^{8}$ |
$3$ |
$106.938104002$ |
|
|
|
? |
$C_2^9.(C_2\times F_5)$ (as 20T514) |
$[2]$ |
$[2, 2, 2]$ |
$2$ |
$15$ |
$11885863991700$ |
| 20.8.147...768.1 |
$x^{20} - 8 x^{19} + 150 x^{17} - 1580 x^{16} + 5238 x^{15} - 11051 x^{14} + 43096 x^{13} - 85652 x^{12} + 77444 x^{11} - 139309 x^{10} + 276316 x^{9} - 152464 x^{8} - 214016 x^{7} + 244692 x^{6} - 169056 x^{5} + 401768 x^{4} - 229984 x^{3} - 143344 x^{2} + 338560 x - 55008$ |
$20$ |
[8,6] |
$2^{30}\cdot 17^{15}\cdot 37^{10}$ |
$3$ |
$144.039812233$ |
$144.0398122329659$ |
|
|
|
$C_2^9.(C_2\times F_5)$ (as 20T514) |
$[2, 2, 4]$ |
$[2, 2, 2, 2, 4]$ |
$2$ |
$13$ |
$47373886869200$ |
| 20.4.880...000.1 |
$x^{20} - 3 x^{19} + 40 x^{18} - 181 x^{17} + 841 x^{16} - 194 x^{15} + 1074 x^{14} + 30360 x^{13} + 320397 x^{12} + 1560717 x^{11} - 16890604 x^{10} - 132762069 x^{9} - 350420257 x^{8} + 359904304 x^{7} + 3834503596 x^{6} + 5441937864 x^{5} + 4046304043 x^{4} + 17243701331 x^{3} + 39990596926 x^{2} + 71285646067 x + 68189268923$ |
$20$ |
[4,8] |
$2^{28}\cdot 5^{4}\cdot 17^{10}\cdot 53^{13}$ |
$4$ |
$198.2621314061775$ |
|
|
|
|
$C_2^9.(C_2\times F_5)$ (as 20T514) |
$[12]$ |
$[2, 2, 12]$ |
$2$ |
$11$ |
$732001283460072.0$ |
| 20.12.151...432.1 |
$x^{20} - 96 x^{18} - 176 x^{17} + 2870 x^{16} + 10360 x^{15} - 28042 x^{14} - 184752 x^{13} + 111169 x^{12} + 1772048 x^{11} + 631684 x^{10} - 7766168 x^{9} - 10707318 x^{8} + 6419272 x^{7} + 9808326 x^{6} - 40973352 x^{5} - 63404238 x^{4} + 8257920 x^{3} + 52708296 x^{2} + 20662004 x - 894183$ |
$20$ |
[12,4] |
$2^{40}\cdot 17^{15}\cdot 37^{10}$ |
$3$ |
$203.703055982$ |
|
|
|
|
$C_2^9.(C_2\times F_5)$ (as 20T514) |
$[2, 2, 4]$ |
$[2, 2, 2, 4, 8]$ |
$2$ |
$15$ |
$8760698272700000$ |
| 20.8.300...712.1 |
$x^{20} - 3 x^{19} - 31 x^{18} - 424 x^{17} - 50490 x^{16} + 148632 x^{15} - 3095720 x^{14} + 80267364 x^{13} + 134269264 x^{12} + 2219734044 x^{11} - 667495188 x^{10} - 134557962776 x^{9} + 347124615896 x^{8} - 2259527805632 x^{7} + 22709966637424 x^{6} - 112005813727248 x^{5} + 341056511522832 x^{4} - 476229216922064 x^{3} - 360470262080048 x^{2} + 1743705769309888 x - 1307059837940608$ |
$20$ |
[8,6] |
$2^{32}\cdot 17^{10}\cdot 53^{13}\cdot 191^{4}$ |
$4$ |
$471.9091981803476$ |
$9555.635948439745$ |
|
|
|
$C_2^9.(C_2\times F_5)$ (as 20T514) |
not computed |
not computed |
$2$ |
$13$ |
|
| 20.16.215...048.1 |
$x^{20} - 1798 x^{18} + 843127 x^{16} - 28023808 x^{14} - 12383777697 x^{12} + 1240898508376 x^{10} - 38325097442182 x^{8} + 50105160738736 x^{6} + 16863332357374268 x^{4} - 226333808273006296 x^{2} + 258940718108698448$ |
$20$ |
[16,2] |
$2^{40}\cdot 17^{10}\cdot 53^{15}\cdot 191^{4}$ |
$4$ |
$926.185606848$ |
|
|
|
|
$C_2^9.(C_2\times F_5)$ (as 20T514) |
$[4]$ |
$[4, 2, 2, 2, 2, 2]$ |
$2$ |
$17$ |
$119234213165000000000000$ |
| 20.0.275...328.1 |
$x^{20} + 11250 x^{18} + 49726769 x^{16} + 108516071358 x^{14} + 120175634897318 x^{12} + 62880691449580556 x^{10} + 14226438381306917489 x^{8} + 1192196572528720193714 x^{6} + 31559592224192628597233 x^{4} + 141850934847386056622446 x^{2} + 119590625533399526082737$ |
$20$ |
[0,10] |
$2^{50}\cdot 17^{13}\cdot 37^{8}\cdot 71^{4}\cdot 4079^{4}$ |
$5$ |
$1870.72473458$ |
|
✓ |
|
? |
$C_2^9.(C_2\times F_5)$ (as 20T514) |
not computed |
not computed |
$2$ |
$9$ |
|
| 20.0.275...328.2 |
$x^{20} + 15950 x^{18} + 88517431 x^{16} + 247371025408 x^{14} + 393253100213225 x^{12} + 367328047710193800 x^{10} + 195959151530074189063 x^{8} + 53859086490382921644938 x^{6} + 6037536774804319840715464 x^{4} + 261706390585087500268651328 x^{2} + 3335262955500979382921452193$ |
$20$ |
[0,10] |
$2^{50}\cdot 17^{13}\cdot 37^{8}\cdot 71^{4}\cdot 4079^{4}$ |
$5$ |
$1870.72473458$ |
|
✓ |
|
? |
$C_2^9.(C_2\times F_5)$ (as 20T514) |
not computed |
not computed |
$2$ |
$9$ |
|
