| 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 |
Unit signature rank |
| 20.0.287...625.1 |
$x^{20} + 60 x^{18} - 30 x^{17} + 1335 x^{16} - 1338 x^{15} + 13500 x^{14} - 20835 x^{13} + 61200 x^{12} - 129960 x^{11} + 128241 x^{10} - 263250 x^{9} + 351405 x^{8} - 268650 x^{7} + 291060 x^{6} - 233388 x^{5} + 176175 x^{4} - 96795 x^{3} + 43740 x^{2} - 12150 x + 1863$ |
$20$ |
(0, 10) |
$3^{16}\cdot 5^{24}\cdot 257^{5}$ |
$3$ |
$66.5187822132$ |
|
|
|
|
$D_5\wr S_3$ (as 20T361) |
trivial |
trivial |
$2$ |
$9$ |
$24601986064.8$ |
$0$ |
| 20.0.930...125.1 |
$x^{20} - 4 x^{19} - 180 x^{18} + 1861 x^{17} + 41285 x^{16} + 56486 x^{15} - 1770231 x^{14} + 13207675 x^{13} + 539202114 x^{12} + 6259348669 x^{11} + 44724494010 x^{10} + 229585020498 x^{9} + 900899023954 x^{8} + 2784140309493 x^{7} + 6871932187949 x^{6} + 13592479679308 x^{5} + 21415551177601 x^{4} + 26404835212626 x^{3} + 24419514025237 x^{2} + 15370942553698 x + 5232878702531$ |
$20$ |
(0, 10) |
$3^{16}\cdot 5^{15}\cdot 11^{12}\cdot 41^{12}$ |
$4$ |
$315.086961494$ |
$1069.7092235816292$ |
|
|
? |
$C_5\times F_5$ (as 20T29) |
$[5, 5, 5, 1665305]$ |
$[1665305, 5, 5, 5]$ |
$10$ |
$9$ |
$963337255.3397985$ |
$0$ |
| 20.16.952...000.1 |
$x^{20} - 918 x^{18} - 7344 x^{17} - 90096 x^{16} - 1221216 x^{15} + 111989304 x^{14} + 2840588352 x^{13} + 35571067632 x^{12} + 382025328768 x^{11} + 3684361129344 x^{10} + 26573154720768 x^{9} + 132474842966016 x^{8} + 455612562339840 x^{7} + 1095993660764160 x^{6} + 1859636606976000 x^{5} + 2217742480281600 x^{4} + 1820908118016000 x^{3} + 981047033856000 x^{2} + 312506449920000 x + 44643778560000$ |
$20$ |
(16, 2) |
$2^{22}\cdot 3^{16}\cdot 5^{10}\cdot 19\cdot 29^{4}\cdot 89^{5}\cdot 37619^{2}\cdot 225530189^{2}$ |
$8$ |
$1581.03314825$ |
$45372808651.6605$ |
|
|
|
$A_5^4.D_4^2.C_2$ (as 20T1103) |
trivial |
$[2]$ |
$2$ |
$17$ |
$88416176044900000000000000$ |
$15$ |
| 20.14.749...000.1 |
$x^{20} + 1242 x^{18} - 9936 x^{17} + 205944 x^{16} - 2997024 x^{15} - 118141416 x^{14} + 3211627968 x^{13} - 42471188208 x^{12} + 498138452352 x^{11} - 5073841397376 x^{10} + 37296662326272 x^{9} - 186944864523264 x^{8} + 643869446031360 x^{7} - 1549387953008640 x^{6} + 2629118490624000 x^{5} - 3135429023846400 x^{4} + 2574387339264000 x^{3} - 1386997530624000 x^{2} + 441819463680000 x - 63117066240000$ |
$20$ |
(14, 3) |
$-\,2^{22}\cdot 3^{16}\cdot 5^{10}\cdot 29^{5}\cdot 41^{4}\cdot 89^{5}\cdot 8539^{2}\cdot 42434501^{2}$ |
$8$ |
$2475.89022363$ |
$49418019978.615746$ |
|
|
|
$A_5^4.D_4^2.C_2$ (as 20T1103) |
trivial |
trivial |
$2$ |
$16$ |
$5192696267900000000000000000$ |
$14$ |
| 20.16.800...000.1 |
$x^{20} - 918 x^{18} - 7344 x^{17} - 17196 x^{16} - 54816 x^{15} + 75620304 x^{14} + 1820765952 x^{13} + 19737202032 x^{12} + 149523648768 x^{11} + 1038862047744 x^{10} + 6442434413568 x^{9} + 30605856431616 x^{8} + 103882081443840 x^{7} + 249091792220160 x^{6} + 422377445376000 x^{5} + 503672786841600 x^{4} + 413547503616000 x^{3} + 222806163456000 x^{2} + 70973521920000 x + 10139074560000$ |
$20$ |
(16, 2) |
$2^{24}\cdot 3^{16}\cdot 5^{8}\cdot 191^{4}\cdot 2777^{5}\cdot 488797^{2}\cdot 7348603^{2}$ |
$7$ |
$3936.90536556$ |
$186384390602.9628$ |
|
|
|
$A_5^4.C_2^3.S_4$ (as 20T1108) |
trivial |
trivial |
$2$ |
$17$ |
$1689999347120000000000000000000$ |
$16$ |
| 20.0.122...125.1 |
$x^{20} - 78330153 x^{15} + 2737990582811559 x^{10} - 24499004414433966486927 x^{5} + 75302901891158409924316939431$ |
$20$ |
(0, 10) |
$3^{16}\cdot 5^{35}\cdot 31^{12}\cdot 181^{12}$ |
$4$ |
$7150.20794974$ |
$45713.48451303589$ |
|
|
|
$C_5\times F_5$ (as 20T29) |
not computed |
not computed |
$10$ |
$9$ |
|
|
| 20.10.252...000.1 |
$x^{20} - 243 x^{18} - 1944 x^{17} - 316521 x^{16} - 5006016 x^{15} + 2357829 x^{14} + 687073752 x^{13} + 36468620307 x^{12} + 966836217168 x^{11} + 13040667831744 x^{10} + 103736039957568 x^{9} + 531087350603616 x^{8} + 1839245262243840 x^{7} + 4431755367740160 x^{6} + 7522118510976000 x^{5} + 8971012258041600 x^{4} + 7365773615616000 x^{3} + 3968443155456000 x^{2} + 1264122961920000 x + 180588994560000$ |
$20$ |
(10, 5) |
$-\,2^{20}\cdot 3^{16}\cdot 5^{8}\cdot 13^{4}\cdot 53^{4}\cdot 79^{4}\cdot 283^{5}\cdot 193507^{2}\cdot 490226833^{2}$ |
$9$ |
$8320.32419557$ |
|
|
|
? |
$A_5\wr C_2^2.D_6$ (as 20T1092) |
not computed |
not computed |
$2$ |
$14$ |
|
|
| 20.0.154...000.1 |
$x^{20} - 851737518 x^{15} + 2128761163619493418224 x^{10} - 2467172500874840049039927482832 x^{5} + 67777855648151168856132999894099006781776$ |
$20$ |
(0, 10) |
$2^{16}\cdot 3^{16}\cdot 5^{35}\cdot 11^{12}\cdot 41^{12}\cdot 61^{12}$ |
$6$ |
$32316.3523028$ |
$249645.42374627848$ |
|
|
? |
$C_5\times F_5$ (as 20T29) |
not computed |
not computed |
$10$ |
$9$ |
|
|
