| 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 |
Max $p$ |
| 20.0.152...384.1 |
$x^{20} - 2 x^{19} + 6 x^{18} - 8 x^{17} + 16 x^{16} - 14 x^{15} + 32 x^{14} - 12 x^{13} + 32 x^{12} + 8 x^{11} + 48 x^{10} - 16 x^{9} + 48 x^{8} + 8 x^{7} + 24 x^{6} + 8 x^{5} + 32 x^{4} + 16 x^{3} + 32 x^{2} + 16 x + 16$ |
$20$ |
(0, 10) |
$2^{16}\cdot 3^{10}\cdot 89^{8}$ |
$3$ |
$18.1610363028$ |
$28.44982682753188$ |
|
|
|
$S_5$ (as 20T32) |
$[2]$ |
$[2]$ |
$6$ |
$9$ |
$64033.5089322$ |
$0$ |
$89$ |
| 20.4.288...000.1 |
$x^{20} - 5 x^{18} - 2 x^{17} + 5 x^{16} + 8 x^{15} + 2 x^{14} - 16 x^{13} + 21 x^{12} + 28 x^{11} - 119 x^{10} - 150 x^{9} + 61 x^{8} + 164 x^{7} + 62 x^{6} - 4 x^{5} + 149 x^{4} + 396 x^{3} + 327 x^{2} + 58 x - 31$ |
$20$ |
(4, 8) |
$2^{36}\cdot 3^{16}\cdot 5^{10}$ |
$3$ |
$18.7514993051$ |
$24.1776264427508$ |
|
|
|
$S_5$ (as 20T32) |
trivial |
trivial |
$2$ |
$11$ |
$110122.225791$ |
$4$ |
$5$ |
| 20.0.161...144.1 |
$x^{20} - 3 x^{19} + 12 x^{18} - 23 x^{17} + 66 x^{16} - 117 x^{15} + 222 x^{14} - 297 x^{13} + 411 x^{12} - 454 x^{11} + 456 x^{10} - 312 x^{9} + 147 x^{8} + 69 x^{7} - 150 x^{6} + 127 x^{5} - 78 x^{4} + 21 x^{3} + 16 x^{2} - 15 x + 9$ |
$20$ |
(0, 10) |
$2^{16}\cdot 3^{22}\cdot 23^{8}$ |
$3$ |
$20.4337704904$ |
$30.08357041040144$ |
|
|
|
$S_5$ (as 20T32) |
$[2]$ |
$[2]$ |
$6$ |
$9$ |
$314083.885561$ |
$0$ |
$23$ |
| 20.4.163...000.1 |
$x^{20} - 10 x^{19} + 45 x^{18} - 120 x^{17} + 215 x^{16} - 292 x^{15} + 350 x^{14} - 400 x^{13} + 385 x^{12} - 230 x^{11} + 11 x^{10} + 60 x^{9} + 55 x^{8} - 140 x^{7} + 90 x^{6} - 20 x^{5} + 25 x^{4} - 50 x^{3} - 75 x^{2} + 100 x - 25$ |
$20$ |
(4, 8) |
$2^{36}\cdot 5^{22}$ |
$2$ |
$20.4513036513$ |
$28.57900880593445$ |
|
|
|
$S_5$ (as 20T32) |
trivial |
trivial |
$2$ |
$11$ |
$331332.875442$ |
$4$ |
$5$ |
| 20.20.850...000.1 |
$x^{20} - 4 x^{19} - 33 x^{18} + 120 x^{17} + 468 x^{16} - 1392 x^{15} - 3799 x^{14} + 8012 x^{13} + 19008 x^{12} - 23720 x^{11} - 57969 x^{10} + 31228 x^{9} + 101057 x^{8} - 964 x^{7} - 86922 x^{6} - 33928 x^{5} + 22258 x^{4} + 19672 x^{3} + 5396 x^{2} + 600 x + 20$ |
$20$ |
(20, 0) |
$2^{36}\cdot 5^{10}\cdot 103^{8}$ |
$3$ |
$49.7134478267$ |
$101.89087030315206$ |
|
|
|
$S_5$ (as 20T32) |
trivial |
$[2, 2]$ |
$2$ |
$19$ |
$70785617543.0$ |
$18$ |
$103$ |
| 20.20.500...841.1 |
$x^{20} - 8 x^{19} - 30 x^{18} + 396 x^{17} - 172 x^{16} - 6657 x^{15} + 12415 x^{14} + 48573 x^{13} - 145810 x^{12} - 136440 x^{11} + 758752 x^{10} - 106552 x^{9} - 1920339 x^{8} + 1396889 x^{7} + 2101035 x^{6} - 2676014 x^{5} - 273208 x^{4} + 1559242 x^{3} - 729758 x^{2} + 126529 x - 7417$ |
$20$ |
(20, 0) |
$29^{10}\cdot 431^{8}$ |
$2$ |
$60.9522731792$ |
$111.79892664958818$ |
|
|
? |
$S_5$ (as 20T32) |
trivial |
$[2, 2, 2, 2]$ |
$2$ |
$19$ |
$479833200273$ |
$16$ |
$431$ |
