| 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 |
| 20.2.627...672.1 |
$x^{20} - 2 x^{19} + 5 x^{17} - x^{16} - 6 x^{15} - 8 x^{14} + 22 x^{13} + 4 x^{12} - 32 x^{11} + 16 x^{10} + 10 x^{9} + 3 x^{8} - 30 x^{7} + 22 x^{6} + 5 x^{5} - 12 x^{4} + 4 x^{3} - 2 x^{2} + 3 x - 1$ |
$20$ |
[2,9] |
$-\,2^{16}\cdot 3^{5}\cdot 13^{14}$ |
$3$ |
$13.7995414981$ |
$20.646295463608727$ |
|
|
? |
$D_{10}:C_4$ (as 20T22) |
trivial |
$2$ |
$10$ |
$1516.67926689$ |
| 20.2.640...000.1 |
$x^{20} - 5 x^{18} + 5 x^{16} - 10 x^{14} + 45 x^{12} + x^{10} - 45 x^{8} - 10 x^{6} - 5 x^{4} - 5 x^{2} - 1$ |
$20$ |
[2,9] |
$-\,2^{28}\cdot 5^{22}$ |
$2$ |
$15.4991898755$ |
$20.6807601406833$ |
|
|
? |
$D_{10}:C_4$ (as 20T22) |
trivial |
$2$ |
$10$ |
$6343.32708051$ |
| 20.4.320...000.1 |
$x^{20} - 72 x^{15} - 712 x^{10} + 288 x^{5} + 16$ |
$20$ |
[4,8] |
$2^{16}\cdot 5^{22}\cdot 29^{5}$ |
$3$ |
$23.729604547$ |
$59.68133104862686$ |
|
|
? |
$D_{10}:C_4$ (as 20T22) |
trivial |
$2$ |
$11$ |
$527936.193913$ |
| 20.0.160...000.1 |
$x^{20} - 5 x^{19} + 10 x^{18} - 25 x^{17} + 70 x^{16} - 51 x^{15} - 50 x^{14} - 235 x^{13} + 895 x^{12} - 180 x^{11} - 384 x^{10} - 1430 x^{9} + 2595 x^{8} + 2575 x^{7} + 5100 x^{6} + 3749 x^{5} + 5420 x^{4} + 2385 x^{3} + 1760 x^{2} + 445 x + 431$ |
$20$ |
[0,10] |
$2^{16}\cdot 5^{23}\cdot 29^{5}$ |
$3$ |
$25.7181071259$ |
$59.68133104862686$ |
|
|
|
$D_{10}:C_4$ (as 20T22) |
$[2]$ |
$2$ |
$9$ |
$615825.309667$ |
| 20.4.191...125.1 |
$x^{20} - 4 x^{15} - 183 x^{10} + 104 x^{5} + 1$ |
$20$ |
[4,8] |
$5^{30}\cdot 29^{5}$ |
$2$ |
$25.9450496413$ |
$65.25330389102201$ |
|
|
|
$D_{10}:C_4$ (as 20T22) |
trivial |
$2$ |
$11$ |
$1748237.43405$ |
| 20.0.955...625.1 |
$x^{20} - 6 x^{15} - 439 x^{10} + 5344 x^{5} + 161051$ |
$20$ |
[0,10] |
$5^{31}\cdot 29^{5}$ |
$2$ |
$28.119202945$ |
$65.25330389102201$ |
|
|
|
$D_{10}:C_4$ (as 20T22) |
$[2]$ |
$2$ |
$9$ |
$2039278.36661$ |
| 20.10.368...000.1 |
$x^{20} - 5 x^{18} - 115 x^{16} - 250 x^{14} + 525 x^{12} + 1201 x^{10} - 525 x^{8} - 250 x^{6} + 115 x^{4} - 5 x^{2} - 1$ |
$20$ |
[10,5] |
$-\,2^{28}\cdot 5^{22}\cdot 7^{8}$ |
$3$ |
$33.7557852041$ |
$54.71614825602517$ |
|
|
? |
$D_{10}:C_4$ (as 20T22) |
trivial |
$2$ |
$14$ |
$79536181.4047$ |
| 20.10.184...000.1 |
$x^{20} - 160 x^{16} + 2360 x^{12} - 4240 x^{8} + 1520 x^{4} - 80$ |
$20$ |
[10,5] |
$-\,2^{28}\cdot 5^{23}\cdot 7^{8}$ |
$3$ |
$36.5844655471$ |
$54.71614825602517$ |
|
|
? |
$D_{10}:C_4$ (as 20T22) |
trivial |
$2$ |
$14$ |
$291170226.718$ |
| 20.2.190...000.1 |
$x^{20} - 5$ |
$20$ |
[2,9] |
$-\,2^{20}\cdot 5^{39}$ |
$2$ |
$46.1340417295$ |
$65.24338750098681$ |
|
|
? |
$D_{10}:C_4$ (as 20T22) |
trivial |
$2$ |
$10$ |
$745710353.59$ |
| 20.20.184...000.1 |
$x^{20} - 5 x^{19} - 30 x^{18} + 160 x^{17} + 330 x^{16} - 1933 x^{15} - 1700 x^{14} + 11500 x^{13} + 4245 x^{12} - 36760 x^{11} - 5160 x^{10} + 65020 x^{9} + 4050 x^{8} - 63410 x^{7} - 3400 x^{6} + 31774 x^{5} + 1655 x^{4} - 6755 x^{3} + 100 x^{2} + 460 x - 41$ |
$20$ |
[20,0] |
$2^{16}\cdot 5^{22}\cdot 7^{8}\cdot 29^{5}$ |
$4$ |
$51.6808581933$ |
$157.90195986798437$ |
|
|
? |
$D_{10}:C_4$ (as 20T22) |
trivial |
$2$ |
$19$ |
$49401883665.9$ |
| 20.0.193...712.1 |
$x^{20} - 5 x^{19} - 11 x^{18} + 83 x^{17} + 56 x^{16} - 700 x^{15} + 105 x^{14} + 2882 x^{13} - 1781 x^{12} - 5757 x^{11} + 7777 x^{10} + 3940 x^{9} - 13469 x^{8} - 7812 x^{7} + 52825 x^{6} - 87721 x^{5} + 99762 x^{4} - 30932 x^{3} + 54617 x^{2} - 18028 x + 20591$ |
$20$ |
[0,10] |
$2^{15}\cdot 17^{14}\cdot 37^{8}$ |
$3$ |
$51.8044934332$ |
$144.0398122329659$ |
✓ |
|
? |
$D_{10}:C_4$ (as 20T22) |
$[4, 20]$ |
$2$ |
$9$ |
$7343104.2357$ |
| 20.20.128...288.1 |
$x^{20} - 3 x^{19} - 38 x^{18} + 109 x^{17} + 461 x^{16} - 1366 x^{15} - 2392 x^{14} + 7958 x^{13} + 5346 x^{12} - 23708 x^{11} - 2958 x^{10} + 37354 x^{9} - 7565 x^{8} - 29683 x^{7} + 13316 x^{6} + 9335 x^{5} - 6991 x^{4} + 252 x^{3} + 780 x^{2} - 208 x + 16$ |
$20$ |
[20,0] |
$2^{16}\cdot 17^{5}\cdot 53^{14}$ |
$3$ |
$56.9415566526$ |
$161.9799865445327$ |
|
|
|
$D_{10}:C_4$ (as 20T22) |
trivial |
$2$ |
$19$ |
$576057394786$ |
| 20.0.185...616.1 |
$x^{20} - 3 x^{19} - 8 x^{18} + 28 x^{17} - x^{16} - 28 x^{15} + 212 x^{14} - 658 x^{13} + 2547 x^{12} - 587 x^{11} + 12252 x^{10} + 10456 x^{9} + 54982 x^{8} + 70259 x^{7} + 186965 x^{6} + 205103 x^{5} + 344870 x^{4} + 251547 x^{3} + 274509 x^{2} + 116534 x + 141499$ |
$20$ |
[0,10] |
$2^{16}\cdot 29^{5}\cdot 53^{14}$ |
$3$ |
$65.0753638061$ |
$211.56113915201115$ |
✓ |
|
? |
$D_{10}:C_4$ (as 20T22) |
$[2, 410]$ |
$2$ |
$9$ |
$7826958.70528$ |
