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 |
20.0.330...961.1 |
$x^{20} - 2 x^{19} + 4 x^{18} - 6 x^{17} + 10 x^{16} - 15 x^{15} + 21 x^{14} - 27 x^{13} + 37 x^{12} - 34 x^{11} + 47 x^{10} - 34 x^{9} + 37 x^{8} - 27 x^{7} + 21 x^{6} - 15 x^{5} + 10 x^{4} - 6 x^{3} + 4 x^{2} - 2 x + 1$ |
$20$ |
[0,10] |
$653^{8}$ |
$1$ |
$13.3648864263$ |
$25.553864678361276$ |
|
|
? |
$C_2\times A_5$ (as 20T36) |
trivial |
$2$ |
$9$ |
$932.282807106$ |
20.4.436...184.1 |
$x^{20} - 8 x^{16} - 22 x^{14} - 6 x^{12} + 22 x^{10} + 33 x^{8} - 22 x^{6} + 19 x^{4} - 2 x^{2} + 1$ |
$20$ |
[4,8] |
$2^{30}\cdot 67^{8}$ |
$2$ |
$15.2045970343$ |
$23.15167380558045$ |
|
|
? |
$C_2\times A_5$ (as 20T36) |
trivial |
$2$ |
$11$ |
$7917.88619089$ |
20.0.865...744.1 |
$x^{20} + 2 x^{18} - 2 x^{17} + 4 x^{16} - 4 x^{15} - 14 x^{13} + 9 x^{12} - 2 x^{11} + 6 x^{10} - 2 x^{9} + 7 x^{8} - 12 x^{7} + 26 x^{6} - 28 x^{5} + 19 x^{4} - 20 x^{3} + 24 x^{2} - 16 x + 4$ |
$20$ |
[0,10] |
$2^{30}\cdot 73^{8}$ |
$2$ |
$15.7352677614$ |
$24.166091947189145$ |
|
|
? |
$C_2\times A_5$ (as 20T36) |
trivial |
$2$ |
$9$ |
$15341.0740173$ |
20.4.250...256.1 |
$x^{20} + 6 x^{18} + 11 x^{16} - 2 x^{14} - 43 x^{12} - 102 x^{10} - 146 x^{8} - 134 x^{6} - 84 x^{4} - 32 x^{2} + 1$ |
$20$ |
[4,8] |
$2^{32}\cdot 17^{12}$ |
$2$ |
$16.5927108803$ |
$22.238309660442344$ |
|
|
? |
$C_2\times A_5$ (as 20T36) |
trivial |
$2$ |
$11$ |
$28505.6799029$ |
20.0.922...641.1 |
$x^{20} - 4 x^{19} + 11 x^{18} - 21 x^{17} + 35 x^{16} - 50 x^{15} + 65 x^{14} - 77 x^{13} + 79 x^{12} - 81 x^{11} + 87 x^{10} - 162 x^{9} + 316 x^{8} - 616 x^{7} + 1040 x^{6} - 1600 x^{5} + 2240 x^{4} - 2688 x^{3} + 2816 x^{2} - 2048 x + 1024$ |
$20$ |
[0,10] |
$19^{8}\cdot 293^{8}$ |
$2$ |
$31.4954986391$ |
$74.61233142048303$ |
✓ |
|
? |
$C_2\times A_5$ (as 20T36) |
trivial |
$2$ |
$9$ |
$3891860.51282$ |
20.0.227...281.1 |
$x^{20} - 3 x^{19} + 10 x^{18} - 26 x^{17} + 59 x^{16} - 129 x^{15} + 241 x^{14} - 438 x^{13} + 729 x^{12} - 1124 x^{11} + 1669 x^{10} - 2248 x^{9} + 2916 x^{8} - 3504 x^{7} + 3856 x^{6} - 4128 x^{5} + 3776 x^{4} - 3328 x^{3} + 2560 x^{2} - 1536 x + 1024$ |
$20$ |
[0,10] |
$8311^{8}$ |
$1$ |
$36.9710098151$ |
$91.16468614545876$ |
✓ |
|
? |
$C_2\times A_5$ (as 20T36) |
$[4]$ |
$2$ |
$9$ |
$10106391.1313$ |
20.20.333...401.1 |
$x^{20} - 6 x^{19} - 16 x^{18} + 121 x^{17} + 95 x^{16} - 933 x^{15} - 226 x^{14} + 3630 x^{13} - 25 x^{12} - 7849 x^{11} + 1238 x^{10} + 9696 x^{9} - 2643 x^{8} - 6638 x^{7} + 2522 x^{6} + 2214 x^{5} - 1128 x^{4} - 209 x^{3} + 182 x^{2} - 26 x + 1$ |
$20$ |
[20,0] |
$19^{10}\cdot 293^{8}$ |
$2$ |
$42.27891647$ |
$74.61233142048303$ |
|
|
? |
$C_2\times A_5$ (as 20T36) |
trivial |
$2$ |
$19$ |
$6609693766.39$ |
20.20.117...321.1 |
$x^{20} - 29 x^{18} + 296 x^{16} - 1485 x^{14} + 4169 x^{12} - 6905 x^{10} + 6821 x^{8} - 3925 x^{6} + 1212 x^{4} - 157 x^{2} + 1$ |
$20$ |
[20,0] |
$13613^{8}$ |
$1$ |
$45.0382531653$ |
$116.67476162392619$ |
|
|
? |
$C_2\times A_5$ (as 20T36) |
trivial |
$2$ |
$19$ |
$10159591011.6$ |