| 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 |
| 20.0.288...625.1 |
$x^{20} - 3 x^{19} + 3 x^{18} - 6 x^{17} + 12 x^{16} - 4 x^{15} - 6 x^{14} + 7 x^{13} - 34 x^{12} + 26 x^{11} + 68 x^{10} - 96 x^{9} + 19 x^{8} + 44 x^{7} - 12 x^{6} + 26 x^{5} + 23 x^{4} + 4 x^{3} + 5 x^{2} + x + 1$ |
$20$ |
[0,10] |
$3^{10}\cdot 5^{10}\cdot 29^{8}$ |
$3$ |
$14.8937763721$ |
$57.27485888607036$ |
|
|
|
$D_5^2$ (as 20T28) |
trivial |
$6$ |
$9$ |
$9642.05211515$ |
| 20.0.591...625.1 |
$x^{20} - 3 x^{19} + 5 x^{18} - 9 x^{17} + 18 x^{16} - 29 x^{15} + 37 x^{14} - 24 x^{13} + 26 x^{12} - 13 x^{11} + 31 x^{10} - 13 x^{9} + 26 x^{8} - 24 x^{7} + 37 x^{6} - 29 x^{5} + 18 x^{4} - 9 x^{3} + 5 x^{2} - 3 x + 1$ |
$20$ |
[0,10] |
$5^{10}\cdot 7^{10}\cdot 11^{8}$ |
$3$ |
$15.4380021202$ |
$40.28544546409263$ |
|
|
? |
$D_5^2$ (as 20T28) |
trivial |
$2$ |
$9$ |
$4090.28443721$ |
| 20.0.108...625.1 |
$x^{20} - 10 x^{19} + 71 x^{18} - 354 x^{17} + 1498 x^{16} - 5252 x^{15} + 15921 x^{14} - 41161 x^{13} + 91806 x^{12} - 175591 x^{11} + 279549 x^{10} - 360176 x^{9} + 349654 x^{8} - 219873 x^{7} + 5435 x^{6} + 182237 x^{5} - 39506 x^{4} - 227550 x^{3} + 229548 x^{2} - 86247 x + 12321$ |
$20$ |
[0,10] |
$3^{10}\cdot 5^{18}\cdot 37^{10}$ |
$3$ |
$44.8471132483$ |
$85.37338377515825$ |
|
|
|
$D_5^2$ (as 20T28) |
$[16]$ |
$2$ |
$9$ |
$85002563.2373$ |
| 20.0.750...625.1 |
$x^{20} - 5 x^{19} + 5 x^{18} + 30 x^{17} - 460 x^{16} + 1594 x^{15} - 660 x^{14} - 6250 x^{13} + 56490 x^{12} - 105110 x^{11} + 59367 x^{10} + 111430 x^{9} - 1315060 x^{8} + 1129650 x^{7} + 448205 x^{6} + 7848131 x^{5} + 15953485 x^{4} - 43775185 x^{3} - 32489355 x^{2} + 70381245 x + 55238851$ |
$20$ |
[0,10] |
$3^{10}\cdot 5^{26}\cdot 31^{8}$ |
$3$ |
$55.4327354748$ |
$218.93287896315394$ |
|
|
|
$D_5^2$ (as 20T28) |
$[5]$ |
$6$ |
$9$ |
$1625055692.34$ |
| 20.20.516...944.1 |
$x^{20} - 83 x^{18} - 108 x^{17} + 2380 x^{16} + 5760 x^{15} - 27524 x^{14} - 103968 x^{13} + 77348 x^{12} + 735960 x^{11} + 616108 x^{10} - 1615050 x^{9} - 3200232 x^{8} - 714960 x^{7} + 2411685 x^{6} + 1666554 x^{5} - 423490 x^{4} - 635688 x^{3} - 65073 x^{2} + 67764 x + 15313$ |
$20$ |
[20,0] |
$2^{20}\cdot 3^{10}\cdot 7^{10}\cdot 11^{8}\cdot 13^{10}$ |
$5$ |
$86.2319869611$ |
$225.02225229230086$ |
|
|
? |
$D_5^2$ (as 20T28) |
$[2]$ |
$2$ |
$19$ |
$8904025444480$ |
| 20.20.176...000.1 |
$x^{20} - 160 x^{18} + 10790 x^{16} - 372 x^{15} - 400000 x^{14} + 37080 x^{13} + 8908075 x^{12} - 1405800 x^{11} - 122060112 x^{10} + 25437000 x^{9} + 1009834870 x^{8} - 221247000 x^{7} - 4729220200 x^{6} + 784838688 x^{5} + 10914530225 x^{4} - 681612780 x^{3} - 8806862800 x^{2} + 1007795640 x + 916095316$ |
$20$ |
[20,0] |
$2^{20}\cdot 3^{10}\cdot 5^{26}\cdot 61^{8}$ |
$4$ |
$145.339466827$ |
$752.5155812562069$ |
|
|
|
$D_5^2$ (as 20T28) |
trivial |
$2$ |
$19$ |
$9814449721720000$ |
