| 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 |
| 6.4.771142902272.1 |
$x^{6} - 2 x^{5} - 49 x^{4} + 96 x^{3} + 450 x^{2} - 1064 x + 180$ |
$6$ |
[4,1] |
$-\,2^{9}\cdot 197^{4}$ |
$2$ |
$95.7611039994$ |
$161.05033814759088$ |
|
|
? |
$S_6$ (as 6T16) |
trivial |
trivial |
$2$ |
$4$ |
$17066.8338578$ |
| 6.2.3308986242757.1 |
$x^{6} - 2 x^{5} - 9 x^{4} - 220 x^{3} - 954 x^{2} - 605 x - 243$ |
$6$ |
[2,2] |
$13^{3}\cdot 197^{4}$ |
$2$ |
$122.071934484$ |
$122.07193448397432$ |
|
|
? |
$S_6$ (as 6T16) |
$[2, 2]$ |
$[2, 4]$ |
$2$ |
$3$ |
$25155.5836107$ |
| 6.0.2058703036216875.1 |
$x^{6} + 369 x^{4} + 18792 x^{2} - 79785 x + 158787$ |
$6$ |
[0,3] |
$-\,3^{7}\cdot 5^{4}\cdot 197^{4}$ |
$3$ |
$356.669208083$ |
$356.6692080825396$ |
|
|
? |
$S_6$ (as 6T16) |
$[12]$ |
$[12]$ |
$2$ |
$2$ |
$40692.3478334$ |
| 6.2.64023761420374069.1 |
$x^{6} - 2 x^{5} + 29 x^{4} + 1765 x^{3} - 15208 x^{2} + 34176 x + 1162048$ |
$6$ |
[2,2] |
$197^{4}\cdot 349^{3}$ |
$2$ |
$632.494661506$ |
$632.4946615063392$ |
|
|
? |
$S_6$ (as 6T16) |
$[2]$ |
$[4]$ |
$2$ |
$3$ |
$1138337.06574$ |
| 6.0.768254729614695919.1 |
$x^{6} - 3 x^{5} - 181 x^{4} - 1012 x^{3} + 59826 x^{2} + 678346 x + 5433283$ |
$6$ |
[0,3] |
$-\,17^{3}\cdot 47^{3}\cdot 197^{4}$ |
$3$ |
$957.012345943$ |
$957.0123459431567$ |
|
|
? |
$S_6$ (as 6T16) |
$[2, 2, 2]$ |
$[2, 2, 2]$ |
$2$ |
$2$ |
$924170.021059$ |
| 6.6.116...728.1 |
$x^{6} - 2 x^{5} - 2418 x^{4} + 71942 x^{3} - 688504 x^{2} + 1012172 x + 8883170$ |
$6$ |
[6,0] |
$2^{8}\cdot 197^{4}\cdot 1447^{3}$ |
$3$ |
$3245.2767911$ |
$3245.2767911028536$ |
|
|
? |
$S_6$ (as 6T16) |
$[2]$ |
$[2, 2, 4]$ |
$2$ |
$5$ |
$287661241.618$ |
| 6.6.169...968.1 |
$x^{6} - 2 x^{5} - 7434 x^{4} - 337434 x^{3} - 5478042 x^{2} - 36394224 x - 82067567$ |
$6$ |
[6,0] |
$2^{6}\cdot 13^{3}\cdot 197^{4}\cdot 431^{3}$ |
$4$ |
$5068.55843345$ |
$5068.558433445288$ |
|
|
? |
$S_6$ (as 6T16) |
$[2, 2]$ |
$[2, 2, 2, 2]$ |
$2$ |
$5$ |
$1289134533.11$ |
| 9.3.44869371487471.1 |
$x^{9} - 2 x^{8} - 25 x^{7} + 40 x^{6} + 314 x^{5} - 654 x^{4} - 1063 x^{3} + 3528 x^{2} - 2244 x - 1832$ |
$9$ |
[3,3] |
$-\,31^{3}\cdot 197^{4}$ |
$2$ |
$32.8763300542$ |
$188.50592172874553$ |
|
|
|
$(C_3^2:C_3):C_2$ (as 9T12) |
trivial |
trivial |
$2$ |
$5$ |
$3111.74669351$ |
| 9.3.128298900365504.1 |
$x^{9} - x^{7} - 41 x^{6} - 91 x^{5} - 228 x^{4} - 1962 x^{3} - 5281 x^{2} - 5375 x - 1849$ |
$9$ |
[3,3] |
$-\,2^{6}\cdot 11^{3}\cdot 197^{4}$ |
$3$ |
$36.9470974458$ |
$178.2490225931779$ |
|
|
? |
$(C_3^2:C_3):C_2$ (as 9T12) |
trivial |
trivial |
$2$ |
$5$ |
$4827.20122102$ |
| 18.18.160...064.1 |
$x^{18} - 180 x^{16} - 120 x^{15} + 10908 x^{14} + 14544 x^{13} - 272226 x^{12} - 554148 x^{11} + 2822616 x^{10} + 8430032 x^{9} - 7572528 x^{8} - 49832352 x^{7} - 42565071 x^{6} + 65508804 x^{5} + 172725660 x^{4} + 165536736 x^{3} + 83827440 x^{2} + 22353984 x + 2483776$ |
$18$ |
[18,0] |
$2^{18}\cdot 3^{24}\cdot 197^{4}\cdot 229^{6}$ |
$4$ |
$171.271412591$ |
|
|
|
|
$C_3^5:S_4$ (as 18T510) |
trivial |
$[2]$ |
$2$ |
$17$ |
$3509750726440000$ |
| 18.18.290...376.1 |
$x^{18} - 2694 x^{16} - 3336 x^{15} + 2597787 x^{14} + 8641692 x^{13} - 1119005570 x^{12} - 7198543116 x^{11} + 225827964465 x^{10} + 2300154078516 x^{9} - 16615938449916 x^{8} - 292200954101640 x^{7} - 420745662756108 x^{6} + 10758471758781408 x^{5} + 64627251132351120 x^{4} + 123813367121310144 x^{3} + 26830278605886912 x^{2} - 138989639991151872 x - 89792650683453952$ |
$18$ |
[18,0] |
$2^{18}\cdot 3^{24}\cdot 197^{8}\cdot 229^{9}$ |
$4$ |
$1370.47834297$ |
|
|
|
|
$C_3^4:S_4$ (as 18T360) |
$[6]$ |
$[2, 6]$ |
$2$ |
$17$ |
$54573832318800000000000$ |
