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 |
30.0.131...536.1 |
$x^{30} + 6 x^{28} + 25 x^{26} + 45 x^{24} - 44 x^{22} - 197 x^{20} - 20 x^{18} + 411 x^{16} + 283 x^{14} - 424 x^{12} - 397 x^{10} + 348 x^{8} + 358 x^{6} + 8 x^{4} - 7 x^{2} + 1$ |
$30$ |
[0,15] |
$-\,2^{40}\cdot 11^{26}$ |
$2$ |
$20.13323926187899$ |
$21.808547634345086$ |
|
|
? |
$S_3\times C_{10}$ (as 30T12) |
trivial |
$4$ |
$14$ |
$18931497.119988322$ |
30.10.144...896.1 |
$x^{30} - 15 x^{28} + 104 x^{26} - 482 x^{24} + 1708 x^{22} - 4753 x^{20} + 10608 x^{18} - 18925 x^{16} + 26563 x^{14} - 28460 x^{12} + 22463 x^{10} - 12716 x^{8} + 5049 x^{6} - 1331 x^{4} + 198 x^{2} - 11$ |
$30$ |
[10,10] |
$2^{40}\cdot 11^{27}$ |
$2$ |
$21.808547634345086$ |
$21.808547634345086$ |
|
|
? |
$S_3\times C_{10}$ (as 30T12) |
trivial |
$2$ |
$19$ |
$397294072.2356694$ |
30.0.218...571.1 |
$x^{30} - x^{29} - 7 x^{28} + 10 x^{27} + 7 x^{26} - 19 x^{25} + 56 x^{24} - 38 x^{23} - 238 x^{22} + 196 x^{21} + 1084 x^{20} + 255 x^{19} - 3219 x^{18} - 4472 x^{17} + 2252 x^{16} + 12483 x^{15} + 13641 x^{14} + 1966 x^{13} - 11281 x^{12} - 13340 x^{11} - 5077 x^{10} + 3378 x^{9} + 6156 x^{8} + 4833 x^{7} + 3411 x^{6} + 3672 x^{5} + 4671 x^{4} + 4536 x^{3} + 2997 x^{2} + 1215 x + 243$ |
$30$ |
[0,15] |
$-\,3^{10}\cdot 7^{10}\cdot 11^{27}$ |
$3$ |
$23.877737944442764$ |
$39.66094555677728$ |
|
|
? |
$S_3\times C_{10}$ (as 30T12) |
trivial |
$22$ |
$14$ |
$2830009383.1065817$ |
30.10.531...753.1 |
$x^{30} - 7 x^{29} + 24 x^{28} - 23 x^{27} - 141 x^{26} + 633 x^{25} - 1481 x^{24} + 2556 x^{23} - 3432 x^{22} + 2970 x^{21} + 2520 x^{20} - 16434 x^{19} + 36814 x^{18} - 58793 x^{17} + 75906 x^{16} - 86484 x^{15} + 87441 x^{14} - 74977 x^{13} + 56249 x^{12} - 35409 x^{11} + 19416 x^{10} - 7865 x^{9} + 726 x^{8} + 1323 x^{7} - 1451 x^{6} + 413 x^{5} - 168 x^{4} + 17 x^{3} - 15 x^{2} + x + 1$ |
$30$ |
[10,10] |
$3^{15}\cdot 7^{10}\cdot 11^{27}$ |
$3$ |
$28.6756579034896$ |
$39.66094555677728$ |
|
|
? |
$S_3\times C_{10}$ (as 30T12) |
trivial |
$2$ |
$19$ |
$26520700757.33144$ |