| 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 |
| 15.1.794...688.1 |
$x^{15} - 5 x^{14} - 13 x^{13} - 25 x^{12} + 1066 x^{11} - 3852 x^{10} + 17727 x^{9} - 161749 x^{8} + 746379 x^{7} - 1641741 x^{6} + 1741752 x^{5} - 4012116 x^{4} + 41364864 x^{3} - 183172288 x^{2} + 369095680 x - 409279744$ |
$15$ |
[1,7] |
$-\,2^{14}\cdot 19^{8}\cdot 433^{7}$ |
$3$ |
$156.071738514$ |
$438.8103116988051$ |
|
|
|
$C_5^3:S_4$ (as 15T48) |
$[2]$ |
$2$ |
$7$ |
$463572992103$ |
| 15.7.110...749.1 |
$x^{15} - 3 x^{14} - 15691 x^{13} + 215385 x^{12} + 38842907 x^{11} + 1106306238 x^{10} - 27717468995 x^{9} - 2380181235483 x^{8} - 57828570766468 x^{7} + 35582772872952 x^{6} + 31236364450391152 x^{5} + 927255109184758544 x^{4} + 15819541345795830848 x^{3} + 172778346922476550912 x^{2} + 1061857604265640723456 x + 2664795024960878546944$ |
$15$ |
[7,4] |
$229^{7}\cdot 541^{4}\cdot 250229701^{4}$ |
$3$ |
$11739.9484783$ |
$12165967132.34205$ |
|
|
? |
$C_5^3:S_4$ (as 15T48) |
$[5]$ |
$2$ |
$10$ |
$1682212466290000000000000$ |
| 15.1.186...504.1 |
$x^{15} - 18994 x^{13} - 1133008 x^{12} + 86964215 x^{11} + 13103162268 x^{10} + 533228094032 x^{9} - 11160258257892 x^{8} - 2566914340949249 x^{7} - 162578031975372552 x^{6} - 6359731734673496810 x^{5} - 173115997374755324728 x^{4} - 3394681526819160320279 x^{3} - 47733821804558780746772 x^{2} - 450826849981549178240020 x - 2414037401865775754839444$ |
$15$ |
[1,7] |
$-\,2^{14}\cdot 11^{7}\cdot 911^{4}\cdot 1181^{4}\cdot 2570851^{4}$ |
$5$ |
$12155.4198506$ |
$121821044980.7401$ |
|
|
|
$C_5^3:S_4$ (as 15T48) |
$[5, 5]$ |
$2$ |
$7$ |
$907073932516000000000000$ |
