| 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 |
| 15.1.957834337125359375.1 |
$x^{15} - 6 x^{14} + 23 x^{13} - 67 x^{12} + 156 x^{11} - 307 x^{10} + 523 x^{9} - 771 x^{8} + 994 x^{7} - 1103 x^{6} + 1049 x^{5} - 854 x^{4} + 579 x^{3} - 288 x^{2} + 89 x - 13$ |
$15$ |
[1,7] |
$-\,5^{6}\cdot 11^{2}\cdot 47^{7}$ |
$3$ |
$15.8034786282$ |
$99.14954417983068$ |
|
|
? |
$C_3^4:D_{15}$ (as 15T45) |
trivial |
$2$ |
$7$ |
$738.167831427$ |
| 15.1.957834337125359375.2 |
$x^{15} - 5 x^{14} + 15 x^{13} - 37 x^{12} + 74 x^{11} - 137 x^{10} + 207 x^{9} - 292 x^{8} + 353 x^{7} - 407 x^{6} + 396 x^{5} - 334 x^{4} + 222 x^{3} - 121 x^{2} + 44 x - 11$ |
$15$ |
[1,7] |
$-\,5^{6}\cdot 11^{2}\cdot 47^{7}$ |
$3$ |
$15.8034786282$ |
$99.14954417983068$ |
|
|
? |
$C_3^4:D_{15}$ (as 15T45) |
trivial |
$2$ |
$7$ |
$722.408081993$ |
| 15.15.100...329.1 |
$x^{15} - 792 x^{13} - 3168 x^{12} + 243000 x^{11} + 1944000 x^{10} - 32510241 x^{9} - 436778892 x^{8} + 928289646 x^{7} + 40476996000 x^{6} + 179367970671 x^{5} - 864514862676 x^{4} - 11710445044896 x^{3} - 49581395118720 x^{2} - 99162790237440 x - 79330232189952$ |
$15$ |
[15,0] |
$3^{20}\cdot 251^{2}\cdot 401^{7}\cdot 5227^{2}$ |
$4$ |
$464.179414505$ |
|
|
|
? |
$C_3^4:D_{15}$ (as 15T45) |
trivial |
$2$ |
$14$ |
$2223174963210000$ |
| 15.15.223...761.1 |
$x^{15} - 564 x^{13} - 1318 x^{12} + 106245 x^{11} + 437550 x^{10} - 8513738 x^{9} - 51480954 x^{8} + 250121274 x^{7} + 2496923998 x^{6} + 1781931375 x^{5} - 37671758364 x^{4} - 152139299988 x^{3} - 246875970600 x^{2} - 177750698832 x - 44516048032$ |
$15$ |
[15,0] |
$3^{20}\cdot 401^{7}\cdot 19593331^{2}$ |
$3$ |
$665.646240585$ |
|
|
|
? |
$C_3^4:D_{15}$ (as 15T45) |
trivial |
$2$ |
$14$ |
$35897750262200000$ |
| 15.15.451...249.1 |
$x^{15} - 2 x^{14} - 124138 x^{13} + 1235866 x^{12} + 5955127078 x^{11} - 104730005071 x^{10} - 141955750462242 x^{9} + 3418847184643525 x^{8} + 1782222460765321517 x^{7} - 52379504340376407643 x^{6} - 11129662305379896194779 x^{5} + 375379315225041436764775 x^{4} + 25766502740381844669792909 x^{3} - 995500128685782581696023016 x^{2} + 10254882718425670179686629118 x - 32238836503753136480573122489$ |
$15$ |
[15,0] |
$3^{12}\cdot 251^{6}\cdot 401^{7}\cdot 5227^{6}$ |
$4$ |
$11057.786478541844$ |
$1692018.9836514206$ |
|
|
? |
$C_3^4:D_{15}$ (as 15T45) |
not computed |
$2$ |
$14$ |
|
