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 |
15.5.696...743.1 |
$x^{15} - 5 x^{14} + 21 x^{13} - 43 x^{12} - 108 x^{11} + 528 x^{10} - 737 x^{9} + 60 x^{8} + 1108 x^{7} - 920 x^{6} - 290 x^{5} + 1067 x^{4} - 91 x^{3} - 30 x^{2} + 16 x - 8$ |
$15$ |
[5,5] |
$-\,23^{5}\cdot 101^{8}$ |
$2$ |
$33.3334816772$ |
$192.45137442657924$ |
|
|
|
$(C_5^2 : C_3):C_2$ (as 15T13) |
trivial |
$2$ |
$9$ |
$577959.629224$ |
15.5.383...375.1 |
$x^{15} - 30 x^{13} - 45 x^{12} + 230 x^{11} + 871 x^{10} + 750 x^{9} - 2445 x^{8} - 8010 x^{7} - 9505 x^{6} - 3026 x^{5} + 8475 x^{4} + 9910 x^{3} + 4635 x^{2} - 2935 x - 2521$ |
$15$ |
[5,5] |
$-\,5^{24}\cdot 23^{5}$ |
$2$ |
$37.347478473$ |
$105.41109538118516$ |
|
|
|
$(C_5^2 : C_3):C_2$ (as 15T13) |
trivial |
$2$ |
$9$ |
$2022515.38523$ |
15.5.151...183.1 |
$x^{15} - 4 x^{14} - 221 x^{13} + 88 x^{12} + 18939 x^{11} + 53340 x^{10} - 589284 x^{9} - 3408587 x^{8} - 355479 x^{7} + 28046861 x^{6} + 17660016 x^{5} - 107839033 x^{4} - 56728994 x^{3} + 155082226 x^{2} + 86703126 x - 114198011$ |
$15$ |
[5,5] |
$-\,23^{5}\cdot 191^{12}$ |
$2$ |
$189.99228785129813$ |
$320.39860152359097$ |
|
|
|
$(C_5^2 : C_3):C_2$ (as 15T13) |
$[5]$ |
$2$ |
$9$ |
$61784107320.743546$ |
15.15.203...928.1 |
$x^{15} - 3 x^{14} - 892509 x^{13} - 89072821 x^{12} + 291116427176 x^{11} + 53550385971468 x^{10} - 40168727583503152 x^{9} - 10310407818341917488 x^{8} + 1941351085012979462976 x^{7} + 696538506670849818021440 x^{6} + 5760971201312575426356160 x^{5} - 8381661447592221588178895680 x^{4} - 75264948123079550954015902464 x^{3} + 16384877146005349721822978906880 x^{2} - 103562164349148797000704434199808 x - 51309930300889700898010228382464$ |
$15$ |
[15,0] |
$2^{10}\cdot 37^{5}\cdot 701^{12}\cdot 1061^{12}$ |
$4$ |
$263370.600094$ |
$480766.5543166904$ |
|
|
|
$(C_5^2 : C_3):C_2$ (as 15T13) |
not computed |
$2$ |
$14$ |
|