| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 5.15.18.11 |
$15$ |
$x^{15} - 60 x^{12} + 300 x^{11} + 1815 x^{10} - 75 x^{9} - 13500 x^{8} - 29850 x^{7} - 13125 x^{6} + 9075 x^{5} + 14625 x^{4} - 1500 x^{2} + 125$ |
$5$ |
$5$ |
$3$ |
$18$ |
$(C_5^2 : C_3):C_2$ (as 15T12) |
$3$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + 10 t x^{3} + \left(10 t^{2} + 15 t\right) x^{2} + 5$ |
$[2, 0]$ |
$[1]$ |
| 5.15.18.20 |
$15$ |
$x^{15} + 60 x^{13} + 1275 x^{11} + 615 x^{10} + 10325 x^{9} + 8100 x^{8} + 6000 x^{7} - 17625 x^{6} + 3075 x^{5} + 6000 x^{4} + 1500 x^{3} + 125$ |
$5$ |
$5$ |
$3$ |
$18$ |
$(C_5^2 : C_3):C_2$ (as 15T12) |
$3$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t + 20\right) x^{3} + 20 t x^{2} + 5$ |
$[2, 0]$ |
$[1]$ |
| 5.15.18.4 |
$15$ |
$x^{15} + 30 x^{13} - 90 x^{12} + 375 x^{11} - 285 x^{10} + 7675 x^{9} + 2550 x^{8} + 41100 x^{7} + 50875 x^{6} - 1425 x^{5} + 31500 x^{4} + 750 x^{3} - 2250 x^{2} + 125$ |
$5$ |
$5$ |
$3$ |
$18$ |
$(C_5^2 : C_3):C_2$ (as 15T12) |
$3$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t + 10\right) x^{3} + \left(20 t^{2} + 20 t + 10\right) x^{2} + 5$ |
$[2, 0]$ |
$[1]$ |
| 5.15.18.6 |
$15$ |
$x^{15} - 75 x^{12} + 75 x^{11} + 690 x^{10} + 825 x^{9} + 375 x^{8} - 7500 x^{7} + 38750 x^{6} + 3450 x^{5} + 6000 x^{4} - 1875 x^{2} + 125$ |
$5$ |
$5$ |
$3$ |
$18$ |
$(C_5^2 : C_3):C_2$ (as 15T12) |
$3$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{3}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + 5 t x^{3} + \left(15 t^{2} + 5\right) x^{2} + 5$ |
$[2, 0]$ |
$[1]$ |
| 5.15.24.27 |
$15$ |
$x^{15} - 75 x^{13} + 1375 x^{12} - 585 x^{10} - 1875 x^{9} + 102750 x^{8} + 108450 x^{5} + 2259375 x^{4} + 7260125$ |
$5$ |
$5$ |
$3$ |
$24$ |
$(C_5^2 : C_3):C_2$ (as 15T12) |
$6$ |
$1$ |
$[2]$ |
$[2, 2]^{6}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t^{2} + 10\right) x^{4} + 100 t^{2} + 25 t + 5$ |
$[4, 0]$ |
$[2]$ |
| 5.15.24.41 |
$15$ |
$x^{15} - 30 x^{14} + 2325 x^{13} - 27375 x^{12} - 360 x^{10} + 22200 x^{9} + 73500 x^{8} + 13200 x^{5} + 1518000 x^{4} + 12872000$ |
$5$ |
$5$ |
$3$ |
$24$ |
$(C_5^2 : C_3):C_2$ (as 15T12) |
$6$ |
$1$ |
$[2]$ |
$[2, 2]^{6}$ |
$t^{3} + 3 t + 3$ |
$x^{5} + \left(5 t^{2} + 20 t\right) x^{4} + 100 t^{2} + 80$ |
$[4, 0]$ |
$[2]$ |
