| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 5.15.16.1 |
$15$ |
$x^{15} + 15 x^{3} + 5 x^{2} + 5$ |
$5$ |
$15$ |
$1$ |
$16$ |
$((C_5^2 : C_3):C_2):C_2$ (as 15T18) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6, 7/6]_{6}^{2}$ |
$t + 3$ |
$x^{15} + 15 x^{3} + 5 x^{2} + 5$ |
$[2, 0]$ |
$[1, 2]$ |
| 5.15.16.4 |
$15$ |
$x^{15} + 15 x^{3} + 20 x^{2} + 5$ |
$5$ |
$15$ |
$1$ |
$16$ |
$((C_5^2 : C_3):C_2):C_2$ (as 15T18) |
$2$ |
$6$ |
$[7/6]$ |
$[7/6, 7/6]_{6}^{2}$ |
$t + 3$ |
$x^{15} + 15 x^{3} + 20 x^{2} + 5$ |
$[2, 0]$ |
$[1, 2]$ |
| 5.15.28.13 |
$15$ |
$x^{15} + 10 x^{14} + 5 x^{10} + 15 x^{5} + 50 x^{3} + 100 x^{2} + 25 x + 5$ |
$5$ |
$15$ |
$1$ |
$28$ |
$((C_5^2 : C_3):C_2):C_2$ (as 15T18) |
$2$ |
$6$ |
$[13/6]$ |
$[13/6, 13/6]_{6}^{2}$ |
$t + 3$ |
$x^{15} + 10 x^{14} + 5 x^{10} + 15 x^{5} + 50 x^{3} + 100 x^{2} + 25 x + 5$ |
$[14, 0]$ |
$[1, 2]$ |
| 5.15.28.22 |
$15$ |
$x^{15} + 15 x^{14} + 5 x^{10} + 50 x^{3} + 25 x^{2} + 100 x + 30$ |
$5$ |
$15$ |
$1$ |
$28$ |
$((C_5^2 : C_3):C_2):C_2$ (as 15T18) |
$2$ |
$6$ |
$[13/6]$ |
$[13/6, 13/6]_{6}^{2}$ |
$t + 3$ |
$x^{15} + 15 x^{14} + 5 x^{10} + 50 x^{3} + 25 x^{2} + 100 x + 30$ |
$[14, 0]$ |
$[1, 2]$ |
| 5.15.28.26 |
$15$ |
$x^{15} + 10 x^{14} + 75 x^{3} + 30$ |
$5$ |
$15$ |
$1$ |
$28$ |
$((C_5^2 : C_3):C_2):C_2$ (as 15T18) |
$2$ |
$6$ |
$[13/6]$ |
$[13/6, 13/6]_{6}^{2}$ |
$t + 3$ |
$x^{15} + 10 x^{14} + 75 x^{3} + 30$ |
$[14, 0]$ |
$[1, 2]$ |
| 5.15.28.28 |
$15$ |
$x^{15} + 10 x^{14} + 5 x^{10} + 10 x^{5} + 75 x^{3} + 30$ |
$5$ |
$15$ |
$1$ |
$28$ |
$((C_5^2 : C_3):C_2):C_2$ (as 15T18) |
$2$ |
$6$ |
$[13/6]$ |
$[13/6, 13/6]_{6}^{2}$ |
$t + 3$ |
$x^{15} + 10 x^{14} + 5 x^{10} + 10 x^{5} + 75 x^{3} + 30$ |
$[14, 0]$ |
$[1, 2]$ |
| 5.15.28.33 |
$15$ |
$x^{15} + 10 x^{14} + 5 x^{10} + 15 x^{5} + 100 x^{3} + 25 x^{2} + 25 x + 30$ |
$5$ |
$15$ |
$1$ |
$28$ |
$((C_5^2 : C_3):C_2):C_2$ (as 15T18) |
$2$ |
$6$ |
$[13/6]$ |
$[13/6, 13/6]_{6}^{2}$ |
$t + 3$ |
$x^{15} + 10 x^{14} + 5 x^{10} + 15 x^{5} + 100 x^{3} + 25 x^{2} + 25 x + 30$ |
$[14, 0]$ |
$[1, 2]$ |
| 5.15.28.45 |
$15$ |
$x^{15} + 15 x^{14} + 5 x^{10} + 20 x^{5} + 50 x^{3} + 25 x^{2} + 5$ |
$5$ |
$15$ |
$1$ |
$28$ |
$((C_5^2 : C_3):C_2):C_2$ (as 15T18) |
$2$ |
$6$ |
$[13/6]$ |
$[13/6, 13/6]_{6}^{2}$ |
$t + 3$ |
$x^{15} + 15 x^{14} + 5 x^{10} + 20 x^{5} + 50 x^{3} + 25 x^{2} + 5$ |
$[14, 0]$ |
$[1, 2]$ |
| 5.15.28.54 |
$15$ |
$x^{15} + 15 x^{14} + 5 x^{10} + 100 x^{3} + 100 x^{2} + 100 x + 80$ |
$5$ |
$15$ |
$1$ |
$28$ |
$((C_5^2 : C_3):C_2):C_2$ (as 15T18) |
$2$ |
$6$ |
$[13/6]$ |
$[13/6, 13/6]_{6}^{2}$ |
$t + 3$ |
$x^{15} + 15 x^{14} + 5 x^{10} + 100 x^{3} + 100 x^{2} + 100 x + 80$ |
$[14, 0]$ |
$[1, 2]$ |
| 5.15.28.81 |
$15$ |
$x^{15} + 15 x^{14} + 5 x^{10} + 75 x^{2} + 100 x + 30$ |
$5$ |
$15$ |
$1$ |
$28$ |
$((C_5^2 : C_3):C_2):C_2$ (as 15T18) |
$2$ |
$6$ |
$[13/6]$ |
$[13/6, 13/6]_{6}^{2}$ |
$t + 3$ |
$x^{15} + 15 x^{14} + 5 x^{10} + 75 x^{2} + 100 x + 30$ |
$[14, 0]$ |
$[1, 2]$ |
| 5.15.28.91 |
$15$ |
$x^{15} + 10 x^{14} + 20 x^{10} + 10 x^{5} + 50 x^{3} + 25 x^{2} + 75 x + 30$ |
$5$ |
$15$ |
$1$ |
$28$ |
$((C_5^2 : C_3):C_2):C_2$ (as 15T18) |
$2$ |
$6$ |
$[13/6]$ |
$[13/6, 13/6]_{6}^{2}$ |
$t + 3$ |
$x^{15} + 10 x^{14} + 20 x^{10} + 10 x^{5} + 50 x^{3} + 25 x^{2} + 75 x + 30$ |
$[14, 0]$ |
$[1, 2]$ |
| 5.15.28.96 |
$15$ |
$x^{15} + 15 x^{14} + 75 x^{3} + 50 x^{2} + 5$ |
$5$ |
$15$ |
$1$ |
$28$ |
$((C_5^2 : C_3):C_2):C_2$ (as 15T18) |
$2$ |
$6$ |
$[13/6]$ |
$[13/6, 13/6]_{6}^{2}$ |
$t + 3$ |
$x^{15} + 15 x^{14} + 75 x^{3} + 50 x^{2} + 5$ |
$[14, 0]$ |
$[1, 2]$ |
