| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.15.21.1 |
$15$ |
$x^{15} + 6 x^{11} + 6 x^{10} + 6 x^{9} + 3 x^{8} + 6 x^{7} + 3$ |
$3$ |
$15$ |
$1$ |
$21$ |
$C_3^4:(S_3\times F_5)$ (as 15T64) |
$4$ |
$10$ |
$[17/10]$ |
$[3/2, 17/10, 17/10, 17/10, 17/10]_{10}^{4}$ |
$t + 1$ |
$x^{15} + 6 x^{11} + 6 x^{10} + 6 x^{9} + 3 x^{8} + 6 x^{7} + 3$ |
$[7, 0]$ |
$[1, 4]$ |
| 3.15.21.10 |
$15$ |
$x^{15} + 3 x^{11} + 3 x^{10} + 3 x^{9} + 3 x^{8} + 3 x^{7} + 3$ |
$3$ |
$15$ |
$1$ |
$21$ |
$C_3^4:(S_3\times F_5)$ (as 15T64) |
$4$ |
$10$ |
$[17/10]$ |
$[3/2, 17/10, 17/10, 17/10, 17/10]_{10}^{4}$ |
$t + 1$ |
$x^{15} + 3 x^{11} + 3 x^{10} + 3 x^{9} + 3 x^{8} + 3 x^{7} + 3$ |
$[7, 0]$ |
$[1, 4]$ |
| 3.15.21.11 |
$15$ |
$x^{15} + 3 x^{11} + 6 x^{10} + 6 x^{9} + 3 x^{7} + 3$ |
$3$ |
$15$ |
$1$ |
$21$ |
$C_3^4:(C_2\times F_5)$ (as 15T52) |
$4$ |
$10$ |
$[17/10]$ |
$[17/10, 17/10, 17/10, 17/10]_{10}^{4}$ |
$t + 1$ |
$x^{15} + 3 x^{11} + 6 x^{10} + 6 x^{9} + 3 x^{7} + 3$ |
$[7, 0]$ |
$[1, 4]$ |
| 3.15.21.12 |
$15$ |
$x^{15} + 3 x^{11} + 6 x^{10} + 6 x^{8} + 6 x^{7} + 3$ |
$3$ |
$15$ |
$1$ |
$21$ |
$C_3^4:(S_3\times F_5)$ (as 15T64) |
$4$ |
$10$ |
$[17/10]$ |
$[3/2, 17/10, 17/10, 17/10, 17/10]_{10}^{4}$ |
$t + 1$ |
$x^{15} + 3 x^{11} + 6 x^{10} + 6 x^{8} + 6 x^{7} + 3$ |
$[7, 0]$ |
$[1, 4]$ |
| 3.15.21.13 |
$15$ |
$x^{15} + 6 x^{11} + 6 x^{10} + 3 x^{8} + 6 x^{7} + 3$ |
$3$ |
$15$ |
$1$ |
$21$ |
$C_3^4:(S_3\times F_5)$ (as 15T64) |
$4$ |
$10$ |
$[17/10]$ |
$[3/2, 17/10, 17/10, 17/10, 17/10]_{10}^{4}$ |
$t + 1$ |
$x^{15} + 6 x^{11} + 6 x^{10} + 3 x^{8} + 6 x^{7} + 3$ |
$[7, 0]$ |
$[1, 4]$ |
| 3.15.21.14 |
$15$ |
$x^{15} + 3 x^{11} + 3 x^{10} + 6 x^{8} + 3 x^{7} + 3 x^{6} + 6 x^{3} + 3$ |
$3$ |
$15$ |
$1$ |
$21$ |
$C_3^4:(C_2\times F_5)$ (as 15T52) |
$4$ |
$10$ |
$[17/10]$ |
$[17/10, 17/10, 17/10, 17/10]_{10}^{4}$ |
$t + 1$ |
$x^{15} + 3 x^{11} + 3 x^{10} + 6 x^{8} + 3 x^{7} + 3 x^{6} + 6 x^{3} + 3$ |
$[7, 0]$ |
$[1, 4]$ |
| 3.15.21.15 |
$15$ |
$x^{15} + 6 x^{11} + 6 x^{10} + 6 x^{9} + 3 x^{7} + 3 x^{6} + 6 x^{3} + 3$ |
$3$ |
$15$ |
$1$ |
$21$ |
$C_3^4:(S_3\times F_5)$ (as 15T64) |
$4$ |
$10$ |
$[17/10]$ |
$[3/2, 17/10, 17/10, 17/10, 17/10]_{10}^{4}$ |
$t + 1$ |
$x^{15} + 6 x^{11} + 6 x^{10} + 6 x^{9} + 3 x^{7} + 3 x^{6} + 6 x^{3} + 3$ |
$[7, 0]$ |
$[1, 4]$ |
| 3.15.21.16 |
$15$ |
$x^{15} + 6 x^{10} + 6 x^{8} + 3 x^{7} + 3$ |
$3$ |
$15$ |
$1$ |
$21$ |
$C_3^4:(S_3\times F_5)$ (as 15T64) |
$4$ |
$10$ |
$[17/10]$ |
$[3/2, 17/10, 17/10, 17/10, 17/10]_{10}^{4}$ |
$t + 1$ |
$x^{15} + 6 x^{10} + 6 x^{8} + 3 x^{7} + 3$ |
$[7, 0]$ |
$[1, 4]$ |
| 3.15.21.17 |
$15$ |
$x^{15} + 6 x^{11} + 3 x^{10} + 6 x^{9} + 6 x^{8} + 6 x^{7} + 3$ |
$3$ |
$15$ |
$1$ |
$21$ |
$C_3^4:(S_3\times F_5)$ (as 15T64) |
$4$ |
$10$ |
$[17/10]$ |
$[3/2, 17/10, 17/10, 17/10, 17/10]_{10}^{4}$ |
$t + 1$ |
$x^{15} + 6 x^{11} + 3 x^{10} + 6 x^{9} + 6 x^{8} + 6 x^{7} + 3$ |
$[7, 0]$ |
$[1, 4]$ |
| 3.15.21.18 |
$15$ |
$x^{15} + 3 x^{9} + 3 x^{7} + 3$ |
$3$ |
$15$ |
$1$ |
$21$ |
$C_3^4:(C_2\times F_5)$ (as 15T52) |
$4$ |
$10$ |
$[17/10]$ |
$[17/10, 17/10, 17/10, 17/10]_{10}^{4}$ |
$t + 1$ |
$x^{15} + 3 x^{9} + 3 x^{7} + 3$ |
$[7, 0]$ |
$[1, 4]$ |
| 3.15.21.2 |
$15$ |
$x^{15} + 3 x^{10} + 3 x^{9} + 3 x^{7} + 3 x^{6} + 3 x^{3} + 3$ |
$3$ |
$15$ |
$1$ |
$21$ |
$C_3^4:(S_3\times F_5)$ (as 15T64) |
$4$ |
$10$ |
$[17/10]$ |
$[3/2, 17/10, 17/10, 17/10, 17/10]_{10}^{4}$ |
$t + 1$ |
$x^{15} + 3 x^{10} + 3 x^{9} + 3 x^{7} + 3 x^{6} + 3 x^{3} + 3$ |
$[7, 0]$ |
$[1, 4]$ |
| 3.15.21.3 |
$15$ |
$x^{15} + 3 x^{11} + 3 x^{8} + 6 x^{7} + 3$ |
$3$ |
$15$ |
$1$ |
$21$ |
$C_3^4:(S_3\times F_5)$ (as 15T64) |
$4$ |
$10$ |
$[17/10]$ |
$[3/2, 17/10, 17/10, 17/10, 17/10]_{10}^{4}$ |
$t + 1$ |
$x^{15} + 3 x^{11} + 3 x^{8} + 6 x^{7} + 3$ |
$[7, 0]$ |
$[1, 4]$ |
| 3.15.21.4 |
$15$ |
$x^{15} + 3 x^{10} + 6 x^{8} + 6 x^{7} + 3$ |
$3$ |
$15$ |
$1$ |
$21$ |
$C_3^4:(S_3\times F_5)$ (as 15T64) |
$4$ |
$10$ |
$[17/10]$ |
$[3/2, 17/10, 17/10, 17/10, 17/10]_{10}^{4}$ |
$t + 1$ |
$x^{15} + 3 x^{10} + 6 x^{8} + 6 x^{7} + 3$ |
$[7, 0]$ |
$[1, 4]$ |
| 3.15.21.5 |
$15$ |
$x^{15} + 6 x^{9} + 3 x^{7} + 3 x^{6} + 6 x^{3} + 3$ |
$3$ |
$15$ |
$1$ |
$21$ |
$C_3^4:(S_3\times F_5)$ (as 15T64) |
$4$ |
$10$ |
$[17/10]$ |
$[3/2, 17/10, 17/10, 17/10, 17/10]_{10}^{4}$ |
$t + 1$ |
$x^{15} + 6 x^{9} + 3 x^{7} + 3 x^{6} + 6 x^{3} + 3$ |
$[7, 0]$ |
$[1, 4]$ |
| 3.15.21.6 |
$15$ |
$x^{15} + 6 x^{8} + 6 x^{7} + 3 x^{6} + 3 x^{3} + 3$ |
$3$ |
$15$ |
$1$ |
$21$ |
$C_3^4:(C_2\times F_5)$ (as 15T52) |
$4$ |
$10$ |
$[17/10]$ |
$[17/10, 17/10, 17/10, 17/10]_{10}^{4}$ |
$t + 1$ |
$x^{15} + 6 x^{8} + 6 x^{7} + 3 x^{6} + 3 x^{3} + 3$ |
$[7, 0]$ |
$[1, 4]$ |
| 3.15.21.7 |
$15$ |
$x^{15} + 3 x^{11} + 3 x^{10} + 3 x^{9} + 6 x^{7} + 3$ |
$3$ |
$15$ |
$1$ |
$21$ |
$C_3^4:(C_2\times F_5)$ (as 15T52) |
$4$ |
$10$ |
$[17/10]$ |
$[17/10, 17/10, 17/10, 17/10]_{10}^{4}$ |
$t + 1$ |
$x^{15} + 3 x^{11} + 3 x^{10} + 3 x^{9} + 6 x^{7} + 3$ |
$[7, 0]$ |
$[1, 4]$ |
| 3.15.21.8 |
$15$ |
$x^{15} + 3 x^{11} + 3 x^{9} + 6 x^{8} + 6 x^{7} + 3 x^{6} + 3 x^{3} + 3$ |
$3$ |
$15$ |
$1$ |
$21$ |
$C_3^4:(C_2\times F_5)$ (as 15T52) |
$4$ |
$10$ |
$[17/10]$ |
$[17/10, 17/10, 17/10, 17/10]_{10}^{4}$ |
$t + 1$ |
$x^{15} + 3 x^{11} + 3 x^{9} + 6 x^{8} + 6 x^{7} + 3 x^{6} + 3 x^{3} + 3$ |
$[7, 0]$ |
$[1, 4]$ |
| 3.15.21.9 |
$15$ |
$x^{15} + 6 x^{11} + 3 x^{9} + 3 x^{8} + 3 x^{7} + 3 x^{6} + 6 x^{3} + 3$ |
$3$ |
$15$ |
$1$ |
$21$ |
$C_3^4:(S_3\times F_5)$ (as 15T64) |
$4$ |
$10$ |
$[17/10]$ |
$[3/2, 17/10, 17/10, 17/10, 17/10]_{10}^{4}$ |
$t + 1$ |
$x^{15} + 6 x^{11} + 3 x^{9} + 3 x^{8} + 3 x^{7} + 3 x^{6} + 6 x^{3} + 3$ |
$[7, 0]$ |
$[1, 4]$ |
