Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
2.4.6.1 |
$4$ |
$x^{4} + 2 x^{3} + 31 x^{2} + 30 x + 183$ |
$2$ |
$2$ |
$2$ |
$6$ |
$C_2^2$ (as 4T2) |
$2$ |
$1$ |
$[3]$ |
$[3]^{2}$ |
$t^{2} + t + 1$ |
$x^{2} + 14$ |
$[2, 0]$ |
$[1]$ |
2.4.6.2 |
$4$ |
$x^{4} + 4 x^{3} + 16 x^{2} + 24 x + 12$ |
$2$ |
$2$ |
$2$ |
$6$ |
$C_2^2$ (as 4T2) |
$2$ |
$1$ |
$[3]$ |
$[3]^{2}$ |
$t^{2} + t + 1$ |
$x^{2} + \left(4 t + 4\right) x + 4 t + 2$ |
$[2, 0]$ |
$[1]$ |
2.4.6.3 |
$4$ |
$x^{4} + 8 x^{3} + 28 x^{2} + 48 x + 84$ |
$2$ |
$2$ |
$2$ |
$6$ |
$C_4$ (as 4T1) |
$2$ |
$1$ |
$[3]$ |
$[3]^{2}$ |
$t^{2} + t + 1$ |
$x^{2} + 4 x + 8 t + 10$ |
$[2, 0]$ |
$[1]$ |
2.4.6.4 |
$4$ |
$x^{4} + 4 x^{3} + 24 x^{2} + 88 x + 124$ |
$2$ |
$2$ |
$2$ |
$6$ |
$C_4$ (as 4T1) |
$2$ |
$1$ |
$[3]$ |
$[3]^{2}$ |
$t^{2} + t + 1$ |
$x^{2} + \left(4 t + 4\right) x + 12 t + 10$ |
$[2, 0]$ |
$[1]$ |
2.4.6.5 |
$4$ |
$x^{4} - 4 x^{3} + 36 x^{2} + 8 x + 148$ |
$2$ |
$2$ |
$2$ |
$6$ |
$D_{4}$ (as 4T3) |
$2$ |
$1$ |
$[3]$ |
$[2, 3]^{2}$ |
$t^{2} + t + 1$ |
$x^{2} + 4 t x + 8 t + 14$ |
$[2, 0]$ |
$[1]$ |
2.4.6.6 |
$4$ |
$x^{4} - 4 x^{3} + 28 x^{2} - 24 x + 36$ |
$2$ |
$2$ |
$2$ |
$6$ |
$D_{4}$ (as 4T3) |
$2$ |
$1$ |
$[3]$ |
$[2, 3]^{2}$ |
$t^{2} + t + 1$ |
$x^{2} + 4 t x + 6$ |
$[2, 0]$ |
$[1]$ |
2.4.6.7 |
$4$ |
$x^{4} + 2 x^{3} + 2 x^{2} + 2$ |
$2$ |
$4$ |
$1$ |
$6$ |
$A_4$ (as 4T4) |
$3$ |
$1$ |
$[2, 2]$ |
$[2, 2]^{3}$ |
$t + 1$ |
$x^{4} + 2 x^{3} + 2 x^{2} + 2$ |
$[3, 2, 0]$ |
$[3]$ |
2.4.6.8 |
$4$ |
$x^{4} + 2 x^{3} + 2$ |
$2$ |
$4$ |
$1$ |
$6$ |
$D_{4}$ (as 4T3) |
$2$ |
$1$ |
$[2, 2]$ |
$[2, 2]^{2}$ |
$t + 1$ |
$x^{4} + 2 x^{3} + 2$ |
$[3, 3, 0]$ |
$[2]$ |
2.4.6.9 |
$4$ |
$x^{4} + 2 x^{3} + 6$ |
$2$ |
$4$ |
$1$ |
$6$ |
$D_{4}$ (as 4T3) |
$2$ |
$1$ |
$[2, 2]$ |
$[2, 2]^{2}$ |
$t + 1$ |
$x^{4} + 2 x^{3} + 6$ |
$[3, 3, 0]$ |
$[2]$ |