Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
5.5.0.1 |
$5$ |
$x^{5} + 4 x + 3$ |
$5$ |
$1$ |
$5$ |
$0$ |
$C_5$ (as 5T1) |
$5$ |
$1$ |
$[\ ]$ |
$[\ ]^{5}$ |
$t^{5} + 4 t + 3$ |
$x - 5$ |
$[0]$ |
$[]$ |
5.5.5.1 |
$5$ |
$x^{5} + 20 x + 5$ |
$5$ |
$5$ |
$1$ |
$5$ |
$F_5$ (as 5T3) |
$1$ |
$4$ |
$[5/4]$ |
$[5/4]_{4}$ |
$t + 3$ |
$x^{5} + 20 x + 5$ |
$[1, 0]$ |
$[1]$ |
5.5.5.2 |
$5$ |
$x^{5} + 5 x + 5$ |
$5$ |
$5$ |
$1$ |
$5$ |
$F_5$ (as 5T3) |
$1$ |
$4$ |
$[5/4]$ |
$[5/4]_{4}$ |
$t + 3$ |
$x^{5} + 5 x + 5$ |
$[1, 0]$ |
$[1]$ |
5.5.5.3 |
$5$ |
$x^{5} + 15 x + 5$ |
$5$ |
$5$ |
$1$ |
$5$ |
$F_5$ (as 5T3) |
$1$ |
$4$ |
$[5/4]$ |
$[5/4]_{4}$ |
$t + 3$ |
$x^{5} + 15 x + 5$ |
$[1, 0]$ |
$[1]$ |
5.5.5.4 |
$5$ |
$x^{5} + 10 x + 5$ |
$5$ |
$5$ |
$1$ |
$5$ |
$F_5$ (as 5T3) |
$1$ |
$4$ |
$[5/4]$ |
$[5/4]_{4}$ |
$t + 3$ |
$x^{5} + 10 x + 5$ |
$[1, 0]$ |
$[1]$ |
5.5.6.1 |
$5$ |
$x^{5} + 10 x^{2} + 5$ |
$5$ |
$5$ |
$1$ |
$6$ |
$D_{5}$ (as 5T2) |
$1$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}$ |
$t + 3$ |
$x^{5} + 10 x^{2} + 5$ |
$[2, 0]$ |
$[1]$ |
5.5.6.2 |
$5$ |
$x^{5} + 15 x^{2} + 5$ |
$5$ |
$5$ |
$1$ |
$6$ |
$D_{5}$ (as 5T2) |
$1$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}$ |
$t + 3$ |
$x^{5} + 15 x^{2} + 5$ |
$[2, 0]$ |
$[1]$ |
5.5.6.3 |
$5$ |
$x^{5} + 5 x^{2} + 5$ |
$5$ |
$5$ |
$1$ |
$6$ |
$F_5$ (as 5T3) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{2}$ |
$t + 3$ |
$x^{5} + 5 x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
5.5.6.4 |
$5$ |
$x^{5} + 20 x^{2} + 5$ |
$5$ |
$5$ |
$1$ |
$6$ |
$F_5$ (as 5T3) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{2}$ |
$t + 3$ |
$x^{5} + 20 x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
5.5.7.1 |
$5$ |
$x^{5} + 15 x^{3} + 5$ |
$5$ |
$5$ |
$1$ |
$7$ |
$F_5$ (as 5T3) |
$1$ |
$4$ |
$[7/4]$ |
$[7/4]_{4}$ |
$t + 3$ |
$x^{5} + 15 x^{3} + 5$ |
$[3, 0]$ |
$[1]$ |
5.5.7.2 |
$5$ |
$x^{5} + 10 x^{3} + 5$ |
$5$ |
$5$ |
$1$ |
$7$ |
$F_5$ (as 5T3) |
$1$ |
$4$ |
$[7/4]$ |
$[7/4]_{4}$ |
$t + 3$ |
$x^{5} + 10 x^{3} + 5$ |
$[3, 0]$ |
$[1]$ |
5.5.7.3 |
$5$ |
$x^{5} + 20 x^{3} + 5$ |
$5$ |
$5$ |
$1$ |
$7$ |
$F_5$ (as 5T3) |
$1$ |
$4$ |
$[7/4]$ |
$[7/4]_{4}$ |
$t + 3$ |
$x^{5} + 20 x^{3} + 5$ |
$[3, 0]$ |
$[1]$ |
5.5.7.4 |
$5$ |
$x^{5} + 5 x^{3} + 5$ |
$5$ |
$5$ |
$1$ |
$7$ |
$F_5$ (as 5T3) |
$1$ |
$4$ |
$[7/4]$ |
$[7/4]_{4}$ |
$t + 3$ |
$x^{5} + 5 x^{3} + 5$ |
$[3, 0]$ |
$[1]$ |
5.5.8.1 |
$5$ |
$x^{5} + 20 x^{4} + 105$ |
$5$ |
$5$ |
$1$ |
$8$ |
$C_5$ (as 5T1) |
$1$ |
$1$ |
$[2]$ |
$[2]$ |
$t + 3$ |
$x^{5} + 20 x^{4} + 105$ |
$[4, 0]$ |
$[1]$ |
5.5.8.2 |
$5$ |
$x^{5} + 20 x^{4} + 5$ |
$5$ |
$5$ |
$1$ |
$8$ |
$C_5$ (as 5T1) |
$1$ |
$1$ |
$[2]$ |
$[2]$ |
$t + 3$ |
$x^{5} + 20 x^{4} + 5$ |
$[4, 0]$ |
$[1]$ |
5.5.8.3 |
$5$ |
$x^{5} + 20 x^{4} + 30$ |
$5$ |
$5$ |
$1$ |
$8$ |
$C_5$ (as 5T1) |
$1$ |
$1$ |
$[2]$ |
$[2]$ |
$t + 3$ |
$x^{5} + 20 x^{4} + 30$ |
$[4, 0]$ |
$[1]$ |
5.5.8.4 |
$5$ |
$x^{5} + 20 x^{4} + 55$ |
$5$ |
$5$ |
$1$ |
$8$ |
$C_5$ (as 5T1) |
$1$ |
$1$ |
$[2]$ |
$[2]$ |
$t + 3$ |
$x^{5} + 20 x^{4} + 55$ |
$[4, 0]$ |
$[1]$ |
5.5.8.5 |
$5$ |
$x^{5} + 20 x^{4} + 80$ |
$5$ |
$5$ |
$1$ |
$8$ |
$C_5$ (as 5T1) |
$1$ |
$1$ |
$[2]$ |
$[2]$ |
$t + 3$ |
$x^{5} + 20 x^{4} + 80$ |
$[4, 0]$ |
$[1]$ |
5.5.8.6 |
$5$ |
$x^{5} + 5 x^{4} + 5$ |
$5$ |
$5$ |
$1$ |
$8$ |
$D_{5}$ (as 5T2) |
$2$ |
$1$ |
$[2]$ |
$[2]^{2}$ |
$t + 3$ |
$x^{5} + 5 x^{4} + 5$ |
$[4, 0]$ |
$[2]$ |
5.5.8.7 |
$5$ |
$x^{5} + 10 x^{4} + 5$ |
$5$ |
$5$ |
$1$ |
$8$ |
$F_5$ (as 5T3) |
$4$ |
$1$ |
$[2]$ |
$[2]^{4}$ |
$t + 3$ |
$x^{5} + 10 x^{4} + 5$ |
$[4, 0]$ |
$[4]$ |
5.5.8.8 |
$5$ |
$x^{5} + 15 x^{4} + 5$ |
$5$ |
$5$ |
$1$ |
$8$ |
$F_5$ (as 5T3) |
$4$ |
$1$ |
$[2]$ |
$[2]^{4}$ |
$t + 3$ |
$x^{5} + 15 x^{4} + 5$ |
$[4, 0]$ |
$[4]$ |
5.5.9.1 |
$5$ |
$x^{5} + 5$ |
$5$ |
$5$ |
$1$ |
$9$ |
$F_5$ (as 5T3) |
$1$ |
$4$ |
$[9/4]$ |
$[9/4]_{4}$ |
$t + 3$ |
$x^{5} + 5$ |
$[5, 0]$ |
$[1]$ |
5.5.9.2 |
$5$ |
$x^{5} + 100 x^{2} + 50 x + 5$ |
$5$ |
$5$ |
$1$ |
$9$ |
$F_5$ (as 5T3) |
$1$ |
$4$ |
$[9/4]$ |
$[9/4]_{4}$ |
$t + 3$ |
$x^{5} + 100 x^{2} + 50 x + 5$ |
$[5, 0]$ |
$[1]$ |
5.5.9.3 |
$5$ |
$x^{5} + 100 x^{2} + 75 x + 5$ |
$5$ |
$5$ |
$1$ |
$9$ |
$F_5$ (as 5T3) |
$1$ |
$4$ |
$[9/4]$ |
$[9/4]_{4}$ |
$t + 3$ |
$x^{5} + 100 x^{2} + 75 x + 5$ |
$[5, 0]$ |
$[1]$ |
5.5.9.4 |
$5$ |
$x^{5} + 25 x^{2} + 25 x + 5$ |
$5$ |
$5$ |
$1$ |
$9$ |
$F_5$ (as 5T3) |
$1$ |
$4$ |
$[9/4]$ |
$[9/4]_{4}$ |
$t + 3$ |
$x^{5} + 25 x^{2} + 25 x + 5$ |
$[5, 0]$ |
$[1]$ |
5.5.9.5 |
$5$ |
$x^{5} + 25 x^{2} + 100 x + 5$ |
$5$ |
$5$ |
$1$ |
$9$ |
$F_5$ (as 5T3) |
$1$ |
$4$ |
$[9/4]$ |
$[9/4]_{4}$ |
$t + 3$ |
$x^{5} + 25 x^{2} + 100 x + 5$ |
$[5, 0]$ |
$[1]$ |