| Label |
$n$ |
Polynomial |
$p$ |
$f$ |
$e$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible Artin slopes |
Visible Swan slopes |
Artin slope content |
Swan slope content |
Hidden Artin slopes |
Hidden Swan slopes |
$\#\Aut(K/\Q_p)$ |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
Resid. Poly |
Jump Set |
| 2.4.2.8a1.1 |
$8$ |
$( x^{4} + x + 1 )^{2} + 2 ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$2$ |
$8$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{4}$ |
$[1]^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + t + 1$ |
$x^{2} + 2 x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 2]$ |
| 2.4.2.12a1.1 |
$8$ |
$( x^{4} + x + 1 )^{2} + 2$ |
$2$ |
$4$ |
$2$ |
$12$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$1$ |
$[3]$ |
$[2]$ |
$[3]^{4}$ |
$[2]^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + t + 1$ |
$x^{2} + 2$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.4.2.12a1.9 |
$8$ |
$( x^{4} + x + 1 )^{2} + 4 ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$2$ |
$12$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$1$ |
$[3]$ |
$[2]$ |
$[3]^{4}$ |
$[2]^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + t + 1$ |
$x^{2} + 4 x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.2.4.16b1.2 |
$8$ |
$( x^{2} + x + 1 )^{4} + 2 ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$16$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$1$ |
$[2, 3]$ |
$[1,2]$ |
$[2, 3]^{2}$ |
$[1,2]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{4} + 2 x^{2} + 4 x + 8 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 8, 12]$ |
| 2.2.4.16b1.8 |
$8$ |
$( x^{2} + x + 1 )^{4} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 )^{2} + 4 x + 2$ |
$2$ |
$2$ |
$4$ |
$16$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$1$ |
$[2, 3]$ |
$[1,2]$ |
$[2, 3]^{2}$ |
$[1,2]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{3} + 2 x^{2} + 4 x + 4 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 8]$ |
| 2.2.4.16b1.9 |
$8$ |
$( x^{2} + x + 1 )^{4} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 )^{2} + 12 x + 2$ |
$2$ |
$2$ |
$4$ |
$16$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$1$ |
$[2, 3]$ |
$[1,2]$ |
$[2, 3]^{2}$ |
$[1,2]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{3} + 2 x^{2} + 4 x + 12 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 8]$ |
| 2.2.4.22a1.49 |
$8$ |
$( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[3, 4]^{2}$ |
$[2,3]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{2} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.50 |
$8$ |
$( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + 16 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[3, 4]^{2}$ |
$[2,3]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{2} + 16 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.53 |
$8$ |
$( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[3, 4]^{2}$ |
$[2,3]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + 4 x^{2} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.54 |
$8$ |
$( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + 16 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[3, 4]^{2}$ |
$[2,3]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + 4 x^{2} + 16 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.1.8.24c1.1 |
$8$ |
$x^{8} + 2 x^{4} + 4 x^{2} + 8 x + 2$ |
$2$ |
$1$ |
$8$ |
$24$ |
$C_4\times C_2$ (as 8T2) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t + 1$ |
$x^{8} + 2 x^{4} + 4 x^{2} + 8 x + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8]$ |
| 2.1.8.24c1.2 |
$8$ |
$x^{8} + 2 x^{4} + 4 x^{2} + 8 x + 18$ |
$2$ |
$1$ |
$8$ |
$24$ |
$C_4\times C_2$ (as 8T2) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t + 1$ |
$x^{8} + 2 x^{4} + 4 x^{2} + 8 x + 18$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 16, 24, 32]$ |
| 2.1.8.24c1.12 |
$8$ |
$x^{8} + 8 x^{7} + 2 x^{4} + 4 x^{2} + 8 x + 10$ |
$2$ |
$1$ |
$8$ |
$24$ |
$C_4\times C_2$ (as 8T2) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 2 x^{4} + 4 x^{2} + 8 x + 10$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 16, 24]$ |
| 2.1.8.24c1.13 |
$8$ |
$x^{8} + 8 x^{7} + 2 x^{4} + 4 x^{2} + 8 x + 26$ |
$2$ |
$1$ |
$8$ |
$24$ |
$C_4\times C_2$ (as 8T2) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 2 x^{4} + 4 x^{2} + 8 x + 26$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 16, 24]$ |
| 2.1.8.24c1.50 |
$8$ |
$x^{8} + 4 x^{6} + 2 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 6$ |
$2$ |
$1$ |
$8$ |
$24$ |
$C_4\times C_2$ (as 8T2) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 2 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 6$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.1.8.24c1.51 |
$8$ |
$x^{8} + 4 x^{6} + 2 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 22$ |
$2$ |
$1$ |
$8$ |
$24$ |
$C_4\times C_2$ (as 8T2) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t + 1$ |
$x^{8} + 4 x^{6} + 2 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 22$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.1.8.24c1.61 |
$8$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 2 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 14$ |
$2$ |
$1$ |
$8$ |
$24$ |
$C_4\times C_2$ (as 8T2) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 2 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 14$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.1.8.24c1.62 |
$8$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 2 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 30$ |
$2$ |
$1$ |
$8$ |
$24$ |
$C_4\times C_2$ (as 8T2) |
$1$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 2 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 30$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 3.4.2.4a1.2 |
$8$ |
$( x^{4} + 2 x^{3} + 2 )^{2} + 3$ |
$3$ |
$4$ |
$2$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$[\ ]_{2}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{2} + 3$ |
$[0]$ |
$[1]$ |
$z + 2$ |
$[1]$ |
| 5.4.2.4a1.2 |
$8$ |
$( x^{4} + 4 x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$4$ |
$2$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$[\ ]_{2}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + 4 t^{2} + 4 t + 2$ |
$x^{2} + 5$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 5.2.4.6a1.2 |
$8$ |
$( x^{2} + 4 x + 2 )^{4} + 5$ |
$5$ |
$2$ |
$4$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 4 t + 2$ |
$x^{4} + 5$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + z + 4$ |
$[1]$ |
| 5.2.4.6a1.3 |
$8$ |
$( x^{2} + 4 x + 2 )^{4} + 5 x + 15$ |
$5$ |
$2$ |
$4$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 4 t + 2$ |
$x^{4} + 5 t + 15$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + z + 4$ |
undefined |
| 7.4.2.4a1.2 |
$8$ |
$( x^{4} + 5 x^{2} + 4 x + 3 )^{2} + 7$ |
$7$ |
$4$ |
$2$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$[\ ]_{2}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + 5 t^{2} + 4 t + 3$ |
$x^{2} + 7$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 11.4.2.4a1.2 |
$8$ |
$( x^{4} + 8 x^{2} + 10 x + 2 )^{2} + 11$ |
$11$ |
$4$ |
$2$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$[\ ]_{2}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + 8 t^{2} + 10 t + 2$ |
$x^{2} + 11$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 13.4.2.4a1.2 |
$8$ |
$( x^{4} + 3 x^{2} + 12 x + 2 )^{2} + 13$ |
$13$ |
$4$ |
$2$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$[\ ]_{2}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + 3 t^{2} + 12 t + 2$ |
$x^{2} + 13$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 13.2.4.6a1.2 |
$8$ |
$( x^{2} + 12 x + 2 )^{4} + 13$ |
$13$ |
$2$ |
$4$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 12 t + 2$ |
$x^{4} + 13$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 13.2.4.6a1.3 |
$8$ |
$( x^{2} + 12 x + 2 )^{4} + 13 x + 143$ |
$13$ |
$2$ |
$4$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 12 t + 2$ |
$x^{4} + 13 t + 143$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 17.4.2.4a1.2 |
$8$ |
$( x^{4} + 7 x^{2} + 10 x + 3 )^{2} + 17$ |
$17$ |
$4$ |
$2$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$[\ ]_{2}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + 7 t^{2} + 10 t + 3$ |
$x^{2} + 17$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 17.2.4.6a1.2 |
$8$ |
$( x^{2} + 16 x + 3 )^{4} + 17$ |
$17$ |
$2$ |
$4$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 16 t + 3$ |
$x^{4} + 17$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 17.2.4.6a1.3 |
$8$ |
$( x^{2} + 16 x + 3 )^{4} + 17 x + 238$ |
$17$ |
$2$ |
$4$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 16 t + 3$ |
$x^{4} + 17 t + 238$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 19.4.2.4a1.2 |
$8$ |
$( x^{4} + 2 x^{2} + 11 x + 2 )^{2} + 19$ |
$19$ |
$4$ |
$2$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$[\ ]_{2}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + 2 t^{2} + 11 t + 2$ |
$x^{2} + 19$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 23.4.2.4a1.2 |
$8$ |
$( x^{4} + 3 x^{2} + 19 x + 5 )^{2} + 23$ |
$23$ |
$4$ |
$2$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$[\ ]_{2}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + 3 t^{2} + 19 t + 5$ |
$x^{2} + 23$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 29.4.2.4a1.2 |
$8$ |
$( x^{4} + 2 x^{2} + 15 x + 2 )^{2} + 29$ |
$29$ |
$4$ |
$2$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$[\ ]_{2}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + 2 t^{2} + 15 t + 2$ |
$x^{2} + 29$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 29.2.4.6a1.2 |
$8$ |
$( x^{2} + 24 x + 2 )^{4} + 29$ |
$29$ |
$2$ |
$4$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 24 t + 2$ |
$x^{4} + 29$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 29.2.4.6a1.4 |
$8$ |
$( x^{2} + 24 x + 2 )^{4} + 145 x + 783$ |
$29$ |
$2$ |
$4$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 24 t + 2$ |
$x^{4} + 145 t + 783$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 31.4.2.4a1.2 |
$8$ |
$( x^{4} + 3 x^{2} + 16 x + 3 )^{2} + 31$ |
$31$ |
$4$ |
$2$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$[\ ]_{2}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + 3 t^{2} + 16 t + 3$ |
$x^{2} + 31$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 37.4.2.4a1.2 |
$8$ |
$( x^{4} + 6 x^{2} + 24 x + 2 )^{2} + 37$ |
$37$ |
$4$ |
$2$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$[\ ]_{2}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + 6 t^{2} + 24 t + 2$ |
$x^{2} + 37$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 37.2.4.6a1.2 |
$8$ |
$( x^{2} + 33 x + 2 )^{4} + 37$ |
$37$ |
$2$ |
$4$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 33 t + 2$ |
$x^{4} + 37$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 37.2.4.6a1.4 |
$8$ |
$( x^{2} + 33 x + 2 )^{4} + 148 x + 1295$ |
$37$ |
$2$ |
$4$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 33 t + 2$ |
$x^{4} + 148 t + 1295$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 41.4.2.4a1.2 |
$8$ |
$( x^{4} + 23 x + 6 )^{2} + 41$ |
$41$ |
$4$ |
$2$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$[\ ]_{2}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + 23 t + 6$ |
$x^{2} + 41$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 41.2.4.6a1.2 |
$8$ |
$( x^{2} + 38 x + 6 )^{4} + 41$ |
$41$ |
$2$ |
$4$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 38 t + 6$ |
$x^{4} + 41$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 41.2.4.6a1.4 |
$8$ |
$( x^{2} + 38 x + 6 )^{4} + 123 x + 1435$ |
$41$ |
$2$ |
$4$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 38 t + 6$ |
$x^{4} + 123 t + 1435$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 43.4.2.4a1.2 |
$8$ |
$( x^{4} + 5 x^{2} + 42 x + 3 )^{2} + 43$ |
$43$ |
$4$ |
$2$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$[\ ]_{2}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + 5 t^{2} + 42 t + 3$ |
$x^{2} + 43$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 47.4.2.4a1.2 |
$8$ |
$( x^{4} + 8 x^{2} + 40 x + 5 )^{2} + 47$ |
$47$ |
$4$ |
$2$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$[\ ]_{2}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + 8 t^{2} + 40 t + 5$ |
$x^{2} + 47$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 53.4.2.4a1.2 |
$8$ |
$( x^{4} + 9 x^{2} + 38 x + 2 )^{2} + 53$ |
$53$ |
$4$ |
$2$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$[\ ]_{2}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + 9 t^{2} + 38 t + 2$ |
$x^{2} + 53$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 53.2.4.6a1.2 |
$8$ |
$( x^{2} + 49 x + 2 )^{4} + 53$ |
$53$ |
$2$ |
$4$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 49 t + 2$ |
$x^{4} + 53$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 53.2.4.6a1.4 |
$8$ |
$( x^{2} + 49 x + 2 )^{4} + 212 x + 2703$ |
$53$ |
$2$ |
$4$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 49 t + 2$ |
$x^{4} + 212 t + 2703$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 59.4.2.4a1.2 |
$8$ |
$( x^{4} + 2 x^{2} + 40 x + 2 )^{2} + 59$ |
$59$ |
$4$ |
$2$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$[\ ]_{2}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + 2 t^{2} + 40 t + 2$ |
$x^{2} + 59$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 61.4.2.4a1.2 |
$8$ |
$( x^{4} + 3 x^{2} + 40 x + 2 )^{2} + 61$ |
$61$ |
$4$ |
$2$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$[\ ]_{2}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + 3 t^{2} + 40 t + 2$ |
$x^{2} + 61$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 61.2.4.6a1.2 |
$8$ |
$( x^{2} + 60 x + 2 )^{4} + 61$ |
$61$ |
$2$ |
$4$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 60 t + 2$ |
$x^{4} + 61$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
