| 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 |
| 2.4.1.0a1.1 |
$4$ |
$x^{4} + x + 1$ |
$2$ |
$4$ |
$1$ |
$0$ |
$C_4$ (as 4T1) |
$4$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t^{4} + t + 1$ |
$x - 2$ |
$[0]$ |
$[\ ]$ |
|
$[1]$ |
| 2.2.2.4a1.1 |
$4$ |
$( x^{2} + x + 1 )^{2} + 2 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$2$ |
$4$ |
$C_2^2$ (as 4T2) |
$2$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{2}$ |
$[1]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{2} + 2 x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 2]$ |
| 2.2.2.4a1.2 |
$4$ |
$( x^{2} + x + 1 )^{2} + 2 ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$2$ |
$4$ |
$C_4$ (as 4T1) |
$2$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{2}$ |
$[1]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{2} + 2 x + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 4]$ |
| 2.2.2.4a2.1 |
$4$ |
$( x^{2} + x + 1 )^{2} + 2 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$2$ |
$4$ |
$D_{4}$ (as 4T3) |
$2$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2]^{2}$ |
$[1,1]^{2}$ |
$[2]$ |
$[1]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{2} + 2 t x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + t$ |
$[1, 3]$ |
| 2.2.2.4a2.2 |
$4$ |
$( x^{2} + x + 1 )^{2} + 2 x ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$2$ |
$4$ |
$D_{4}$ (as 4T3) |
$2$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2]^{2}$ |
$[1,1]^{2}$ |
$[2]$ |
$[1]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{2} + \left(2 t + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + t$ |
$[1, 3]$ |
| 2.2.2.6a1.1 |
$4$ |
$( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$2$ |
$6$ |
$C_2^2$ (as 4T2) |
$2$ |
$1$ |
$[3]$ |
$[2]$ |
$[3]^{2}$ |
$[2]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{2} + 2$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.2.2.6a1.2 |
$4$ |
$( x^{2} + x + 1 )^{2} + 8 x + 2$ |
$2$ |
$2$ |
$2$ |
$6$ |
$C_4$ (as 4T1) |
$2$ |
$1$ |
$[3]$ |
$[2]$ |
$[3]^{2}$ |
$[2]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{2} + 8 t + 2$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.2.2.6a1.3 |
$4$ |
$( x^{2} + x + 1 )^{2} + 4 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$2$ |
$6$ |
$D_{4}$ (as 4T3) |
$2$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 3]^{2}$ |
$[1,2]^{2}$ |
$[2]$ |
$[1]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{2} + \left(4 t + 4\right) x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.2.2.6a1.4 |
$4$ |
$( x^{2} + x + 1 )^{2} + 4 x ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$2$ |
$6$ |
$D_{4}$ (as 4T3) |
$2$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 3]^{2}$ |
$[1,2]^{2}$ |
$[2]$ |
$[1]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{2} + \left(4 t + 4\right) x + 8 t + 2$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.2.2.6a1.5 |
$4$ |
$( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$2$ |
$6$ |
$C_2^2$ (as 4T2) |
$2$ |
$1$ |
$[3]$ |
$[2]$ |
$[3]^{2}$ |
$[2]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{2} + 4 x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.2.2.6a1.6 |
$4$ |
$( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$2$ |
$6$ |
$C_4$ (as 4T1) |
$2$ |
$1$ |
$[3]$ |
$[2]$ |
$[3]^{2}$ |
$[2]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{2} + 4 x + 8 t + 2$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.1.4.4a1.1 |
$4$ |
$x^{4} + 2 x + 2$ |
$2$ |
$1$ |
$4$ |
$4$ |
$S_4$ (as 4T5) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}]$ |
$[\frac{1}{3},\frac{1}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3}]_{3}^{2}$ |
$[\ ]^{2}_{3}$ |
$[\ ]^{2}_{3}$ |
$1$ |
$t + 1$ |
$x^{4} + 2 x + 2$ |
$[1, 1, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 2, 5]$ |
| 2.1.4.6a1.1 |
$4$ |
$x^{4} + 2 x^{3} + 2$ |
$2$ |
$1$ |
$4$ |
$6$ |
$D_{4}$ (as 4T3) |
$2$ |
$1$ |
$[2, 2]$ |
$[1,1]$ |
$[2, 2]^{2}$ |
$[1,1]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t + 1$ |
$x^{4} + 2 x^{3} + 2$ |
$[3, 3, 0]$ |
$[2]$ |
$z^3 + 1$ |
$[1, 3, 6]$ |
| 2.1.4.6a1.2 |
$4$ |
$x^{4} + 2 x^{3} + 6$ |
$2$ |
$1$ |
$4$ |
$6$ |
$D_{4}$ (as 4T3) |
$2$ |
$1$ |
$[2, 2]$ |
$[1,1]$ |
$[2, 2]^{2}$ |
$[1,1]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t + 1$ |
$x^{4} + 2 x^{3} + 6$ |
$[3, 3, 0]$ |
$[2]$ |
$z^3 + 1$ |
$[1, 3, 8]$ |
| 2.1.4.6a2.1 |
$4$ |
$x^{4} + 2 x^{3} + 2 x^{2} + 2$ |
$2$ |
$1$ |
$4$ |
$6$ |
$A_4$ (as 4T4) |
$3$ |
$1$ |
$[2, 2]$ |
$[1,1]$ |
$[2, 2]^{3}$ |
$[1,1]^{3}$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$1$ |
$t + 1$ |
$x^{4} + 2 x^{3} + 2 x^{2} + 2$ |
$[3, 2, 0]$ |
$[3]$ |
$z^3 + z + 1$ |
$[1, 2, 7]$ |
| 2.1.4.8a1.1 |
$4$ |
$x^{4} + 4 x + 2$ |
$2$ |
$1$ |
$4$ |
$8$ |
$S_4$ (as 4T5) |
$2$ |
$3$ |
$[\frac{8}{3}, \frac{8}{3}]$ |
$[\frac{5}{3},\frac{5}{3}]$ |
$[\frac{8}{3}, \frac{8}{3}]_{3}^{2}$ |
$[\frac{5}{3},\frac{5}{3}]_{3}^{2}$ |
$[\ ]^{2}_{3}$ |
$[\ ]^{2}_{3}$ |
$1$ |
$t + 1$ |
$x^{4} + 4 x + 2$ |
$[5, 4, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3, 7]$ |
| 2.1.4.8a1.2 |
$4$ |
$x^{4} + 4 x^{2} + 4 x + 2$ |
$2$ |
$1$ |
$4$ |
$8$ |
$S_4$ (as 4T5) |
$2$ |
$3$ |
$[\frac{8}{3}, \frac{8}{3}]$ |
$[\frac{5}{3},\frac{5}{3}]$ |
$[\frac{8}{3}, \frac{8}{3}]_{3}^{2}$ |
$[\frac{5}{3},\frac{5}{3}]_{3}^{2}$ |
$[\ ]^{2}_{3}$ |
$[\ ]^{2}_{3}$ |
$1$ |
$t + 1$ |
$x^{4} + 4 x^{2} + 4 x + 2$ |
$[5, 4, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3, 7]$ |
| 2.1.4.8b1.1 |
$4$ |
$x^{4} + 2 x^{2} + 4 x + 2$ |
$2$ |
$1$ |
$4$ |
$8$ |
$C_2^2$ (as 4T2) |
$1$ |
$1$ |
$[2, 3]$ |
$[1,2]$ |
$[2, 3]$ |
$[1,2]$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t + 1$ |
$x^{4} + 2 x^{2} + 4 x + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 4]$ |
| 2.1.4.8b1.2 |
$4$ |
$x^{4} + 2 x^{2} + 4 x + 10$ |
$2$ |
$1$ |
$4$ |
$8$ |
$C_2^2$ (as 4T2) |
$1$ |
$1$ |
$[2, 3]$ |
$[1,2]$ |
$[2, 3]$ |
$[1,2]$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t + 1$ |
$x^{4} + 2 x^{2} + 4 x + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 8, 12]$ |
| 2.1.4.8b1.3 |
$4$ |
$x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 2$ |
$2$ |
$1$ |
$4$ |
$8$ |
$D_{4}$ (as 4T3) |
$2$ |
$1$ |
$[2, 3]$ |
$[1,2]$ |
$[2, 3]^{2}$ |
$[1,2]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t + 1$ |
$x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 7, 11]$ |
| 2.1.4.8b1.4 |
$4$ |
$x^{4} + 2 x^{2} + 4 x + 6$ |
$2$ |
$1$ |
$4$ |
$8$ |
$D_{4}$ (as 4T3) |
$2$ |
$1$ |
$[2, 3]$ |
$[1,2]$ |
$[2, 3]^{2}$ |
$[1,2]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t + 1$ |
$x^{4} + 2 x^{2} + 4 x + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 8]$ |
| 2.1.4.8b1.5 |
$4$ |
$x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 6$ |
$2$ |
$1$ |
$4$ |
$8$ |
$C_2^2$ (as 4T2) |
$1$ |
$1$ |
$[2, 3]$ |
$[1,2]$ |
$[2, 3]$ |
$[1,2]$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t + 1$ |
$x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 8]$ |
| 2.1.4.8b1.6 |
$4$ |
$x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 14$ |
$2$ |
$1$ |
$4$ |
$8$ |
$C_2^2$ (as 4T2) |
$1$ |
$1$ |
$[2, 3]$ |
$[1,2]$ |
$[2, 3]$ |
$[1,2]$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t + 1$ |
$x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 8]$ |
| 2.1.4.9a1.1 |
$4$ |
$x^{4} + 2 x^{2} + 2$ |
$2$ |
$1$ |
$4$ |
$9$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[3]$ |
$[2]$ |
$2$ |
$t + 1$ |
$x^{4} + 2 x^{2} + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 5, 9]$ |
| 2.1.4.9a1.2 |
$4$ |
$x^{4} + 10 x^{2} + 2$ |
$2$ |
$1$ |
$4$ |
$9$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[3]$ |
$[2]$ |
$2$ |
$t + 1$ |
$x^{4} + 10 x^{2} + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 5, 9]$ |
| 2.1.4.9a1.3 |
$4$ |
$x^{4} + 4 x^{3} + 2 x^{2} + 2$ |
$2$ |
$1$ |
$4$ |
$9$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[3]$ |
$[2]$ |
$2$ |
$t + 1$ |
$x^{4} + 4 x^{3} + 2 x^{2} + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 5, 9]$ |
| 2.1.4.9a1.4 |
$4$ |
$x^{4} + 4 x^{3} + 10 x^{2} + 2$ |
$2$ |
$1$ |
$4$ |
$9$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[3]$ |
$[2]$ |
$2$ |
$t + 1$ |
$x^{4} + 4 x^{3} + 10 x^{2} + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 5, 9]$ |
| 2.1.4.9a1.5 |
$4$ |
$x^{4} + 2 x^{2} + 6$ |
$2$ |
$1$ |
$4$ |
$9$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[3]$ |
$[2]$ |
$2$ |
$t + 1$ |
$x^{4} + 2 x^{2} + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 8]$ |
| 2.1.4.9a1.6 |
$4$ |
$x^{4} + 10 x^{2} + 6$ |
$2$ |
$1$ |
$4$ |
$9$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[3]$ |
$[2]$ |
$2$ |
$t + 1$ |
$x^{4} + 10 x^{2} + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 8]$ |
| 2.1.4.9a1.7 |
$4$ |
$x^{4} + 2 x^{2} + 8 x + 6$ |
$2$ |
$1$ |
$4$ |
$9$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[3]$ |
$[2]$ |
$2$ |
$t + 1$ |
$x^{4} + 2 x^{2} + 8 x + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 8]$ |
| 2.1.4.9a1.8 |
$4$ |
$x^{4} + 4 x^{3} + 2 x^{2} + 8 x + 6$ |
$2$ |
$1$ |
$4$ |
$9$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[3]$ |
$[2]$ |
$2$ |
$t + 1$ |
$x^{4} + 4 x^{3} + 2 x^{2} + 8 x + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 8]$ |
| 2.1.4.10a1.1 |
$4$ |
$x^{4} + 4 x^{3} + 2$ |
$2$ |
$1$ |
$4$ |
$10$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[3, \frac{7}{2}]$ |
$[2,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2]$ |
$[1]$ |
$2$ |
$t + 1$ |
$x^{4} + 4 x^{3} + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.1.4.10a1.2 |
$4$ |
$x^{4} + 4 x^{3} + 8 x^{2} + 2$ |
$2$ |
$1$ |
$4$ |
$10$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[3, \frac{7}{2}]$ |
$[2,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2]$ |
$[1]$ |
$2$ |
$t + 1$ |
$x^{4} + 4 x^{3} + 8 x^{2} + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.1.4.10a1.3 |
$4$ |
$x^{4} + 4 x^{3} + 10$ |
$2$ |
$1$ |
$4$ |
$10$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[3, \frac{7}{2}]$ |
$[2,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2]$ |
$[1]$ |
$2$ |
$t + 1$ |
$x^{4} + 4 x^{3} + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.1.4.10a1.4 |
$4$ |
$x^{4} + 4 x^{3} + 8 x^{2} + 10$ |
$2$ |
$1$ |
$4$ |
$10$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[3, \frac{7}{2}]$ |
$[2,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2]$ |
$[1]$ |
$2$ |
$t + 1$ |
$x^{4} + 4 x^{3} + 8 x^{2} + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.1.4.10a1.5 |
$4$ |
$x^{4} + 4 x^{3} + 4 x^{2} + 2$ |
$2$ |
$1$ |
$4$ |
$10$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[3, \frac{7}{2}]$ |
$[2,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2]$ |
$[1]$ |
$2$ |
$t + 1$ |
$x^{4} + 4 x^{3} + 4 x^{2} + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.1.4.10a1.6 |
$4$ |
$x^{4} + 4 x^{3} + 12 x^{2} + 2$ |
$2$ |
$1$ |
$4$ |
$10$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[3, \frac{7}{2}]$ |
$[2,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2]$ |
$[1]$ |
$2$ |
$t + 1$ |
$x^{4} + 4 x^{3} + 12 x^{2} + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.1.4.10a1.7 |
$4$ |
$x^{4} + 4 x^{3} + 4 x^{2} + 10$ |
$2$ |
$1$ |
$4$ |
$10$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[3, \frac{7}{2}]$ |
$[2,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2]$ |
$[1]$ |
$2$ |
$t + 1$ |
$x^{4} + 4 x^{3} + 4 x^{2} + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.1.4.10a1.8 |
$4$ |
$x^{4} + 4 x^{3} + 12 x^{2} + 10$ |
$2$ |
$1$ |
$4$ |
$10$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[3, \frac{7}{2}]$ |
$[2,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2]$ |
$[1]$ |
$2$ |
$t + 1$ |
$x^{4} + 4 x^{3} + 12 x^{2} + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.1.4.11a1.1 |
$4$ |
$x^{4} + 2$ |
$2$ |
$1$ |
$4$ |
$11$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2]$ |
$[1]$ |
$2$ |
$t + 1$ |
$x^{4} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.1.4.11a1.2 |
$4$ |
$x^{4} + 18$ |
$2$ |
$1$ |
$4$ |
$11$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2]$ |
$[1]$ |
$2$ |
$t + 1$ |
$x^{4} + 18$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.1.4.11a1.3 |
$4$ |
$x^{4} + 8 x + 2$ |
$2$ |
$1$ |
$4$ |
$11$ |
$D_{4}$ (as 4T3) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[3, 4]^{2}$ |
$[2,3]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t + 1$ |
$x^{4} + 8 x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.1.4.11a1.4 |
$4$ |
$x^{4} + 8 x^{3} + 8 x + 2$ |
$2$ |
$1$ |
$4$ |
$11$ |
$D_{4}$ (as 4T3) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[3, 4]^{2}$ |
$[2,3]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t + 1$ |
$x^{4} + 8 x^{3} + 8 x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.1.4.11a1.5 |
$4$ |
$x^{4} + 10$ |
$2$ |
$1$ |
$4$ |
$11$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2]$ |
$[1]$ |
$2$ |
$t + 1$ |
$x^{4} + 10$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.1.4.11a1.6 |
$4$ |
$x^{4} + 26$ |
$2$ |
$1$ |
$4$ |
$11$ |
$D_{4}$ (as 4T3) |
$1$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2]$ |
$[1]$ |
$2$ |
$t + 1$ |
$x^{4} + 26$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.1.4.11a1.7 |
$4$ |
$x^{4} + 8 x + 10$ |
$2$ |
$1$ |
$4$ |
$11$ |
$D_{4}$ (as 4T3) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[3, 4]^{2}$ |
$[2,3]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t + 1$ |
$x^{4} + 8 x + 10$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.1.4.11a1.8 |
$4$ |
$x^{4} + 8 x^{3} + 8 x + 10$ |
$2$ |
$1$ |
$4$ |
$11$ |
$D_{4}$ (as 4T3) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[3, 4]^{2}$ |
$[2,3]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t + 1$ |
$x^{4} + 8 x^{3} + 8 x + 10$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.1.4.11a1.9 |
$4$ |
$x^{4} + 4 x^{2} + 2$ |
$2$ |
$1$ |
$4$ |
$11$ |
$C_4$ (as 4T1) |
$1$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[3, 4]$ |
$[2,3]$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t + 1$ |
$x^{4} + 4 x^{2} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.1.4.11a1.10 |
$4$ |
$x^{4} + 4 x^{2} + 18$ |
$2$ |
$1$ |
$4$ |
$11$ |
$C_4$ (as 4T1) |
$1$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[3, 4]$ |
$[2,3]$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t + 1$ |
$x^{4} + 4 x^{2} + 18$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.1.4.11a1.11 |
$4$ |
$x^{4} + 8 x^{3} + 4 x^{2} + 2$ |
$2$ |
$1$ |
$4$ |
$11$ |
$C_4$ (as 4T1) |
$1$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[3, 4]$ |
$[2,3]$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t + 1$ |
$x^{4} + 8 x^{3} + 4 x^{2} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
