| 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 |
| 2.2.3.4a1.2 |
$6$ |
$( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$3$ |
$4$ |
$S_3$ (as 6T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + t + 1$ |
$x^{3} + 2$ |
$[0]$ |
$[1]$ |
$z^2 + z + 1$ |
$[3]$ |
| 3.2.3.8a1.1 |
$6$ |
$( x^{2} + 2 x + 2 )^{3} + 3 ( x^{2} + 2 x + 2 )^{2} + 3$ |
$3$ |
$2$ |
$3$ |
$8$ |
$S_3$ (as 6T2) |
$2$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{2}$ |
$[1]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 2 t + 2$ |
$x^{3} + 3 x^{2} + 3$ |
$[2, 0]$ |
$[1]$ |
$z^2 + 1$ |
undefined |
| 3.1.6.7a1.1 |
$6$ |
$x^{6} + 3 x^{2} + 3$ |
$3$ |
$1$ |
$6$ |
$7$ |
$S_3$ (as 6T2) |
$1$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t + 1$ |
$x^{6} + 3 x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
$[1, 5]$ |
| 3.1.6.7a1.3 |
$6$ |
$x^{6} + 6 x^{2} + 6$ |
$3$ |
$1$ |
$6$ |
$7$ |
$S_3$ (as 6T2) |
$1$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t + 1$ |
$x^{6} + 6 x^{2} + 6$ |
$[2, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
undefined |
| 3.1.6.11a1.1 |
$6$ |
$x^{6} + 3$ |
$3$ |
$1$ |
$6$ |
$11$ |
$S_3$ (as 6T2) |
$1$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{5}{2}]_{2}$ |
$[\frac{3}{2}]_{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t + 1$ |
$x^{6} + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
$[1, 7]$ |
| 3.1.6.11a1.3 |
$6$ |
$x^{6} + 9 x^{2} + 3$ |
$3$ |
$1$ |
$6$ |
$11$ |
$S_3$ (as 6T2) |
$1$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{5}{2}]_{2}$ |
$[\frac{3}{2}]_{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t + 1$ |
$x^{6} + 9 x^{2} + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
$[1, 7]$ |
| 3.1.6.11a1.5 |
$6$ |
$x^{6} + 18 x^{2} + 3$ |
$3$ |
$1$ |
$6$ |
$11$ |
$S_3$ (as 6T2) |
$1$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{5}{2}]_{2}$ |
$[\frac{3}{2}]_{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t + 1$ |
$x^{6} + 18 x^{2} + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
$[1, 7]$ |
| 5.2.3.4a1.2 |
$6$ |
$( x^{2} + 4 x + 2 )^{3} + 5$ |
$5$ |
$2$ |
$3$ |
$4$ |
$S_3$ (as 6T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 4 t + 2$ |
$x^{3} + 5$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 11.2.3.4a1.2 |
$6$ |
$( x^{2} + 7 x + 2 )^{3} + 11$ |
$11$ |
$2$ |
$3$ |
$4$ |
$S_3$ (as 6T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 7 t + 2$ |
$x^{3} + 11$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 17.2.3.4a1.2 |
$6$ |
$( x^{2} + 16 x + 3 )^{3} + 17$ |
$17$ |
$2$ |
$3$ |
$4$ |
$S_3$ (as 6T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 16 t + 3$ |
$x^{3} + 17$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 23.2.3.4a1.2 |
$6$ |
$( x^{2} + 21 x + 5 )^{3} + 23$ |
$23$ |
$2$ |
$3$ |
$4$ |
$S_3$ (as 6T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 21 t + 5$ |
$x^{3} + 23$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 29.2.3.4a1.2 |
$6$ |
$( x^{2} + 24 x + 2 )^{3} + 29$ |
$29$ |
$2$ |
$3$ |
$4$ |
$S_3$ (as 6T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 24 t + 2$ |
$x^{3} + 29$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 41.2.3.4a1.2 |
$6$ |
$( x^{2} + 38 x + 6 )^{3} + 41$ |
$41$ |
$2$ |
$3$ |
$4$ |
$S_3$ (as 6T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 38 t + 6$ |
$x^{3} + 41$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 47.2.3.4a1.2 |
$6$ |
$( x^{2} + 45 x + 5 )^{3} + 47$ |
$47$ |
$2$ |
$3$ |
$4$ |
$S_3$ (as 6T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 45 t + 5$ |
$x^{3} + 47$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 53.2.3.4a1.2 |
$6$ |
$( x^{2} + 49 x + 2 )^{3} + 53$ |
$53$ |
$2$ |
$3$ |
$4$ |
$S_3$ (as 6T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 49 t + 2$ |
$x^{3} + 53$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 59.2.3.4a1.2 |
$6$ |
$( x^{2} + 58 x + 2 )^{3} + 59$ |
$59$ |
$2$ |
$3$ |
$4$ |
$S_3$ (as 6T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 58 t + 2$ |
$x^{3} + 59$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 71.2.3.4a1.2 |
$6$ |
$( x^{2} + 69 x + 7 )^{3} + 71$ |
$71$ |
$2$ |
$3$ |
$4$ |
$S_3$ (as 6T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 69 t + 7$ |
$x^{3} + 71$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 83.2.3.4a1.2 |
$6$ |
$( x^{2} + 82 x + 2 )^{3} + 83$ |
$83$ |
$2$ |
$3$ |
$4$ |
$S_3$ (as 6T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 82 t + 2$ |
$x^{3} + 83$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 89.2.3.4a1.2 |
$6$ |
$( x^{2} + 82 x + 3 )^{3} + 89$ |
$89$ |
$2$ |
$3$ |
$4$ |
$S_3$ (as 6T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 82 t + 3$ |
$x^{3} + 89$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 101.2.3.4a1.2 |
$6$ |
$( x^{2} + 97 x + 2 )^{3} + 101$ |
$101$ |
$2$ |
$3$ |
$4$ |
$S_3$ (as 6T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 97 t + 2$ |
$x^{3} + 101$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 107.2.3.4a1.2 |
$6$ |
$( x^{2} + 103 x + 2 )^{3} + 107$ |
$107$ |
$2$ |
$3$ |
$4$ |
$S_3$ (as 6T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 103 t + 2$ |
$x^{3} + 107$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 113.2.3.4a1.2 |
$6$ |
$( x^{2} + 101 x + 3 )^{3} + 113$ |
$113$ |
$2$ |
$3$ |
$4$ |
$S_3$ (as 6T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 101 t + 3$ |
$x^{3} + 113$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 131.2.3.4a1.2 |
$6$ |
$( x^{2} + 127 x + 2 )^{3} + 131$ |
$131$ |
$2$ |
$3$ |
$4$ |
$S_3$ (as 6T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 127 t + 2$ |
$x^{3} + 131$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 137.2.3.4a1.2 |
$6$ |
$( x^{2} + 131 x + 3 )^{3} + 137$ |
$137$ |
$2$ |
$3$ |
$4$ |
$S_3$ (as 6T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 131 t + 3$ |
$x^{3} + 137$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 149.2.3.4a1.2 |
$6$ |
$( x^{2} + 145 x + 2 )^{3} + 149$ |
$149$ |
$2$ |
$3$ |
$4$ |
$S_3$ (as 6T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 145 t + 2$ |
$x^{3} + 149$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 167.2.3.4a1.2 |
$6$ |
$( x^{2} + 166 x + 5 )^{3} + 167$ |
$167$ |
$2$ |
$3$ |
$4$ |
$S_3$ (as 6T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 166 t + 5$ |
$x^{3} + 167$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 173.2.3.4a1.2 |
$6$ |
$( x^{2} + 169 x + 2 )^{3} + 173$ |
$173$ |
$2$ |
$3$ |
$4$ |
$S_3$ (as 6T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 169 t + 2$ |
$x^{3} + 173$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 179.2.3.4a1.2 |
$6$ |
$( x^{2} + 172 x + 2 )^{3} + 179$ |
$179$ |
$2$ |
$3$ |
$4$ |
$S_3$ (as 6T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 172 t + 2$ |
$x^{3} + 179$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 191.2.3.4a1.2 |
$6$ |
$( x^{2} + 190 x + 19 )^{3} + 191$ |
$191$ |
$2$ |
$3$ |
$4$ |
$S_3$ (as 6T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 190 t + 19$ |
$x^{3} + 191$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 197.2.3.4a1.2 |
$6$ |
$( x^{2} + 192 x + 2 )^{3} + 197$ |
$197$ |
$2$ |
$3$ |
$4$ |
$S_3$ (as 6T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 192 t + 2$ |
$x^{3} + 197$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
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