The results below are complete, since the LMFDB contains all p-adic fields of degree at most 23 and residue characteristic at most 199
| 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 |
| 7.7.1.0a1.1 |
$7$ |
$x^{7} + 6 x + 4$ |
$7$ |
$7$ |
$1$ |
$0$ |
$C_7$ (as 7T1) |
$7$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{7}$ |
$[\ ]^{7}$ |
$[\ ]$ |
$[\ ]$ |
$7$ |
$t^{7} + 6 t + 4$ |
$x - 7$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 7.1.7.7a1.1 |
$7$ |
$x^{7} + 7 x + 7$ |
$7$ |
$1$ |
$7$ |
$7$ |
$F_7$ (as 7T4) |
$1$ |
$6$ |
$[\frac{7}{6}]$ |
$[\frac{1}{6}]$ |
$[\frac{7}{6}]_{6}$ |
$[\frac{1}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 4$ |
$x^{7} + 7 x + 7$ |
$[1, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 7.1.7.7a1.2 |
$7$ |
$x^{7} + 14 x + 7$ |
$7$ |
$1$ |
$7$ |
$7$ |
$F_7$ (as 7T4) |
$1$ |
$6$ |
$[\frac{7}{6}]$ |
$[\frac{1}{6}]$ |
$[\frac{7}{6}]_{6}$ |
$[\frac{1}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 4$ |
$x^{7} + 14 x + 7$ |
$[1, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 7.1.7.7a1.3 |
$7$ |
$x^{7} + 21 x + 7$ |
$7$ |
$1$ |
$7$ |
$7$ |
$F_7$ (as 7T4) |
$1$ |
$6$ |
$[\frac{7}{6}]$ |
$[\frac{1}{6}]$ |
$[\frac{7}{6}]_{6}$ |
$[\frac{1}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 4$ |
$x^{7} + 21 x + 7$ |
$[1, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 7.1.7.7a1.4 |
$7$ |
$x^{7} + 28 x + 7$ |
$7$ |
$1$ |
$7$ |
$7$ |
$F_7$ (as 7T4) |
$1$ |
$6$ |
$[\frac{7}{6}]$ |
$[\frac{1}{6}]$ |
$[\frac{7}{6}]_{6}$ |
$[\frac{1}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 4$ |
$x^{7} + 28 x + 7$ |
$[1, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 7.1.7.7a1.5 |
$7$ |
$x^{7} + 35 x + 7$ |
$7$ |
$1$ |
$7$ |
$7$ |
$F_7$ (as 7T4) |
$1$ |
$6$ |
$[\frac{7}{6}]$ |
$[\frac{1}{6}]$ |
$[\frac{7}{6}]_{6}$ |
$[\frac{1}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 4$ |
$x^{7} + 35 x + 7$ |
$[1, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 7.1.7.7a1.6 |
$7$ |
$x^{7} + 42 x + 7$ |
$7$ |
$1$ |
$7$ |
$7$ |
$F_7$ (as 7T4) |
$1$ |
$6$ |
$[\frac{7}{6}]$ |
$[\frac{1}{6}]$ |
$[\frac{7}{6}]_{6}$ |
$[\frac{1}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 4$ |
$x^{7} + 42 x + 7$ |
$[1, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 7.1.7.8a1.1 |
$7$ |
$x^{7} + 21 x^{2} + 7$ |
$7$ |
$1$ |
$7$ |
$8$ |
$F_7$ (as 7T4) |
$2$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}]_{3}^{2}$ |
$[\frac{1}{3}]_{3}^{2}$ |
$[\ ]^{2}_{3}$ |
$[\ ]^{2}_{3}$ |
$1$ |
$t + 4$ |
$x^{7} + 21 x^{2} + 7$ |
$[2, 0]$ |
$[2]$ |
$z^2 + 1$ |
undefined |
| 7.1.7.8a1.2 |
$7$ |
$x^{7} + 35 x^{2} + 7$ |
$7$ |
$1$ |
$7$ |
$8$ |
$F_7$ (as 7T4) |
$2$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}]_{3}^{2}$ |
$[\frac{1}{3}]_{3}^{2}$ |
$[\ ]^{2}_{3}$ |
$[\ ]^{2}_{3}$ |
$1$ |
$t + 4$ |
$x^{7} + 35 x^{2} + 7$ |
$[2, 0]$ |
$[2]$ |
$z^2 + 1$ |
undefined |
| 7.1.7.8a1.3 |
$7$ |
$x^{7} + 42 x^{2} + 7$ |
$7$ |
$1$ |
$7$ |
$8$ |
$F_7$ (as 7T4) |
$2$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}]_{3}^{2}$ |
$[\frac{1}{3}]_{3}^{2}$ |
$[\ ]^{2}_{3}$ |
$[\ ]^{2}_{3}$ |
$1$ |
$t + 4$ |
$x^{7} + 42 x^{2} + 7$ |
$[2, 0]$ |
$[2]$ |
$z^2 + 1$ |
undefined |
| 7.1.7.8a2.1 |
$7$ |
$x^{7} + 7 x^{2} + 7$ |
$7$ |
$1$ |
$7$ |
$8$ |
$C_7:C_3$ (as 7T3) |
$1$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}]_{3}$ |
$[\frac{1}{3}]_{3}$ |
$[\ ]_{3}$ |
$[\ ]_{3}$ |
$1$ |
$t + 4$ |
$x^{7} + 7 x^{2} + 7$ |
$[2, 0]$ |
$[1]$ |
$z^2 + 3$ |
undefined |
| 7.1.7.8a2.2 |
$7$ |
$x^{7} + 14 x^{2} + 7$ |
$7$ |
$1$ |
$7$ |
$8$ |
$C_7:C_3$ (as 7T3) |
$1$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}]_{3}$ |
$[\frac{1}{3}]_{3}$ |
$[\ ]_{3}$ |
$[\ ]_{3}$ |
$1$ |
$t + 4$ |
$x^{7} + 14 x^{2} + 7$ |
$[2, 0]$ |
$[1]$ |
$z^2 + 3$ |
undefined |
| 7.1.7.8a2.3 |
$7$ |
$x^{7} + 28 x^{2} + 7$ |
$7$ |
$1$ |
$7$ |
$8$ |
$C_7:C_3$ (as 7T3) |
$1$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}]_{3}$ |
$[\frac{1}{3}]_{3}$ |
$[\ ]_{3}$ |
$[\ ]_{3}$ |
$1$ |
$t + 4$ |
$x^{7} + 28 x^{2} + 7$ |
$[2, 0]$ |
$[1]$ |
$z^2 + 3$ |
undefined |
| 7.1.7.9a1.1 |
$7$ |
$x^{7} + 14 x^{3} + 7$ |
$7$ |
$1$ |
$7$ |
$9$ |
$D_{7}$ (as 7T2) |
$1$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$1$ |
$t + 4$ |
$x^{7} + 14 x^{3} + 7$ |
$[3, 0]$ |
$[1]$ |
$z^3 + 1$ |
undefined |
| 7.1.7.9a1.2 |
$7$ |
$x^{7} + 35 x^{3} + 7$ |
$7$ |
$1$ |
$7$ |
$9$ |
$D_{7}$ (as 7T2) |
$1$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$1$ |
$t + 4$ |
$x^{7} + 35 x^{3} + 7$ |
$[3, 0]$ |
$[1]$ |
$z^3 + 1$ |
undefined |
| 7.1.7.9a2.1 |
$7$ |
$x^{7} + 21 x^{3} + 7$ |
$7$ |
$1$ |
$7$ |
$9$ |
$F_7$ (as 7T4) |
$3$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{3}$ |
$[\frac{1}{2}]_{2}^{3}$ |
$[\ ]^{3}_{2}$ |
$[\ ]^{3}_{2}$ |
$1$ |
$t + 4$ |
$x^{7} + 21 x^{3} + 7$ |
$[3, 0]$ |
$[3]$ |
$z^3 + 2$ |
undefined |
| 7.1.7.9a2.2 |
$7$ |
$x^{7} + 28 x^{3} + 7$ |
$7$ |
$1$ |
$7$ |
$9$ |
$F_7$ (as 7T4) |
$3$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{3}$ |
$[\frac{1}{2}]_{2}^{3}$ |
$[\ ]^{3}_{2}$ |
$[\ ]^{3}_{2}$ |
$1$ |
$t + 4$ |
$x^{7} + 28 x^{3} + 7$ |
$[3, 0]$ |
$[3]$ |
$z^3 + 2$ |
undefined |
| 7.1.7.9a3.1 |
$7$ |
$x^{7} + 7 x^{3} + 7$ |
$7$ |
$1$ |
$7$ |
$9$ |
$F_7$ (as 7T4) |
$3$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{3}$ |
$[\frac{1}{2}]_{2}^{3}$ |
$[\ ]^{3}_{2}$ |
$[\ ]^{3}_{2}$ |
$1$ |
$t + 4$ |
$x^{7} + 7 x^{3} + 7$ |
$[3, 0]$ |
$[3]$ |
$z^3 + 3$ |
undefined |
| 7.1.7.9a3.2 |
$7$ |
$x^{7} + 42 x^{3} + 7$ |
$7$ |
$1$ |
$7$ |
$9$ |
$F_7$ (as 7T4) |
$3$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{3}$ |
$[\frac{1}{2}]_{2}^{3}$ |
$[\ ]^{3}_{2}$ |
$[\ ]^{3}_{2}$ |
$1$ |
$t + 4$ |
$x^{7} + 42 x^{3} + 7$ |
$[3, 0]$ |
$[3]$ |
$z^3 + 3$ |
undefined |
| 7.1.7.10a1.1 |
$7$ |
$x^{7} + 21 x^{4} + 7$ |
$7$ |
$1$ |
$7$ |
$10$ |
$F_7$ (as 7T4) |
$2$ |
$3$ |
$[\frac{5}{3}]$ |
$[\frac{2}{3}]$ |
$[\frac{5}{3}]_{3}^{2}$ |
$[\frac{2}{3}]_{3}^{2}$ |
$[\ ]^{2}_{3}$ |
$[\ ]^{2}_{3}$ |
$1$ |
$t + 4$ |
$x^{7} + 21 x^{4} + 7$ |
$[4, 0]$ |
$[2]$ |
$z^2 + 1$ |
undefined |
| 7.1.7.10a1.2 |
$7$ |
$x^{7} + 35 x^{4} + 7$ |
$7$ |
$1$ |
$7$ |
$10$ |
$F_7$ (as 7T4) |
$2$ |
$3$ |
$[\frac{5}{3}]$ |
$[\frac{2}{3}]$ |
$[\frac{5}{3}]_{3}^{2}$ |
$[\frac{2}{3}]_{3}^{2}$ |
$[\ ]^{2}_{3}$ |
$[\ ]^{2}_{3}$ |
$1$ |
$t + 4$ |
$x^{7} + 35 x^{4} + 7$ |
$[4, 0]$ |
$[2]$ |
$z^2 + 1$ |
undefined |
| 7.1.7.10a1.3 |
$7$ |
$x^{7} + 42 x^{4} + 7$ |
$7$ |
$1$ |
$7$ |
$10$ |
$F_7$ (as 7T4) |
$2$ |
$3$ |
$[\frac{5}{3}]$ |
$[\frac{2}{3}]$ |
$[\frac{5}{3}]_{3}^{2}$ |
$[\frac{2}{3}]_{3}^{2}$ |
$[\ ]^{2}_{3}$ |
$[\ ]^{2}_{3}$ |
$1$ |
$t + 4$ |
$x^{7} + 42 x^{4} + 7$ |
$[4, 0]$ |
$[2]$ |
$z^2 + 1$ |
undefined |
| 7.1.7.10a2.1 |
$7$ |
$x^{7} + 7 x^{4} + 7$ |
$7$ |
$1$ |
$7$ |
$10$ |
$C_7:C_3$ (as 7T3) |
$1$ |
$3$ |
$[\frac{5}{3}]$ |
$[\frac{2}{3}]$ |
$[\frac{5}{3}]_{3}$ |
$[\frac{2}{3}]_{3}$ |
$[\ ]_{3}$ |
$[\ ]_{3}$ |
$1$ |
$t + 4$ |
$x^{7} + 7 x^{4} + 7$ |
$[4, 0]$ |
$[1]$ |
$z^2 + 3$ |
undefined |
| 7.1.7.10a2.2 |
$7$ |
$x^{7} + 14 x^{4} + 7$ |
$7$ |
$1$ |
$7$ |
$10$ |
$C_7:C_3$ (as 7T3) |
$1$ |
$3$ |
$[\frac{5}{3}]$ |
$[\frac{2}{3}]$ |
$[\frac{5}{3}]_{3}$ |
$[\frac{2}{3}]_{3}$ |
$[\ ]_{3}$ |
$[\ ]_{3}$ |
$1$ |
$t + 4$ |
$x^{7} + 14 x^{4} + 7$ |
$[4, 0]$ |
$[1]$ |
$z^2 + 3$ |
undefined |
| 7.1.7.10a2.3 |
$7$ |
$x^{7} + 28 x^{4} + 7$ |
$7$ |
$1$ |
$7$ |
$10$ |
$C_7:C_3$ (as 7T3) |
$1$ |
$3$ |
$[\frac{5}{3}]$ |
$[\frac{2}{3}]$ |
$[\frac{5}{3}]_{3}$ |
$[\frac{2}{3}]_{3}$ |
$[\ ]_{3}$ |
$[\ ]_{3}$ |
$1$ |
$t + 4$ |
$x^{7} + 28 x^{4} + 7$ |
$[4, 0]$ |
$[1]$ |
$z^2 + 3$ |
undefined |
| 7.1.7.11a1.1 |
$7$ |
$x^{7} + 7 x^{5} + 7$ |
$7$ |
$1$ |
$7$ |
$11$ |
$F_7$ (as 7T4) |
$1$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 4$ |
$x^{7} + 7 x^{5} + 7$ |
$[5, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 7.1.7.11a1.2 |
$7$ |
$x^{7} + 14 x^{5} + 7$ |
$7$ |
$1$ |
$7$ |
$11$ |
$F_7$ (as 7T4) |
$1$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 4$ |
$x^{7} + 14 x^{5} + 7$ |
$[5, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 7.1.7.11a1.3 |
$7$ |
$x^{7} + 21 x^{5} + 7$ |
$7$ |
$1$ |
$7$ |
$11$ |
$F_7$ (as 7T4) |
$1$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 4$ |
$x^{7} + 21 x^{5} + 7$ |
$[5, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 7.1.7.11a1.4 |
$7$ |
$x^{7} + 28 x^{5} + 7$ |
$7$ |
$1$ |
$7$ |
$11$ |
$F_7$ (as 7T4) |
$1$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 4$ |
$x^{7} + 28 x^{5} + 7$ |
$[5, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 7.1.7.11a1.5 |
$7$ |
$x^{7} + 35 x^{5} + 7$ |
$7$ |
$1$ |
$7$ |
$11$ |
$F_7$ (as 7T4) |
$1$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 4$ |
$x^{7} + 35 x^{5} + 7$ |
$[5, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 7.1.7.11a1.6 |
$7$ |
$x^{7} + 42 x^{5} + 7$ |
$7$ |
$1$ |
$7$ |
$11$ |
$F_7$ (as 7T4) |
$1$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 4$ |
$x^{7} + 42 x^{5} + 7$ |
$[5, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 7.1.7.12a1.1 |
$7$ |
$x^{7} + 7 x^{6} + 7$ |
$7$ |
$1$ |
$7$ |
$12$ |
$D_{7}$ (as 7T2) |
$2$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{2}$ |
$[1]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$1$ |
$t + 4$ |
$x^{7} + 7 x^{6} + 7$ |
$[6, 0]$ |
$[2]$ |
$z^6 + 1$ |
undefined |
| 7.1.7.12a2.1 |
$7$ |
$x^{7} + 14 x^{6} + 7$ |
$7$ |
$1$ |
$7$ |
$12$ |
$F_7$ (as 7T4) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{6}$ |
$[1]^{6}$ |
$[\ ]^{6}$ |
$[\ ]^{6}$ |
$1$ |
$t + 4$ |
$x^{7} + 14 x^{6} + 7$ |
$[6, 0]$ |
$[6]$ |
$z^6 + 2$ |
undefined |
| 7.1.7.12a3.1 |
$7$ |
$x^{7} + 21 x^{6} + 7$ |
$7$ |
$1$ |
$7$ |
$12$ |
$C_7:C_3$ (as 7T3) |
$3$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{3}$ |
$[1]^{3}$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$1$ |
$t + 4$ |
$x^{7} + 21 x^{6} + 7$ |
$[6, 0]$ |
$[3]$ |
$z^6 + 3$ |
undefined |
| 7.1.7.12a4.1 |
$7$ |
$x^{7} + 28 x^{6} + 7$ |
$7$ |
$1$ |
$7$ |
$12$ |
$F_7$ (as 7T4) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{6}$ |
$[1]^{6}$ |
$[\ ]^{6}$ |
$[\ ]^{6}$ |
$1$ |
$t + 4$ |
$x^{7} + 28 x^{6} + 7$ |
$[6, 0]$ |
$[6]$ |
$z^6 + 4$ |
undefined |
| 7.1.7.12a5.1 |
$7$ |
$x^{7} + 35 x^{6} + 7$ |
$7$ |
$1$ |
$7$ |
$12$ |
$C_7:C_3$ (as 7T3) |
$3$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{3}$ |
$[1]^{3}$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$1$ |
$t + 4$ |
$x^{7} + 35 x^{6} + 7$ |
$[6, 0]$ |
$[3]$ |
$z^6 + 5$ |
undefined |
| 7.1.7.12a6.1 |
$7$ |
$x^{7} + 42 x^{6} + 7$ |
$7$ |
$1$ |
$7$ |
$12$ |
$C_7$ (as 7T1) |
$1$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]$ |
$[1]$ |
$[\ ]$ |
$[\ ]$ |
$7$ |
$t + 4$ |
$x^{7} + 42 x^{6} + 7$ |
$[6, 0]$ |
$[1]$ |
$z^6 + 6$ |
undefined |
| 7.1.7.12a6.2 |
$7$ |
$x^{7} + 42 x^{6} + 56$ |
$7$ |
$1$ |
$7$ |
$12$ |
$C_7$ (as 7T1) |
$1$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]$ |
$[1]$ |
$[\ ]$ |
$[\ ]$ |
$7$ |
$t + 4$ |
$x^{7} + 42 x^{6} + 56$ |
$[6, 0]$ |
$[1]$ |
$z^6 + 6$ |
undefined |
| 7.1.7.12a6.3 |
$7$ |
$x^{7} + 42 x^{6} + 105$ |
$7$ |
$1$ |
$7$ |
$12$ |
$C_7$ (as 7T1) |
$1$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]$ |
$[1]$ |
$[\ ]$ |
$[\ ]$ |
$7$ |
$t + 4$ |
$x^{7} + 42 x^{6} + 105$ |
$[6, 0]$ |
$[1]$ |
$z^6 + 6$ |
undefined |
| 7.1.7.12a6.4 |
$7$ |
$x^{7} + 42 x^{6} + 154$ |
$7$ |
$1$ |
$7$ |
$12$ |
$C_7$ (as 7T1) |
$1$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]$ |
$[1]$ |
$[\ ]$ |
$[\ ]$ |
$7$ |
$t + 4$ |
$x^{7} + 42 x^{6} + 154$ |
$[6, 0]$ |
$[1]$ |
$z^6 + 6$ |
undefined |
| 7.1.7.12a6.5 |
$7$ |
$x^{7} + 42 x^{6} + 203$ |
$7$ |
$1$ |
$7$ |
$12$ |
$C_7$ (as 7T1) |
$1$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]$ |
$[1]$ |
$[\ ]$ |
$[\ ]$ |
$7$ |
$t + 4$ |
$x^{7} + 42 x^{6} + 203$ |
$[6, 0]$ |
$[1]$ |
$z^6 + 6$ |
undefined |
| 7.1.7.12a6.6 |
$7$ |
$x^{7} + 42 x^{6} + 252$ |
$7$ |
$1$ |
$7$ |
$12$ |
$C_7$ (as 7T1) |
$1$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]$ |
$[1]$ |
$[\ ]$ |
$[\ ]$ |
$7$ |
$t + 4$ |
$x^{7} + 42 x^{6} + 252$ |
$[6, 0]$ |
$[1]$ |
$z^6 + 6$ |
undefined |
| 7.1.7.12a6.7 |
$7$ |
$x^{7} + 42 x^{6} + 301$ |
$7$ |
$1$ |
$7$ |
$12$ |
$C_7$ (as 7T1) |
$1$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]$ |
$[1]$ |
$[\ ]$ |
$[\ ]$ |
$7$ |
$t + 4$ |
$x^{7} + 42 x^{6} + 301$ |
$[6, 0]$ |
$[1]$ |
$z^6 + 6$ |
undefined |
| 7.1.7.13a1.1 |
$7$ |
$x^{7} + 7$ |
$7$ |
$1$ |
$7$ |
$13$ |
$F_7$ (as 7T4) |
$1$ |
$6$ |
$[\frac{13}{6}]$ |
$[\frac{7}{6}]$ |
$[\frac{13}{6}]_{6}$ |
$[\frac{7}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 4$ |
$x^{7} + 7$ |
$[7, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 7.1.7.13a1.2 |
$7$ |
$x^{7} + 49 x + 7$ |
$7$ |
$1$ |
$7$ |
$13$ |
$F_7$ (as 7T4) |
$1$ |
$6$ |
$[\frac{13}{6}]$ |
$[\frac{7}{6}]$ |
$[\frac{13}{6}]_{6}$ |
$[\frac{7}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 4$ |
$x^{7} + 49 x + 7$ |
$[7, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 7.1.7.13a1.3 |
$7$ |
$x^{7} + 98 x + 7$ |
$7$ |
$1$ |
$7$ |
$13$ |
$F_7$ (as 7T4) |
$1$ |
$6$ |
$[\frac{13}{6}]$ |
$[\frac{7}{6}]$ |
$[\frac{13}{6}]_{6}$ |
$[\frac{7}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 4$ |
$x^{7} + 98 x + 7$ |
$[7, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 7.1.7.13a1.4 |
$7$ |
$x^{7} + 147 x + 7$ |
$7$ |
$1$ |
$7$ |
$13$ |
$F_7$ (as 7T4) |
$1$ |
$6$ |
$[\frac{13}{6}]$ |
$[\frac{7}{6}]$ |
$[\frac{13}{6}]_{6}$ |
$[\frac{7}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 4$ |
$x^{7} + 147 x + 7$ |
$[7, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 7.1.7.13a1.5 |
$7$ |
$x^{7} + 196 x + 7$ |
$7$ |
$1$ |
$7$ |
$13$ |
$F_7$ (as 7T4) |
$1$ |
$6$ |
$[\frac{13}{6}]$ |
$[\frac{7}{6}]$ |
$[\frac{13}{6}]_{6}$ |
$[\frac{7}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 4$ |
$x^{7} + 196 x + 7$ |
$[7, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 7.1.7.13a1.6 |
$7$ |
$x^{7} + 245 x + 7$ |
$7$ |
$1$ |
$7$ |
$13$ |
$F_7$ (as 7T4) |
$1$ |
$6$ |
$[\frac{13}{6}]$ |
$[\frac{7}{6}]$ |
$[\frac{13}{6}]_{6}$ |
$[\frac{7}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 4$ |
$x^{7} + 245 x + 7$ |
$[7, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 7.1.7.13a1.7 |
$7$ |
$x^{7} + 294 x + 7$ |
$7$ |
$1$ |
$7$ |
$13$ |
$F_7$ (as 7T4) |
$1$ |
$6$ |
$[\frac{13}{6}]$ |
$[\frac{7}{6}]$ |
$[\frac{13}{6}]_{6}$ |
$[\frac{7}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 4$ |
$x^{7} + 294 x + 7$ |
$[7, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
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