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Degree Residue characteristic Galois group Galois unramified degree Assoc. Inertia
Ramification index Discriminant exponent Inertia subgroup Galois tame degree Indices
Residue field degree Top slope Wild Visible Wild inertia subgroup
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Results (47 matches)

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Label Polynomial $p$ $e$ $f$ $c$ Galois group $u$ $t$ Visible slopes Slope content Unram. Ext. Eisen. Poly. Ind. of Insep. Assoc. Inertia
3.7.6.1 $x^{7} + 3$ $3$ $7$ $1$ $6$ $F_7$ (as 7T4) $6$ $7$ $[\ ]$ $[\ ]_{7}^{6}$ $t + 1$ $x^{7} + 3$ $[0]$ $[6]$
5.7.6.1 $x^{7} + 5$ $5$ $7$ $1$ $6$ $F_7$ (as 7T4) $6$ $7$ $[\ ]$ $[\ ]_{7}^{6}$ $t + 3$ $x^{7} + 5$ $[0]$ $[6]$
7.7.7.1 $x^{7} + 42 x + 7$ $7$ $7$ $1$ $7$ $F_7$ (as 7T4) $1$ $6$ $[7/6]$ $[7/6]_{6}$ $t + 4$ $x^{7} + 42 x + 7$ $[1, 0]$ $[1]$
7.7.7.2 $x^{7} + 21 x + 7$ $7$ $7$ $1$ $7$ $F_7$ (as 7T4) $1$ $6$ $[7/6]$ $[7/6]_{6}$ $t + 4$ $x^{7} + 21 x + 7$ $[1, 0]$ $[1]$
7.7.7.3 $x^{7} + 35 x + 7$ $7$ $7$ $1$ $7$ $F_7$ (as 7T4) $1$ $6$ $[7/6]$ $[7/6]_{6}$ $t + 4$ $x^{7} + 35 x + 7$ $[1, 0]$ $[1]$
7.7.7.4 $x^{7} + 14 x + 7$ $7$ $7$ $1$ $7$ $F_7$ (as 7T4) $1$ $6$ $[7/6]$ $[7/6]_{6}$ $t + 4$ $x^{7} + 14 x + 7$ $[1, 0]$ $[1]$
7.7.7.5 $x^{7} + 7 x + 7$ $7$ $7$ $1$ $7$ $F_7$ (as 7T4) $1$ $6$ $[7/6]$ $[7/6]_{6}$ $t + 4$ $x^{7} + 7 x + 7$ $[1, 0]$ $[1]$
7.7.7.6 $x^{7} + 28 x + 7$ $7$ $7$ $1$ $7$ $F_7$ (as 7T4) $1$ $6$ $[7/6]$ $[7/6]_{6}$ $t + 4$ $x^{7} + 28 x + 7$ $[1, 0]$ $[1]$
7.7.8.4 $x^{7} + 21 x^{2} + 7$ $7$ $7$ $1$ $8$ $F_7$ (as 7T4) $2$ $3$ $[4/3]$ $[4/3]_{3}^{2}$ $t + 4$ $x^{7} + 21 x^{2} + 7$ $[2, 0]$ $[2]$
7.7.8.5 $x^{7} + 42 x^{2} + 7$ $7$ $7$ $1$ $8$ $F_7$ (as 7T4) $2$ $3$ $[4/3]$ $[4/3]_{3}^{2}$ $t + 4$ $x^{7} + 42 x^{2} + 7$ $[2, 0]$ $[2]$
7.7.8.6 $x^{7} + 35 x^{2} + 7$ $7$ $7$ $1$ $8$ $F_7$ (as 7T4) $2$ $3$ $[4/3]$ $[4/3]_{3}^{2}$ $t + 4$ $x^{7} + 35 x^{2} + 7$ $[2, 0]$ $[2]$
7.7.9.2 $x^{7} + 7 x^{3} + 7$ $7$ $7$ $1$ $9$ $F_7$ (as 7T4) $3$ $2$ $[3/2]$ $[3/2]_{2}^{3}$ $t + 4$ $x^{7} + 7 x^{3} + 7$ $[3, 0]$ $[3]$
7.7.9.3 $x^{7} + 28 x^{3} + 7$ $7$ $7$ $1$ $9$ $F_7$ (as 7T4) $3$ $2$ $[3/2]$ $[3/2]_{2}^{3}$ $t + 4$ $x^{7} + 28 x^{3} + 7$ $[3, 0]$ $[3]$
7.7.9.5 $x^{7} + 42 x^{3} + 7$ $7$ $7$ $1$ $9$ $F_7$ (as 7T4) $3$ $2$ $[3/2]$ $[3/2]_{2}^{3}$ $t + 4$ $x^{7} + 42 x^{3} + 7$ $[3, 0]$ $[3]$
7.7.9.6 $x^{7} + 21 x^{3} + 7$ $7$ $7$ $1$ $9$ $F_7$ (as 7T4) $3$ $2$ $[3/2]$ $[3/2]_{2}^{3}$ $t + 4$ $x^{7} + 21 x^{3} + 7$ $[3, 0]$ $[3]$
7.7.10.4 $x^{7} + 21 x^{4} + 7$ $7$ $7$ $1$ $10$ $F_7$ (as 7T4) $2$ $3$ $[5/3]$ $[5/3]_{3}^{2}$ $t + 4$ $x^{7} + 21 x^{4} + 7$ $[4, 0]$ $[2]$
7.7.10.5 $x^{7} + 35 x^{4} + 7$ $7$ $7$ $1$ $10$ $F_7$ (as 7T4) $2$ $3$ $[5/3]$ $[5/3]_{3}^{2}$ $t + 4$ $x^{7} + 35 x^{4} + 7$ $[4, 0]$ $[2]$
7.7.10.6 $x^{7} + 42 x^{4} + 7$ $7$ $7$ $1$ $10$ $F_7$ (as 7T4) $2$ $3$ $[5/3]$ $[5/3]_{3}^{2}$ $t + 4$ $x^{7} + 42 x^{4} + 7$ $[4, 0]$ $[2]$
7.7.11.1 $x^{7} + 7 x^{5} + 7$ $7$ $7$ $1$ $11$ $F_7$ (as 7T4) $1$ $6$ $[11/6]$ $[11/6]_{6}$ $t + 4$ $x^{7} + 7 x^{5} + 7$ $[5, 0]$ $[1]$
7.7.11.2 $x^{7} + 28 x^{5} + 7$ $7$ $7$ $1$ $11$ $F_7$ (as 7T4) $1$ $6$ $[11/6]$ $[11/6]_{6}$ $t + 4$ $x^{7} + 28 x^{5} + 7$ $[5, 0]$ $[1]$
7.7.11.3 $x^{7} + 14 x^{5} + 7$ $7$ $7$ $1$ $11$ $F_7$ (as 7T4) $1$ $6$ $[11/6]$ $[11/6]_{6}$ $t + 4$ $x^{7} + 14 x^{5} + 7$ $[5, 0]$ $[1]$
7.7.11.4 $x^{7} + 21 x^{5} + 7$ $7$ $7$ $1$ $11$ $F_7$ (as 7T4) $1$ $6$ $[11/6]$ $[11/6]_{6}$ $t + 4$ $x^{7} + 21 x^{5} + 7$ $[5, 0]$ $[1]$
7.7.11.5 $x^{7} + 35 x^{5} + 7$ $7$ $7$ $1$ $11$ $F_7$ (as 7T4) $1$ $6$ $[11/6]$ $[11/6]_{6}$ $t + 4$ $x^{7} + 35 x^{5} + 7$ $[5, 0]$ $[1]$
7.7.11.6 $x^{7} + 42 x^{5} + 7$ $7$ $7$ $1$ $11$ $F_7$ (as 7T4) $1$ $6$ $[11/6]$ $[11/6]_{6}$ $t + 4$ $x^{7} + 42 x^{5} + 7$ $[5, 0]$ $[1]$
7.7.12.11 $x^{7} + 14 x^{6} + 7$ $7$ $7$ $1$ $12$ $F_7$ (as 7T4) $6$ $1$ $[2]$ $[2]^{6}$ $t + 4$ $x^{7} + 14 x^{6} + 7$ $[6, 0]$ $[6]$
7.7.12.12 $x^{7} + 28 x^{6} + 7$ $7$ $7$ $1$ $12$ $F_7$ (as 7T4) $6$ $1$ $[2]$ $[2]^{6}$ $t + 4$ $x^{7} + 28 x^{6} + 7$ $[6, 0]$ $[6]$
7.7.13.1 $x^{7} + 7$ $7$ $7$ $1$ $13$ $F_7$ (as 7T4) $1$ $6$ $[13/6]$ $[13/6]_{6}$ $t + 4$ $x^{7} + 7$ $[7, 0]$ $[1]$
7.7.13.2 $x^{7} + 49 x^{2} + 98 x + 7$ $7$ $7$ $1$ $13$ $F_7$ (as 7T4) $1$ $6$ $[13/6]$ $[13/6]_{6}$ $t + 4$ $x^{7} + 49 x^{2} + 98 x + 7$ $[7, 0]$ $[1]$
7.7.13.3 $x^{7} + 98 x^{2} + 294 x + 7$ $7$ $7$ $1$ $13$ $F_7$ (as 7T4) $1$ $6$ $[13/6]$ $[13/6]_{6}$ $t + 4$ $x^{7} + 98 x^{2} + 294 x + 7$ $[7, 0]$ $[1]$
7.7.13.4 $x^{7} + 196 x^{2} + 147 x + 7$ $7$ $7$ $1$ $13$ $F_7$ (as 7T4) $1$ $6$ $[13/6]$ $[13/6]_{6}$ $t + 4$ $x^{7} + 196 x^{2} + 147 x + 7$ $[7, 0]$ $[1]$
7.7.13.5 $x^{7} + 98 x^{2} + 49 x + 7$ $7$ $7$ $1$ $13$ $F_7$ (as 7T4) $1$ $6$ $[13/6]$ $[13/6]_{6}$ $t + 4$ $x^{7} + 98 x^{2} + 49 x + 7$ $[7, 0]$ $[1]$
7.7.13.6 $x^{7} + 196 x^{2} + 196 x + 7$ $7$ $7$ $1$ $13$ $F_7$ (as 7T4) $1$ $6$ $[13/6]$ $[13/6]_{6}$ $t + 4$ $x^{7} + 196 x^{2} + 196 x + 7$ $[7, 0]$ $[1]$
7.7.13.7 $x^{7} + 49 x^{2} + 245 x + 7$ $7$ $7$ $1$ $13$ $F_7$ (as 7T4) $1$ $6$ $[13/6]$ $[13/6]_{6}$ $t + 4$ $x^{7} + 49 x^{2} + 245 x + 7$ $[7, 0]$ $[1]$
17.7.6.1 $x^{7} + 17$ $17$ $7$ $1$ $6$ $F_7$ (as 7T4) $6$ $7$ $[\ ]$ $[\ ]_{7}^{6}$ $t + 14$ $x^{7} + 17$ $[0]$ $[6]$
19.7.6.1 $x^{7} + 19$ $19$ $7$ $1$ $6$ $F_7$ (as 7T4) $6$ $7$ $[\ ]$ $[\ ]_{7}^{6}$ $t + 17$ $x^{7} + 19$ $[0]$ $[6]$
31.7.6.1 $x^{7} + 31$ $31$ $7$ $1$ $6$ $F_7$ (as 7T4) $6$ $7$ $[\ ]$ $[\ ]_{7}^{6}$ $t + 28$ $x^{7} + 31$ $[0]$ $[6]$
47.7.6.1 $x^{7} + 47$ $47$ $7$ $1$ $6$ $F_7$ (as 7T4) $6$ $7$ $[\ ]$ $[\ ]_{7}^{6}$ $t + 42$ $x^{7} + 47$ $[0]$ $[6]$
59.7.6.1 $x^{7} + 59$ $59$ $7$ $1$ $6$ $F_7$ (as 7T4) $6$ $7$ $[\ ]$ $[\ ]_{7}^{6}$ $t + 57$ $x^{7} + 59$ $[0]$ $[6]$
61.7.6.1 $x^{7} + 61$ $61$ $7$ $1$ $6$ $F_7$ (as 7T4) $6$ $7$ $[\ ]$ $[\ ]_{7}^{6}$ $t + 59$ $x^{7} + 61$ $[0]$ $[6]$
73.7.6.1 $x^{7} + 73$ $73$ $7$ $1$ $6$ $F_7$ (as 7T4) $6$ $7$ $[\ ]$ $[\ ]_{7}^{6}$ $t + 68$ $x^{7} + 73$ $[0]$ $[6]$
89.7.6.1 $x^{7} + 89$ $89$ $7$ $1$ $6$ $F_7$ (as 7T4) $6$ $7$ $[\ ]$ $[\ ]_{7}^{6}$ $t + 86$ $x^{7} + 89$ $[0]$ $[6]$
101.7.6.1 $x^{7} + 101$ $101$ $7$ $1$ $6$ $F_7$ (as 7T4) $6$ $7$ $[\ ]$ $[\ ]_{7}^{6}$ $t + 99$ $x^{7} + 101$ $[0]$ $[6]$
103.7.6.1 $x^{7} + 103$ $103$ $7$ $1$ $6$ $F_7$ (as 7T4) $6$ $7$ $[\ ]$ $[\ ]_{7}^{6}$ $t + 98$ $x^{7} + 103$ $[0]$ $[6]$
131.7.6.1 $x^{7} + 131$ $131$ $7$ $1$ $6$ $F_7$ (as 7T4) $6$ $7$ $[\ ]$ $[\ ]_{7}^{6}$ $t + 129$ $x^{7} + 131$ $[0]$ $[6]$
157.7.6.1 $x^{7} + 157$ $157$ $7$ $1$ $6$ $F_7$ (as 7T4) $6$ $7$ $[\ ]$ $[\ ]_{7}^{6}$ $t + 152$ $x^{7} + 157$ $[0]$ $[6]$
173.7.6.1 $x^{7} + 173$ $173$ $7$ $1$ $6$ $F_7$ (as 7T4) $6$ $7$ $[\ ]$ $[\ ]_{7}^{6}$ $t + 171$ $x^{7} + 173$ $[0]$ $[6]$
199.7.6.1 $x^{7} + 199$ $199$ $7$ $1$ $6$ $F_7$ (as 7T4) $6$ $7$ $[\ ]$ $[\ ]_{7}^{6}$ $t + 196$ $x^{7} + 199$ $[0]$ $[6]$
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