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Degree Residue characteristic Galois group Galois unramified degree Assoc. Inertia
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Results (50 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
7.7.0.1 $x^{7} + 6 x + 4$ $7$ $1$ $7$ $0$ $C_7$ (as 7T1) $7$ $1$ $[\ ]$ $[\ ]^{7}$ $t^{7} + 6 t + 4$ $x - 7$ $[0]$ $[\ ]$
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) $1$ $6$ $[7/6]$ $[7/6]_{6}$ $t + 4$ $x^{7} + 28 x + 7$ $[1, 0]$ $[1]$
7.7.8.1 $x^{7} + 14 x^{2} + 7$ $7$ $7$ $1$ $8$ $C_7:C_3$ (as 7T3) $1$ $3$ $[4/3]$ $[4/3]_{3}$ $t + 4$ $x^{7} + 14 x^{2} + 7$ $[2, 0]$ $[1]$
7.7.8.2 $x^{7} + 7 x^{2} + 7$ $7$ $7$ $1$ $8$ $C_7:C_3$ (as 7T3) $1$ $3$ $[4/3]$ $[4/3]_{3}$ $t + 4$ $x^{7} + 7 x^{2} + 7$ $[2, 0]$ $[1]$
7.7.8.3 $x^{7} + 28 x^{2} + 7$ $7$ $7$ $1$ $8$ $C_7:C_3$ (as 7T3) $1$ $3$ $[4/3]$ $[4/3]_{3}$ $t + 4$ $x^{7} + 28 x^{2} + 7$ $[2, 0]$ $[1]$
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) $2$ $3$ $[4/3]$ $[4/3]_{3}^{2}$ $t + 4$ $x^{7} + 35 x^{2} + 7$ $[2, 0]$ $[2]$
7.7.9.1 $x^{7} + 14 x^{3} + 7$ $7$ $7$ $1$ $9$ $D_{7}$ (as 7T2) $1$ $2$ $[3/2]$ $[3/2]_{2}$ $t + 4$ $x^{7} + 14 x^{3} + 7$ $[3, 0]$ $[1]$
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) $3$ $2$ $[3/2]$ $[3/2]_{2}^{3}$ $t + 4$ $x^{7} + 28 x^{3} + 7$ $[3, 0]$ $[3]$
7.7.9.4 $x^{7} + 35 x^{3} + 7$ $7$ $7$ $1$ $9$ $D_{7}$ (as 7T2) $1$ $2$ $[3/2]$ $[3/2]_{2}$ $t + 4$ $x^{7} + 35 x^{3} + 7$ $[3, 0]$ $[1]$
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) $3$ $2$ $[3/2]$ $[3/2]_{2}^{3}$ $t + 4$ $x^{7} + 21 x^{3} + 7$ $[3, 0]$ $[3]$
7.7.10.1 $x^{7} + 28 x^{4} + 7$ $7$ $7$ $1$ $10$ $C_7:C_3$ (as 7T3) $1$ $3$ $[5/3]$ $[5/3]_{3}$ $t + 4$ $x^{7} + 28 x^{4} + 7$ $[4, 0]$ $[1]$
7.7.10.2 $x^{7} + 7 x^{4} + 7$ $7$ $7$ $1$ $10$ $C_7:C_3$ (as 7T3) $1$ $3$ $[5/3]$ $[5/3]_{3}$ $t + 4$ $x^{7} + 7 x^{4} + 7$ $[4, 0]$ $[1]$
7.7.10.3 $x^{7} + 14 x^{4} + 7$ $7$ $7$ $1$ $10$ $C_7:C_3$ (as 7T3) $1$ $3$ $[5/3]$ $[5/3]_{3}$ $t + 4$ $x^{7} + 14 x^{4} + 7$ $[4, 0]$ $[1]$
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) $1$ $6$ $[11/6]$ $[11/6]_{6}$ $t + 4$ $x^{7} + 42 x^{5} + 7$ $[5, 0]$ $[1]$
7.7.12.1 $x^{7} + 42 x^{6} + 7$ $7$ $7$ $1$ $12$ $C_7$ (as 7T1) $1$ $1$ $[2]$ $[2]$ $t + 4$ $x^{7} + 42 x^{6} + 7$ $[6, 0]$ $[1]$
7.7.12.2 $x^{7} + 42 x^{6} + 56$ $7$ $7$ $1$ $12$ $C_7$ (as 7T1) $1$ $1$ $[2]$ $[2]$ $t + 4$ $x^{7} + 42 x^{6} + 56$ $[6, 0]$ $[1]$
7.7.12.3 $x^{7} + 42 x^{6} + 105$ $7$ $7$ $1$ $12$ $C_7$ (as 7T1) $1$ $1$ $[2]$ $[2]$ $t + 4$ $x^{7} + 42 x^{6} + 105$ $[6, 0]$ $[1]$
7.7.12.4 $x^{7} + 42 x^{6} + 154$ $7$ $7$ $1$ $12$ $C_7$ (as 7T1) $1$ $1$ $[2]$ $[2]$ $t + 4$ $x^{7} + 42 x^{6} + 154$ $[6, 0]$ $[1]$
7.7.12.5 $x^{7} + 42 x^{6} + 203$ $7$ $7$ $1$ $12$ $C_7$ (as 7T1) $1$ $1$ $[2]$ $[2]$ $t + 4$ $x^{7} + 42 x^{6} + 203$ $[6, 0]$ $[1]$
7.7.12.6 $x^{7} + 42 x^{6} + 252$ $7$ $7$ $1$ $12$ $C_7$ (as 7T1) $1$ $1$ $[2]$ $[2]$ $t + 4$ $x^{7} + 42 x^{6} + 252$ $[6, 0]$ $[1]$
7.7.12.7 $x^{7} + 42 x^{6} + 301$ $7$ $7$ $1$ $12$ $C_7$ (as 7T1) $1$ $1$ $[2]$ $[2]$ $t + 4$ $x^{7} + 42 x^{6} + 301$ $[6, 0]$ $[1]$
7.7.12.8 $x^{7} + 21 x^{6} + 7$ $7$ $7$ $1$ $12$ $C_7:C_3$ (as 7T3) $3$ $1$ $[2]$ $[2]^{3}$ $t + 4$ $x^{7} + 21 x^{6} + 7$ $[6, 0]$ $[3]$
7.7.12.9 $x^{7} + 35 x^{6} + 7$ $7$ $7$ $1$ $12$ $C_7:C_3$ (as 7T3) $3$ $1$ $[2]$ $[2]^{3}$ $t + 4$ $x^{7} + 35 x^{6} + 7$ $[6, 0]$ $[3]$
7.7.12.10 $x^{7} + 7 x^{6} + 7$ $7$ $7$ $1$ $12$ $D_{7}$ (as 7T2) $2$ $1$ $[2]$ $[2]^{2}$ $t + 4$ $x^{7} + 7 x^{6} + 7$ $[6, 0]$ $[2]$
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) $1$ $6$ $[13/6]$ $[13/6]_{6}$ $t + 4$ $x^{7} + 49 x^{2} + 245 x + 7$ $[7, 0]$ $[1]$
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