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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 (24 matches)

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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
3.6.7.3 $x^{6} + 3 x^{3} + 6 x^{2} + 6$ $3$ $6$ $1$ $7$ $S_3\times C_3$ (as 6T5) $[3/2]$ $[3/2]_{2}^{3}$ $t + 1$ $x^{6} + 3 x^{3} + 6 x^{2} + 6$
3.6.7.6 $x^{6} + 3 x^{3} + 3 x^{2} + 3$ $3$ $6$ $1$ $7$ $S_3\times C_3$ (as 6T5) $[3/2]$ $[3/2]_{2}^{3}$ $t + 1$ $x^{6} + 3 x^{3} + 3 x^{2} + 3$
3.6.8.10 $x^{6} + 9 x^{4} + 42 x^{3} + 441$ $3$ $3$ $2$ $8$ $S_3\times C_3$ (as 6T5) $[2]$ $[2, 2]^{2}$ $t^{2} + 2 t + 2$ $x^{3} + \left(3 t + 3\right) x^{2} + 21$
3.6.8.7 $x^{6} + 6 x^{5} + 9 x^{4} + 6 x^{3} + 18 x^{2} + 90$ $3$ $3$ $2$ $8$ $S_3\times C_3$ (as 6T5) $[2]$ $[2]^{6}$ $t^{2} + 2 t + 2$ $x^{3} + 3 x^{2} + 9 t + 12$
3.6.8.8 $x^{6} + 9 x^{4} + 24 x^{3} + 144$ $3$ $3$ $2$ $8$ $S_3\times C_3$ (as 6T5) $[2]$ $[2, 2]^{2}$ $t^{2} + 2 t + 2$ $x^{3} + \left(3 t + 3\right) x^{2} + 12$
3.6.8.9 $x^{6} + 36 x^{4} + 6 x^{3} + 9$ $3$ $3$ $2$ $8$ $S_3\times C_3$ (as 6T5) $[2]$ $[2, 2]^{2}$ $t^{2} + 2 t + 2$ $x^{3} + \left(6 t + 6\right) x^{2} + 3$
3.6.9.13 $x^{6} + 3 x^{5} + 6 x^{4} + 21$ $3$ $6$ $1$ $9$ $S_3\times C_3$ (as 6T5) $[2]$ $[3/2, 2]_{2}$ $t + 1$ $x^{6} + 3 x^{5} + 6 x^{4} + 21$
3.6.9.14 $x^{6} + 3 x^{5} + 6 x^{4} + 12$ $3$ $6$ $1$ $9$ $S_3\times C_3$ (as 6T5) $[2]$ $[3/2, 2]_{2}$ $t + 1$ $x^{6} + 3 x^{5} + 6 x^{4} + 12$
3.6.9.15 $x^{6} + 6 x^{5} + 6 x^{4} + 3$ $3$ $6$ $1$ $9$ $S_3\times C_3$ (as 6T5) $[2]$ $[3/2, 2]_{2}$ $t + 1$ $x^{6} + 6 x^{5} + 6 x^{4} + 3$
3.6.9.5 $x^{6} + 3 x^{5} + 3 x^{4} + 6$ $3$ $6$ $1$ $9$ $S_3\times C_3$ (as 6T5) $[2]$ $[3/2, 2]_{2}$ $t + 1$ $x^{6} + 3 x^{5} + 3 x^{4} + 6$
3.6.9.6 $x^{6} + 6 x^{5} + 3 x^{4} + 24$ $3$ $6$ $1$ $9$ $S_3\times C_3$ (as 6T5) $[2]$ $[3/2, 2]_{2}$ $t + 1$ $x^{6} + 6 x^{5} + 3 x^{4} + 24$
3.6.9.7 $x^{6} + 3 x^{5} + 3 x^{4} + 15$ $3$ $6$ $1$ $9$ $S_3\times C_3$ (as 6T5) $[2]$ $[3/2, 2]_{2}$ $t + 1$ $x^{6} + 3 x^{5} + 3 x^{4} + 15$
3.6.11.10 $x^{6} + 9 x^{3} + 18 x^{2} + 21$ $3$ $6$ $1$ $11$ $S_3\times C_3$ (as 6T5) $[5/2]$ $[5/2]_{2}^{3}$ $t + 1$ $x^{6} + 9 x^{3} + 18 x^{2} + 21$
3.6.11.11 $x^{6} + 9 x^{3} + 9 x^{2} + 12$ $3$ $6$ $1$ $11$ $S_3\times C_3$ (as 6T5) $[5/2]$ $[5/2]_{2}^{3}$ $t + 1$ $x^{6} + 9 x^{3} + 9 x^{2} + 12$
3.6.11.12 $x^{6} + 9 x^{3} + 3$ $3$ $6$ $1$ $11$ $S_3\times C_3$ (as 6T5) $[5/2]$ $[5/2]_{2}^{3}$ $t + 1$ $x^{6} + 9 x^{3} + 3$
3.6.11.13 $x^{6} + 24 x^{3} + 9 x + 21$ $3$ $6$ $1$ $11$ $S_3\times C_3$ (as 6T5) $[5/2]$ $[2, 5/2]_{2}$ $t + 1$ $x^{6} + 24 x^{3} + 9 x + 21$
3.6.11.14 $x^{6} + 18 x^{2} + 18 x + 3$ $3$ $6$ $1$ $11$ $S_3\times C_3$ (as 6T5) $[5/2]$ $[2, 5/2]_{2}$ $t + 1$ $x^{6} + 18 x^{2} + 18 x + 3$
3.6.11.15 $x^{6} + 18 x + 3$ $3$ $6$ $1$ $11$ $S_3\times C_3$ (as 6T5) $[5/2]$ $[2, 5/2]_{2}$ $t + 1$ $x^{6} + 18 x + 3$
3.6.11.16 $x^{6} + 18 x^{2} + 18 x + 21$ $3$ $6$ $1$ $11$ $S_3\times C_3$ (as 6T5) $[5/2]$ $[2, 5/2]_{2}$ $t + 1$ $x^{6} + 18 x^{2} + 18 x + 21$
3.6.11.17 $x^{6} + 9 x^{3} + 18 x^{2} + 18 x + 21$ $3$ $6$ $1$ $11$ $S_3\times C_3$ (as 6T5) $[5/2]$ $[2, 5/2]_{2}$ $t + 1$ $x^{6} + 9 x^{3} + 18 x^{2} + 18 x + 21$
3.6.11.18 $x^{6} + 3 x^{3} + 18 x^{2} + 18 x + 12$ $3$ $6$ $1$ $11$ $S_3\times C_3$ (as 6T5) $[5/2]$ $[2, 5/2]_{2}$ $t + 1$ $x^{6} + 3 x^{3} + 18 x^{2} + 18 x + 12$
3.6.11.19 $x^{6} + 15 x^{3} + 9 x + 21$ $3$ $6$ $1$ $11$ $S_3\times C_3$ (as 6T5) $[5/2]$ $[2, 5/2]_{2}$ $t + 1$ $x^{6} + 15 x^{3} + 9 x + 21$
3.6.11.20 $x^{6} + 9 x^{2} + 9 x + 12$ $3$ $6$ $1$ $11$ $S_3\times C_3$ (as 6T5) $[5/2]$ $[2, 5/2]_{2}$ $t + 1$ $x^{6} + 9 x^{2} + 9 x + 12$
3.6.11.21 $x^{6} + 9 x^{3} + 9 x^{2} + 9 x + 12$ $3$ $6$ $1$ $11$ $S_3\times C_3$ (as 6T5) $[5/2]$ $[2, 5/2]_{2}$ $t + 1$ $x^{6} + 9 x^{3} + 9 x^{2} + 9 x + 12$
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