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Degree $n$ Residue characteristic $p$ Discriminant exponent $c$ Galois group
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Results (8 matches)

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Label 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 Unram. Ext. Eisen. Poly. Ind. of Insep. Assoc. Inertia Resid. Poly Jump Set
2.1.10.16a1.1 $x^{10} + 2 x^{7} + 2$ $2$ $1$ $10$ $16$ $(C_2^4 : C_5):C_4$ (as 10T25) $4$ $5$ $[\frac{12}{5}]$ $[\frac{7}{5}]$ $[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}]_{5}^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]_{5}^{4}$ $[\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ $t + 1$ $x^{10} + 2 x^{7} + 2$ $[7, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.16a1.2 $x^{10} + 2 x^{7} + 4 x^{4} + 2$ $2$ $1$ $10$ $16$ $(C_2^4 : C_5):C_4$ (as 10T24) $4$ $5$ $[\frac{12}{5}]$ $[\frac{7}{5}]$ $[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}]_{5}^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]_{5}^{4}$ $[\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ $t + 1$ $x^{10} + 2 x^{7} + 4 x^{4} + 2$ $[7, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.16a1.3 $x^{10} + 2 x^{7} + 4 x^{3} + 2$ $2$ $1$ $10$ $16$ $(C_2^4 : C_5):C_4$ (as 10T25) $4$ $5$ $[\frac{12}{5}]$ $[\frac{7}{5}]$ $[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}]_{5}^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]_{5}^{4}$ $[\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ $t + 1$ $x^{10} + 2 x^{7} + 4 x^{3} + 2$ $[7, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.16a1.4 $x^{10} + 2 x^{7} + 4 x^{4} + 4 x^{3} + 2$ $2$ $1$ $10$ $16$ $(C_2^4 : C_5):C_4$ (as 10T24) $4$ $5$ $[\frac{12}{5}]$ $[\frac{7}{5}]$ $[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}]_{5}^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]_{5}^{4}$ $[\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ $t + 1$ $x^{10} + 2 x^{7} + 4 x^{4} + 4 x^{3} + 2$ $[7, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.16a1.5 $x^{10} + 2 x^{7} + 4 x + 2$ $2$ $1$ $10$ $16$ $(C_2^4 : C_5):C_4$ (as 10T25) $4$ $5$ $[\frac{12}{5}]$ $[\frac{7}{5}]$ $[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}]_{5}^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]_{5}^{4}$ $[\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ $t + 1$ $x^{10} + 2 x^{7} + 4 x + 2$ $[7, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.16a1.6 $x^{10} + 2 x^{7} + 4 x^{4} + 4 x + 2$ $2$ $1$ $10$ $16$ $(C_2^4 : C_5):C_4$ (as 10T24) $4$ $5$ $[\frac{12}{5}]$ $[\frac{7}{5}]$ $[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}]_{5}^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]_{5}^{4}$ $[\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ $t + 1$ $x^{10} + 2 x^{7} + 4 x^{4} + 4 x + 2$ $[7, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.16a1.7 $x^{10} + 2 x^{7} + 4 x^{3} + 4 x + 2$ $2$ $1$ $10$ $16$ $(C_2^4 : C_5):C_4$ (as 10T25) $4$ $5$ $[\frac{12}{5}]$ $[\frac{7}{5}]$ $[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}]_{5}^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]_{5}^{4}$ $[\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ $t + 1$ $x^{10} + 2 x^{7} + 4 x^{3} + 4 x + 2$ $[7, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
2.1.10.16a1.8 $x^{10} + 2 x^{7} + 4 x^{4} + 4 x^{3} + 4 x + 2$ $2$ $1$ $10$ $16$ $(C_2^4 : C_5):C_4$ (as 10T24) $4$ $5$ $[\frac{12}{5}]$ $[\frac{7}{5}]$ $[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}]_{5}^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]_{5}^{4}$ $[\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ $[\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ $t + 1$ $x^{10} + 2 x^{7} + 4 x^{4} + 4 x^{3} + 4 x + 2$ $[7, 0]$ $[4, 1]$ $z^8 + z^6 + 1,z + 1$ $[5, 15]$
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