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Residue characteristic $p$ Rel. degree $n$ Rel. ram. index $e$ Rel. res. field degree $f$ Rel. disc. exponent $c$
Base Base degree $n_0$ Base ram. index $e_0$ Base res. field degree $f_0$ Base disc. exponent $c_0$
Herbrand invariant Abs. degree $n_{\mathrm{abs}}$ Abs. ram. index $e_{\mathrm{abs}}$ Abs. res. field degree $f_{\mathrm{abs}}$ Abs. disc. exponent $c_{\mathrm{abs}}$
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Results (5 matches)

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Label $p$ $n$ $f$ $e$ $c$ Base Abs. Artin slopes Swan slopes Means Rams Generic poly Ambiguity Field count Mass
2.1.4.10a $2$ $4$ $1$ $4$ $10$ $\Q_{2}$ $[3, \frac{7}{2}]$ $[2, \frac{5}{2}]$ $\langle1, \frac{7}{4}\rangle$ $(2, 3)$ $x^4 + 4 a_{7} x^3 + (4 b_{6} + 8 c_{10}) x^2 + 8 b_{9} x + 8 c_{8} + 2$ $4$ $8$ $4$
2.1.2.3a1.1-1.2.4a $2$ $2$ $1$ $2$ $4$ $\Q_{2}(\sqrt{-2})$ $[3, \frac{7}{2}]$ $[3]$ $\langle\frac{3}{2}\rangle$ $(3)$ $x^2 + (b_{5} \pi^3 + a_{3} \pi^2) x + c_{6} \pi^4 + \pi$ $2$ $2$ $2$
2.1.2.3a1.2-1.2.4a $2$ $2$ $1$ $2$ $4$ $\Q_{2}(\sqrt{-2\cdot 5})$ $[3, \frac{7}{2}]$ $[3]$ $\langle\frac{3}{2}\rangle$ $(3)$ $x^2 + (b_{5} \pi^3 + a_{3} \pi^2) x + c_{6} \pi^4 + \pi$ $2$ $2$ $2$
2.1.2.3a1.3-1.2.4a $2$ $2$ $1$ $2$ $4$ $\Q_{2}(\sqrt{2})$ $[3, \frac{7}{2}]$ $[3]$ $\langle\frac{3}{2}\rangle$ $(3)$ $x^2 + (b_{5} \pi^3 + a_{3} \pi^2) x + c_{6} \pi^4 + \pi$ $2$ $2$ $2$
2.1.2.3a1.4-1.2.4a $2$ $2$ $1$ $2$ $4$ $\Q_{2}(\sqrt{2\cdot 5})$ $[3, \frac{7}{2}]$ $[3]$ $\langle\frac{3}{2}\rangle$ $(3)$ $x^2 + (b_{5} \pi^3 + a_{3} \pi^2) x + c_{6} \pi^4 + \pi$ $2$ $2$ $2$
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