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$p$-adic field labels
Refine search
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 $c_{\mathrm{abs}}$
Mass
Absolute mass
Ambiguity
Field count
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discriminant exponent
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base res. field degree
abs. residue field degree
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base ram. index
abs. ram. index
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base disc. exponent
abs. disc. exponent
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abs. Artin slopes
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Results (7 matches)
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Label
$p$
$n$
$n_0$
$n_{\mathrm{abs}}$
$f$
$f_0$
$f_{\mathrm{abs}}$
$e$
$e_0$
$e_{\mathrm{abs}}$
$c$
$c_0$
$c_{\mathrm{abs}}$
Base
Abs. Artin slopes
Swan slopes
Means
Rams
Generic poly
Ambiguity
Field count
Mass
Mass (absolute)
Mass stored
Mass found
Wild segments
3.1.6.9a
$3$
$6$
$1$
$6$
$1$
$1$
$1$
$6$
$1$
$6$
$9$
$0$
$9$
$\Q_{3}$
$[2]$
$[1]$
$\langle\frac{2}{3}\rangle$
$(2)$
$x^6 + 3 b_{5} x^5 + 3 a_{4} x^4 + 3 d_{0} + 9 c_{6}$
$6$
$16$
$6$
$6$
$6$
$100\%$
$1$
3.1.2.1a1.1-1.3.6a
$3$
$3$
$2$
$6$
$1$
$1$
$1$
$3$
$2$
$6$
$6$
$1$
$6$
$\Q_{3}(\sqrt{3\cdot 2})$
$[2]$
$[2]$
$\langle\frac{4}{3}\rangle$
$(2)$
$x^3 + b_{5} \pi^2 x^2 + a_{4} \pi^2 x + c_{6} \pi^3 + \pi$
$3$
$8$
$6$
$3$
$3$
$100\%$
$1$
3.1.2.1a1.2-1.3.6a
$3$
$3$
$2$
$6$
$1$
$1$
$1$
$3$
$2$
$6$
$6$
$1$
$6$
$\Q_{3}(\sqrt{3})$
$[2]$
$[2]$
$\langle\frac{4}{3}\rangle$
$(2)$
$x^3 + b_{5} \pi^2 x^2 + a_{4} \pi^2 x + c_{6} \pi^3 + \pi$
$3$
$8$
$6$
$3$
$3$
$100\%$
$1$
3.1.3.4a1.1-1.2.1a
$3$
$2$
$3$
$6$
$1$
$1$
$1$
$2$
$3$
$6$
$1$
$4$
$3$
3.1.3.4a1.1
$[2]$
$[ ]$
$\langle \rangle$
$( )$
$x^2 + d_{0} \pi$
$2$
$2$
$1$
$1$
$1$
$100\%$
$0$
3.1.3.4a2.1-1.2.1a
$3$
$2$
$3$
$6$
$1$
$1$
$1$
$2$
$3$
$6$
$1$
$4$
$3$
3.1.3.4a2.1
$[2]$
$[ ]$
$\langle \rangle$
$( )$
$x^2 + d_{0} \pi$
$2$
$2$
$1$
$1/3$
$1/3$
$100\%$
$0$
3.1.3.4a2.2-1.2.1a
$3$
$2$
$3$
$6$
$1$
$1$
$1$
$2$
$3$
$6$
$1$
$4$
$3$
3.1.3.4a2.2
$[2]$
$[ ]$
$\langle \rangle$
$( )$
$x^2 + d_{0} \pi$
$2$
$2$
$1$
$1/3$
$1/3$
$100\%$
$0$
3.1.3.4a2.3-1.2.1a
$3$
$2$
$3$
$6$
$1$
$1$
$1$
$2$
$3$
$6$
$1$
$4$
$3$
3.1.3.4a2.3
$[2]$
$[ ]$
$\langle \rangle$
$( )$
$x^2 + d_{0} \pi$
$2$
$2$
$1$
$1/3$
$1/3$
$100\%$
$0$
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