$p$-adic family 3.1.4.3a1.2-1.9.75a

• Label: 3.1.4.3a1.2-1.9.75a
• Base: 3.1.4.3a1.2
• Degree: \(9\)
• e: \(9\)
• f: \(1\)
• c: \(75\)

Defining polynomial

$x^{9} + \left(b_{80} \pi^{9} + b_{71} \pi^{8}\right) x^{8} + \left(b_{79} \pi^{9} + b_{70} \pi^{8}\right) x^{7} + \left(b_{42} \pi^{5} + a_{33} \pi^{4}\right) x^{6} + \left(b_{77} \pi^{9} + b_{68} \pi^{8}\right) x^{5} + \left(b_{76} \pi^{9} + a_{67} \pi^{8}\right) x^{4} + \left(c_{84} \pi^{10} + b_{48} \pi^{6} + b_{39} \pi^{5}\right) x^{3} + \left(b_{83} \pi^{10} + b_{74} \pi^{9}\right) x^{2} + \left(b_{82} \pi^{10} + b_{73} \pi^{9}\right) x + \pi$

Invariants

Residue field characteristic:	$3$
Degree:	$9$
Base field:	3.1.4.3a1.2
Ramification index $e$:	$9$
Residue field degree $f$:	$1$
Discriminant exponent $c$:	$75$
Absolute Artin slopes:	$[\frac{19}{8},\frac{10}{3}]$
Swan slopes:	$[\frac{11}{2},\frac{28}{3}]$
Means:	$\langle\frac{11}{3},\frac{67}{9}\rangle$
Rams:	$(\frac{11}{2},17)$
Field count:	$0$ (incomplete)
Ambiguity:	$3$
Mass:	$19131876$
Absolute Mass:	$9565938$ ($0$ currently in the LMFDB)

Diagrams

The LMFDB does not contain any fields from this family.