$p$-adic family 3.1.3.5a1.1-1.15.58a

• Label: 3.1.3.5a1.1-1.15.58a
• Base: 3.1.3.5a1.1
• Degree: \(15\)
• e: \(15\)
• f: \(1\)
• c: \(58\)

Defining polynomial

$x^{15} + \left(b_{59} \pi^{4} + a_{44} \pi^{3}\right) x^{14} + b_{58} \pi^{4} x^{13} + b_{56} \pi^{4} x^{11} + b_{55} \pi^{4} x^{10} + b_{53} \pi^{4} x^{8} + b_{52} \pi^{4} x^{7} + c_{66} \pi^{5} x^{6} + \left(b_{65} \pi^{5} + b_{50} \pi^{4}\right) x^{5} + \left(b_{64} \pi^{5} + b_{49} \pi^{4}\right) x^{4} + \left(b_{62} \pi^{5} + b_{47} \pi^{4}\right) x^{2} + \left(b_{61} \pi^{5} + b_{46} \pi^{4}\right) x + \pi$

Invariants

Residue field characteristic:	$3$
Degree:	$15$
Base field:	3.1.3.5a1.1
Ramification index $e$:	$15$
Residue field degree $f$:	$1$
Discriminant exponent $c$:	$58$
Absolute Artin slopes:	$[\frac{5}{2},\frac{52}{15}]$
Swan slopes:	$[\frac{22}{5}]$
Means:	$\langle\frac{44}{15}\rangle$
Rams:	$(22)$
Field count:	$0$ (incomplete)
Ambiguity:	$3$
Mass:	$9565938$
Absolute Mass:	$9565938$ ($0$ currently in the LMFDB)

Diagrams

The LMFDB does not contain any fields from this family.