$p$-adic family 2.1.24.85a

• Label: 2.1.24.85a
• Base: 2.1.1.0a1.1
• Degree: \(24\)
• e: \(24\)
• f: \(1\)
• c: \(85\)

Defining polynomial

$x^{24} + 8 b_{71} x^{23} + 4 b_{46} x^{22} + 8 b_{69} x^{21} + 2 a_{20} x^{20} + 8 b_{67} x^{19} + 4 b_{42} x^{18} + 8 b_{65} x^{17} + 4 c_{40} x^{16} + 8 b_{63} x^{15} + \left(4 a_{38} + 16 c_{86}\right) x^{14} + 16 b_{85} x^{13} + 4 b_{36} x^{12} + 16 b_{83} x^{11} + 16 b_{81} x^{9} + 8 c_{56} x^{8} + 16 b_{79} x^{7} + 8 b_{54} x^{6} + 16 b_{77} x^{5} + 4 b_{28} x^{4} + 16 b_{75} x^{3} + 8 b_{50} x^{2} + 16 b_{73} x + 2$

Invariants

Residue field characteristic:	$2$
Degree:	$24$
Base field:	$\Q_{2}$
Ramification index $e$:	$24$
Residue field degree $f$:	$1$
Discriminant exponent $c$:	$85$
Artin slopes:	$[\frac{8}{3},\frac{10}{3},\frac{55}{12}]$
Swan slopes:	$[\frac{5}{3},\frac{7}{3},\frac{43}{12}]$
Means:	$\langle\frac{5}{6},\frac{19}{12},\frac{31}{12}\rangle$
Rams:	$(5,9,24)$
Field count:	$0$ (incomplete)
Ambiguity:	$8$
Mass:	$262144$
Absolute Mass:	$262144$ ($0$ currently in the LMFDB)

Diagrams

The LMFDB does not contain any fields from this family.