$p$-adic family 2.1.40.96w

• Label: 2.1.40.96w
• Base: 2.1.1.0a1.1
• Degree: \(40\)
• e: \(40\)
• f: \(1\)
• c: \(96\)

Defining polynomial

$x^{40} + 4 b_{79} x^{39} + 2 b_{38} x^{38} + 4 b_{77} x^{37} + 4 b_{75} x^{35} + 2 a_{34} x^{34} + 4 b_{73} x^{33} + 4 b_{71} x^{31} + 4 b_{69} x^{29} + 4 b_{67} x^{27} + 4 b_{65} x^{25} + 2 c_{24} x^{24} + 4 b_{63} x^{23} + 4 b_{61} x^{21} + 2 b_{20} x^{20} + 4 b_{59} x^{19} + 4 a_{57} x^{17} + 4 c_{56} x^{16} + 4 b_{54} x^{14} + 2 a_{12} x^{12} + 4 b_{50} x^{10} + 4 b_{46} x^{6} + 4 b_{42} x^{2} + 8 c_{80} + 2$

Invariants

Residue field characteristic:	$2$
Degree:	$40$
Base field:	$\Q_{2}$
Ramification index $e$:	$40$
Residue field degree $f$:	$1$
Discriminant exponent $c$:	$96$
Artin slopes:	$[\frac{8}{5},\frac{12}{5},3]$
Swan slopes:	$[\frac{3}{5},\frac{7}{5},2]$
Means:	$\langle\frac{3}{10},\frac{17}{20},\frac{57}{40}\rangle$
Rams:	$(3,11,23)$
Field count:	$0$ (incomplete)
Ambiguity:	$8$
Mass:	$131072$
Absolute Mass:	$131072$ ($0$ currently in the LMFDB)

Diagrams

The LMFDB does not contain any fields from this family.