$p$-adic family 2.1.40.90p

• Label: 2.1.40.90p
• Base: 2.1.1.0a1.1
• Degree: \(40\)
• e: \(40\)
• f: \(1\)
• c: \(90\)

Defining polynomial

$x^{40} + 4 b_{79} x^{39} + 2 b_{38} x^{38} + 4 b_{77} x^{37} + 4 b_{75} x^{35} + 2 b_{34} x^{34} + 4 b_{73} x^{33} + 4 b_{71} x^{31} + 2 b_{30} x^{30} + 4 b_{69} x^{29} + 4 b_{67} x^{27} + 2 b_{26} x^{26} + 4 b_{65} x^{25} + 4 b_{63} x^{23} + 2 a_{22} x^{22} + 4 b_{61} x^{21} + 4 b_{59} x^{19} + 4 b_{57} x^{17} + 4 b_{55} x^{15} + 4 b_{53} x^{13} + 4 a_{51} x^{11} + 2 c_{8} x^{8} + 2 a_{4} x^{4} + 4 c_{40} + 8 c_{80} + 2$

Invariants

Residue field characteristic:	$2$
Degree:	$40$
Base field:	$\Q_{2}$
Ramification index $e$:	$40$
Residue field degree $f$:	$1$
Discriminant exponent $c$:	$90$
Artin slopes:	$[\frac{6}{5},2,3]$
Swan slopes:	$[\frac{1}{5},1,2]$
Means:	$\langle\frac{1}{10},\frac{11}{20},\frac{51}{40}\rangle$
Rams:	$(1,9,29)$
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.