$p$-adic family 3.1.45.133a

• Label: 3.1.45.133a
• Base: 3.1.1.0a1.1
• Degree: \(45\)
• e: \(45\)
• f: \(1\)
• c: \(133\)

Defining polynomial

$x^{45} + 9 a_{89} x^{44} + \left(9 b_{66} + 27 c_{111}\right) x^{21} + 27 b_{110} x^{20} + 27 b_{109} x^{19} + 27 b_{107} x^{17} + 27 b_{106} x^{16} + 9 b_{60} x^{15} + 27 b_{104} x^{14} + 27 b_{103} x^{13} + 9 b_{57} x^{12} + 27 b_{101} x^{11} + 27 b_{100} x^{10} + 27 b_{98} x^{8} + 27 b_{97} x^{7} + 9 b_{51} x^{6} + 27 b_{95} x^{5} + 27 b_{94} x^{4} + 9 b_{48} x^{3} + 27 b_{92} x^{2} + 27 b_{91} x + 3$

Invariants

Residue field characteristic:	$3$
Degree:	$45$
Base field:	$\Q_{3}$
Ramification index $e$:	$45$
Residue field degree $f$:	$1$
Discriminant exponent $c$:	$133$
Artin slopes:	$[\frac{5}{2},\frac{52}{15}]$
Swan slopes:	$[\frac{3}{2},\frac{37}{15}]$
Means:	$\langle1,\frac{89}{45}\rangle$
Rams:	$(\frac{15}{2},22)$
Field count:	$0$ (incomplete)
Ambiguity:	$3$
Mass:	$2324522934$
Absolute Mass:	$2324522934$ ($0$ currently in the LMFDB)

Diagrams

The LMFDB does not contain any fields from this family.