// Magma code for working with p-adic field 11.4.4.12a1.3.


// Define the p-adic field: 
Prec := 100;  // Default precision of 100
Q11 := pAdicField(11, Prec);
K := LocalField(Q11, Polynomial(Q11, [27, 320, 2656, 11840, 30768, 47840, 45280, 28320, 15256, 7920, 2840, 960, 392, 40, 32, 0, 1]));

// Defining polynomial: 
DefiningPolynomial(K);

// Base field Qp: 
Q11;

// Degree over Qp: 
Degree(K);

// Ramification index: 
RamificationIndex(K);

// Residue field degree (Inertia degree): 
InertiaDegree(K);

// Discriminant exponent: 
Valuation(Discriminant(K));