We focus on classifying degree 12 extensions of the 2-adic numbers that have a trivial automorphism group. For each extension, we compute a defining polynomial, the ramification index, residue degree, discriminant, and the Galois group of the normal closure. These results extend previous work in the area of constructive local field theory first initiated by Pauli-Roblot [14] and Jones-Roberts [8-10].

2-adic, extension fields, Galois group, local field.