Non-split multiplicative reduction (reviewed)

An elliptic curve \(E\) defined over a number field \(K\) is said to have non-split multiplicative reduction at a prime \(\mathfrak{p}\) of \(K\) if the reduction of \(E\) modulo \(\mathfrak{p}\) has a nodal singularity with tangent slopes not defined over the residue field at \(\mathfrak{p}\).