Kodaira symbol (reviewed)

The Kodaira symbol of an elliptic curve \(E\) defined over a number field encodes the reduction type of \(E\) at a prime \(\mathfrak{p}\) of \(K\). It describes the combinatorics of the special fiber of the Néron model of the elliptic curve. The Néron model is obtained from the local minimal model for \(E\) at \(\mathfrak{p}\) using Tate's algorithm. For an exact definition and properties, consult a text on elliptic curves.