The label of an elliptic curve over a number field $K$ has three components, denoting the conductor, the isogeny class and the isomorphism class:
- The conductor label depends on the field;
- The isogeny class label consists of one or more letters a-z or A-Z; the ordering of the isogeny classes is based on lexicographical ordering of the Dirichlet coefficients of the L-series;
- The isomorphism class is a positive integer giving the index (starting at 1) of the curve in its isogeny class.
Together these give a label of the form $N.a1$ where $N$ is the conductor label, $a$ the class and $1$ the curve number.
In addition, to specify the elliptic curve completely prepend the label of the base field to give a full label of the curve, for example 18.104.22.168-89.1-A1.