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The label of an elliptic curve over a number field $K$ has three components, denoting the conductor, the isogeny class and the isomorphism 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. Omitting the third component gives an isogeny class label, of the form $N.a$.

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 3.1.23.1-89.1-A1.

Where possible the labelling of isogeny classes matches that of associated cusp forms (Bianchi newforms over imaginary quadratic fields and Hilbert newforms over totally real fields). The prefix "CM" on the isogeny class label for certain elliptic curves over imaginary quadratic fields is used, because the Bianchi modular forms conjecturally attached to such curves are not cuspidal.