Cremona label (reviewed)

The Cremona label of an elliptic curve over $\mathbb{Q}$ is a way of indexing the elliptic curves over $\mathbb Q.$ It has the form $11a1$ or $10050bf2.$ The first number represents the conductor, the letter or letters represent the isogeny class and the last number represents the isomorphism class within the isogeny class as it appears in Cremona's tables. In each isogeny class the curve with number 1 is the $\Gamma_0(N)$-optimal curve.
For more details, see "The elliptic curve database for conductors to 130000" by John Cremona in ANTS-VII proceedings, Lecture Notes in Computer Science, vol. 4076, 2006, 11-29.

In the Cremona labeling, it is somewhat difficult to describe the mechanisms for ordering isogeny classes or curves within a class, since these depend on the order in which the curves were computed (though for conductors over 230,000 the isogeny class labels coincide). Cremona labels are only available for conductors up to 500,000. For these reasons, within this site we also use the LMFDB label, whose definition is somewhat simpler. Note that the lack of internal punctuation distinguishes Cremona labels from LMFDB labels.