Elliptic curve murmurations

Murmurations of elliptic curves

Elliptic curves are central to number theory, play a key role in cryptography and are the subject of the Birch and Swinnerton-Dyer conjecture, one of the most famous problems in mathematics. With the aid of machine learning, we found unexpected patterns in isogeny classes of these curves resembling the murmurations of starlings. We further show that these oscillations, in a property related to their roots, fit to a curve.