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New elliptic curve breaks 18-year-old record

Two mathematicians have renewed a debate about the fundamental nature of some of math’s most important equations.

Now, two mathematicians — Noam Elkies of Harvard University and Zev Klagsbrun of the Center for Communications Research in La Jolla, California — have found an elliptic curve with the most complicated pattern of rational points to date, breaking an 18-year-old record. A rank 1 elliptic curve has infinitely many rational points, but all of them line up in a simple pattern, so that if you know one, you can follow a well-known procedure to find the rest. Years later, he returned to the result, proving that so long as a widely believed conjecture is true, Elkies’ curve has a rank of precisely 28.

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