New record breaking elliptic curve reported

The rank of an elliptic curve measures the number of independent rational points that generate the non-torsion part of its group of rational solutions. By the Mordell–Weil theorem, the rational points on an elliptic curve form a finitely generated abelian group, consisting of a finite torsion subgroup together with a free part whose number of generators is the rank. Rank is one of the fundamental invariants in arithmetic geometry and is closely connected to the Birch and Swinnerton-Dyer conjecture, which predicts a relationship between rank and the behavior of the curve’s L-function. Although many elliptic curves with rank 0, 1, and higher are known, it remains an open question whether elliptic curves over the rational numbers can have arbitrarily large rank.

As part of its mission to empower mathematicians to take advantage of new technologies for mathematical reasoning, ICARM hosts the Elliptic Curve Rank Leaderboard, a public website built by ICARM innovation engineer David Renshaw that invites anyone to submit a curve. Every uploaded submission is verified before it is admitted, so the leaderboard records certified ranks rather than claimed ones. Until today, the best known rank was 29, certified for the curve found by Elkies and Klagsbrun in 2024.

Today a user going by "ranksunbounded" uploaded a curve with rank 30 to ICARM's Elliptic Curve Rank Leaderboard, thus breaking that record!

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