Arbitrarily large ranks over Q
Problèmes ouverts — A. Dujella · 2026 · ★★★★★
Statement
Problem 2.1 (Dujella, 2026). Are there elliptic curves over $\mathbb{Q}$ of arbitrarily large rank?
Remark. The current record over $\mathbb{Q}$ is rank at least 29 (Elkies-Klagsbrun, 2024). Heuristics of Park, Poonen, Voight and Wood (2019) suggest that ranks over $\mathbb{Q}$ might be bounded.
Preview rendered with KaTeX — the compiled PDF is the reference layout.
Source & credits
Origin : Andrej Dujella, Open problems on Diophantine m-tuples and elliptic curves (26 juillet 2026), Problème 2.1
Reproduit à des fins pédagogiques non commerciales, avec attribution à l'auteur. Problème de recherche ouvert : aucune solution connue à ce jour.
Downloads
PDFs are produced by the GitHub Actions pipeline: they may be missing in local development.
＋ Add to problem set