Rank 4 with torsion Z/2×Z/8
Problèmes ouverts — A. Dujella · 2026 · ★★★★★
Statement
Problem 2.2 (Dujella, 2026). Is there an elliptic curve over $\mathbb{Q}$ with torsion group $\mathbb{Z}/2\mathbb{Z}\times\mathbb{Z}/8\mathbb{Z}$ and rank equal to 4?
Remark. There are 34 known curves with torsion group $\mathbb{Z}/2\mathbb{Z}\times\mathbb{Z}/8\mathbb{Z}$ and rank equal to 3: https://web.math.pmf.unizg.hr/~duje/tors/z2z8.html
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 2.2
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