C. R. Hill / Independent research

hillaxiom Resources

Open Problems

Rational Diophantine Septuple

Find seven distinct nonzero rationals whose pairwise products plus one are rational squares.

Diophantine m-tuples and Elliptic Curves

Open problems compiled by Andrej Dujella.

UnsolvedMath

A broader directory of unsolved mathematics problems.

Record Tables

Elliptic Curve Rank Leaderboard

Computational records for elliptic-curve rank over ℚ.

Rank by Prescribed Torsion

Best known elliptic-curve ranks over ℚ for each torsion group.

Infinite Families by Torsion

Rank records over ℚ(t) and in infinite families over ℚ.

References

Portrait of Andrej Dujella

Andrej Dujella

Professor of Mathematics · University of Zagreb

Studies Diophantine equations and elliptic curves; maintains the rank and torsion record tables.

WebsiteGitHubX @dujella1
Portrait of Noam D. Elkies

Noam D. Elkies

Professor of Mathematics · Harvard University

Works in number theory, computation, and algebraic geometry, including high-rank elliptic curves.

Website
Portrait of Zev Klagsbrun

Zev Klagsbrun

Research staff · Center for Communications Research, La Jolla

Studies elliptic curves and Selmer groups; with Noam Elkies, discovered a record high-rank curve.

GitHubMathOverflow

Juan Carlos Peral

Mathematics · University of the Basque Country (UPV/EHU)

Studies elliptic curves and Diophantine equations, including high-rank curves with prescribed torsion.

PublicationsResearch profile
Portrait of Michael Stoll

Michael Stoll

Professor of Computer Algebra · University of Bayreuth

Works in computational arithmetic geometry and organizes the Rational Points workshops.

WebsiteGitHub
Portrait of Álvaro Lozano-Robledo

Álvaro Lozano-Robledo

Professor of Mathematics · University of Connecticut

Studies arithmetic geometry and elliptic curves, and shares mathematics courses and videos online.

WebsiteYouTubeGitHubX @mathandcobb

Maksym Voznyy

Department of Technology · Stephen Leacock Collegiate Institute (TDSB)

Researches high-rank elliptic curves and has contributed records for several torsion groups.

PapersGitHubX @DrVoznyy

Samuel Li

Staff Modeling Engineer · Samsung Semiconductor

Builds scientific computing tools and mathematical visualizations; has contributed high-rank elliptic-curve records.

ProjectsGitHub

Manvir Jaswal

Independent researcher

Publishes constructions of high-rank elliptic-curve families with prescribed torsion.

ResearchORCID