The Structure of Rational Points on Elliptic Curves

This is my poster for the 2026 Directed Reading Program at UCSB. We define elliptic curves, endow the set of rational points on such a curve with a group structure, then seek to prove that group is finitely generated.

Repository Structure

• The poster.pdf file is the latest export of the poster, the code for which is contained in src/.
• The poster content can be found in src/poster.typ, src/sections.typ, and src/references.bib. The images are stored as PNGs in src/assets/.
• The src/generate-assets.sage SageMath script creates plots of two elliptic curves and exports them to src/assets/.
• The src/curve-family/ directory contains a SageMath script that generates rational points on a family of elliptic curves, then loops through real coordinates and matches them to nearby rational points. The Processing script turns the exported data into an image.

Attribution

For this project, I used the simple-research-poster Typst template by Jesse Cobb and Nate Annau, both participants of the 2025 DRP. The poster specifications were sourced from their project's repository.