# [A pointwise 2-converse for elliptic curves with rational two-torsion](paper.pdf)

**Author:** OpenAI

**Date:** October 7, 2026

## Citation

```bibtex
@misc{OAI:A-pointwise-2-converse-for-elliptic-curves-with-rational-two-torsion-October-7-2026,
  author = {{OpenAI}},
  title = {{A pointwise $2$-converse for elliptic curves with rational two-torsion}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/A-pointwise-2-converse-for-elliptic-curves-with-rational-two-torsion-October-7-2026/paper.pdf}{OAI:A-pointwise-2-converse-for-elliptic-curves-with-rational-two-torsion-October-7-2026}},
  year = {2026}
}
```

## Version note

This version updates a citation to a revised manuscript in this collection; see the [previous version](../A-pointwise-2-converse-for-elliptic-curves-with-rational-two-torsion-September-24-2026/paper.pdf).