# Machine learning for moduli space of genus two curves and an application to isogeny based cryptography

arXiv: https://arxiv.org/abs/2403.17250 · HTML: https://mlsanity.com/paper/2403.17250/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Mar 2024.

## Built on by (most cited first, 6 of 6)

- [Graded Neural Networks](https://mlsanity.com/paper/2502.17751/) (2025)
- [A Neurosymbolic Framework for Geometric Reduction of Binary Forms](https://mlsanity.com/paper/2501.15404/) (2025)
- [Neuro-Symbolic Learning for Galois Groups: Unveiling Probabilistic Trends in Polynomials](https://mlsanity.com/paper/2502.20844/) (2025)
- [Graded Transformers](https://mlsanity.com/paper/2507.20108/) (2025)
- [From Polynomials to Databases: Arithmetic Structures in Galois Theory](https://mlsanity.com/paper/2511.16622/) (2025)
- [Exact Quotients of Fresnel-Kummer Surfaces and Certified Biaxial Refraction](https://mlsanity.com/paper/2609.23249/) (2026)

## Abstract (arXiv)

We use machine learning to study the moduli space of genus two curves, specifically focusing on detecting whether a genus two curve has (n, n)-split Jacobian. Based on such techniques, we observe that there are very few rational moduli points with small weighted moduli height and (n, n)-split Jacobian for n=2, 3, 5. We computational prove that there are only 34 genus two curves (resp. 44 curves) with (2,2)-split Jacobians (resp. (3,3)-split Jacobians) and weighted moduli height ≤ 3. We discuss different machine learning models for such applications and demonstrate the ability to detect splitting with high accuracy using only the Igusa invariants of the curve. This shows that artificial neural networks and machine learning techniques can be highly reliable for arithmetic questions in the moduli space of genus two curves and may have potential applications in isogeny-based cryptography.