Machine-Learning Arithmetic Curves

Abstract

We show that standard machine-learning algorithms may be trained to predict certain invariants of low genus arithmetic curves. Using datasets of size around one hundred thousand, we demonstrate the utility of machine-learning in classification problems pertaining to the BSD invariants of an elliptic curve (including its rank and torsion subgroup), and the analogous invariants of a genus 2 curve. Our results show that a trained machine can efficiently classify curves according to these invariants with high accuracies (>0.97). For problems such as distinguishing between torsion orders, and the recognition of integral points, the accuracies can reach 0.998.

21 pages, 1 figure, 9 tables

References in corpus (3)

• Machine Learning meets Number Theory: The Data Science of Birch-Swinnerton-Dyer
• Machine-Learning the Sato--Tate Conjecture
• Machine-Learning Number Fields

Cited by in corpus (5)

• Murmurations of elliptic curves
• Murmurations of Dirichlet characters
• Predicting root numbers with neural networks
• Machine Learning Mutation-Acyclicity of Quivers
• Machine Learning Class Numbers of Real Quadratic Fields