Machine-Learning Arithmetic Curves

Understand

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.