  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.

Number Theory;High Energy Physics - Theory;Machine Learning