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Machine Learning Invariants of Arithmetic Curves

He, Y-H. ORCID: 0000-0002-0787-8380, Lee, K-H. & Oliver, T. (2023). Machine Learning Invariants of Arithmetic Curves. Journal of Symbolic Computation, 115, pp. 478-491. doi: 10.1016/j.jsc.2022.08.017


We show that standard machine learning algorithms may be trained to predict certain invariants of low genus arithmetic curves. Using datasets of size around 105, 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.

Publication Type: Article
Additional Information: © 2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (
Publisher Keywords: Machine-learning, Arithmetic geometry, Elliptic curves, Hyper-elliptic curves, Birch-Swinnerton-Dyer conjecture
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Departments: School of Science & Technology > Mathematics
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