Preprint: Machine-learning arithmetic curves : WestminsterResearch

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Title	Preprint: Machine-learning arithmetic curves
Authors	He, Y.-H., Lee, K.-H. and Oliver, T.
Description	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.
Year	2020
Output media	arXiv preprint
Publisher	arXiv
Published	07 Dec 2020
ISSN	2331-8422
Digital Object Identifier (DOI)	https://doi.org/10.48550/arxiv.2012.04084
Journal	ARXIV

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Preprint: Machine-learning arithmetic curves

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