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Machine-Learning Arithmetic Curves
- Source :
- J. Symb. Comput. 115 (2023) 478-491
- Publication Year :
- 2020
-
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.<br />Comment: 21 pages, 1 figure, 9 tables
Details
- Database :
- arXiv
- Journal :
- J. Symb. Comput. 115 (2023) 478-491
- Publication Type :
- Report
- Accession number :
- edsarx.2012.04084
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.jsc.2022.08.017