Trained transformer models for predicting traces of Frobenius of elliptic curves with conductor up to 10^6
Description
Trained transformer models for predicting traces of Frobenius $a_p(E)$ of elliptic curves $E$ with conductor up to $10^6$ and good reduction at $p$ for $p \in \{2, 3, 97\}$. The input consists of sequences $(a_q(E))_{q < 100, q \ne p}$. The models were trained using Int2Int, and the training and test sets were created from the datasets Frobenius traces of small primes for a subset of isogeny classes of elliptic curves of conductor up to 10^6 and Frobenious traces for a set of isogeny classes of elliptic curves of conductor up to 10^6. The code for generating these datasets, and training and loading the models can be found in LearningEulerFactors, and a discussion of the results in Learning Euler Factors of Elliptic Curves.
Files
predicting_ap.zip
Files
(175.7 MB)
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Additional details
Related works
- Is described by
- Preprint: 10.48550/arXiv.2502.10357 (DOI)
- Is documented by
- Computational notebook: https://github.com/ababei/LearningEulerFactors (URL)
Software
- Repository URL
- https://github.com/ababei/LearningEulerFactors
References
- Babei, A (2025). Frobenius traces of small primes for a subset of isogeny classes of elliptic curves of conductor up to 10^6 [Data set]. Zenodo. https://zenodo.org/records/15832317
- Costa, E (2025). Frobenious traces for a set of isogeny classes of elliptic curves of conductor up to 10^6 [Data set]. Zenodo. https://zenodo.org/records/15777475
- Babei, A., Charton, F., Costa, E., Huang, X., Lee, K. H., Lowry-Duda, D., ... & Pozdnyakov, A. (2025). Learning euler factors of elliptic curves. arXiv preprint arXiv:2502.10357.
- Babei, A., Charton, F., Costa, E., Huang, X., Lee, K. H., Lowry-Duda, D., ... & Pozdnyakov, A. (2025). Learning Euler Factors. Github repository https://github.com/ababei/LearningEulerFactors