Published July 9, 2025 | Version v1
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Trained transformer models for predicting traces of Frobenius of elliptic curves with conductor up to 10^6

Authors/Creators

  • 1. ROR icon Howard University

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.

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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)

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