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arXiv · 2607.24251

Decision trees, Frobenius traces, and Weierstrass coefficients of elliptic curves

Barinder S. Banwait·Xiaoyu Huang·Kyu-Hwan Lee·Seewoo Lee·Thomas Oliver·Alexey Pozdnyakov
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Abstract

We investigate the extent to which the reduced minimal Weierstrass coefficients of an elliptic curve over $\mathbb{Q}$ may be computed from it's Frobenius traces. Decision tree models reveal that the first two reduced minimal Weierstrass coefficients can be recovered with perfect accuracy from the Frobenius traces at the primes $2$ and $3$, and the third by supplementing these two traces with the conductor parity. We subsequently prove explicit formulae for these coefficients using the Frobenius traces and conductor parity. These formulae appear to be new. In particular, we deduce that the first three reduced minimal Weierstrass coefficients of an elliptic curve are determined by its isogeny class.

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Barinder S. Banwait, Xiaoyu Huang, Kyu-Hwan Lee, Seewoo Lee, Thomas Oliver, Alexey Pozdnyakov. 2026-07-27. Decision trees, Frobenius traces, and Weierstrass coefficients of elliptic curves. https://arxiv.org/abs/2607.24251

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