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New method computes elliptic curve coefficients using Frobenius traces

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Researchers have developed a method to compute the reduced minimal Weierstrass coefficients of an elliptic curve over \mathbb{Q} using its Frobenius traces. Decision tree models demonstrate that the first two coefficients can be accurately recovered from Frobenius traces at primes 2 and 3, with the third coefficient determined by supplementing these traces with conductor parity. Explicit new formulae have been derived for these coefficients, indicating that the first three reduced minimal Weierstrass coefficients are determined by the elliptic curve's isogeny class. AI

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New method computes elliptic curve coefficients using Frobenius traces

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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Barinder S. Banwait, Xiaoyu Huang, Kyu-Hwan Lee, Seewoo Lee, Thomas Oliver, Alexey Pozdnyakov ·

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

    arXiv:2607.24251v1 Announce Type: cross 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 Weie…

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