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

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.

Disclosure

“d at the Korea Institute for Advanced Study (KIAS) in 2025, and was concluded during the AI and Mathematics program at KIAS in 2026. The authors are grateful to the organizers for their hospitality and support. The authors also made use of ChatGPT and Claude in order to encode and decode decision tree models. ChatGPT 5.2- Pro was used to help identify the formula for w2 based on the decision-tree experiments, while Claude Code (with Claude Opus 4.8) assisted in identifying the formu”

PDF page 2

Classification

Substantial mathematical content or result generation

Multiplier

10

Verified

2026-08-23T19:08:36.700703Z

Structural counts