How Twist Class Redundancy Drives the Prediction of Traces of Frobenius of Elliptic Curves

Abstract

Recent interest in applying machine learning methods to predict invariants of mathematical objects has yielded models with surprisingly strong performance, including those predicting traces of Frobenius for elliptic curves. We demonstrate that the underlying datasets contain significant redundancy within quadratic twist classes, which alone is sufficient to produce highly accurate predictions. To ensure future models capture new arithmetic properties rather than potentially exploiting these dataset artifacts, we introduce a benchmark dataset consisting exclusively of unique twist class representatives.