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arXiv · 2204.10140

Murmurations of elliptic curves

Yang-Hui He·Kyu-Hwan Lee·Thomas Oliver·Alexey Pozdnyakov
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Abstract

We investigate the average value of the Frobenius trace at p over elliptic curves in a fixed conductor range with given rank. Plotting this average as p varies over the primes yields a striking oscillating pattern, the details of which vary with the rank. Based on this observation, we perform various data-scientific experiments with the goal of classifying elliptic curves according to their ranks.

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Yang-Hui He, Kyu-Hwan Lee, Thomas Oliver, Alexey Pozdnyakov. 2022-04-21. Murmurations of elliptic curves. https://doi.org/10.1080/10586458.2024.2382361

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