mlsanityData to 7 Oct 2026

Murmurations of elliptic curves

arXiv 2204.10140 ↗First posted 21 Apr 2022math.NT hep-th stat.MLcited by 14

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Abstract (arXiv)

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.

Key facts. Cited by 14 papers in the map (data through 7 Oct 2026). Builds on 3 of its 24 references that are in the map. First posted on arXiv 21 Apr 2022.

Builds on

3 of 24 references.

References · 3

  1. 2020Machine-Learning the Sato--Tate Conjecturecited by 14
  2. 2020Machine-Learning Arithmetic Curvescited by 10
  3. 2020Machine-Learning Number Fieldscited by 9

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 3; 2024: 2; 2025: 4; 2026: 4.

14 papers.

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  1. 2023Machine learning detects terminal singularitiescited by 9
  2. 2022Machine Learning Class Numbers of Real Quadratic Fieldscited by 6
  3. 2023Machine Learning Clifford invariants of ADE Coxeter elementscited by 6
  4. 2024A Triumvirate of AI Driven Theoretical Discoverycited by 5
  5. 2026Flow-based Extremal Mathematical Structure Discoverycited by 3
  6. 2025Machines Learn Number Fields, But How? The Case of Galois Groupscited by 2
  7. 2025From Black Box to Bijection: Interpreting Machine Learning to Build a Zeta Map Algorithmcited by 2
  8. 2026Murmurations, Mestre--Nagao sums, and Convolutional Neural Networks for elliptic curvescited by 2
  9. 2024Machine Learning Mutation-Acyclicity of Quiverscited by 1
  10. 2025Learning Fricke signs from Maass form Coefficientscited by 1
  11. 2023Notes on a Path to AI Assistance in Mathematical Reasoningcited by 0
  12. 2025Learning Modular Exponentiation with Transformerscited by 0
2 more
  1. 2026Murmurations: a case study in AI-assisted mathematicscited by 0
  2. 2026Decision trees, Frobenius traces, and Weierstrass coefficients of elliptic curvescited by 0