summer 2018 



Matija Kazalicki, University of Zagreb 21.05.2024 14:00, B137 Title: Ranks of elliptic curves and neural networks
Determining the algebraic rank of an elliptic curve E/Q is challenging, often relying on heuristics to estimate the analytic rank, which is conjecturally equal to the algebraic rank under the Birch and SwinnertonDyer conjecture. This talk presents a novel rank classification method utilizing deep convolutional neural networks (CNNs). The method takes the conductor of E and a sequence of Frobenius traces a_p as input to predict rank or detect "high" rank curves. Our method and eight simple neural network models utilizing MestreNagao sums, commonly employed heuristics are compared. Results from evaluating both methods on the LMFDB dataset and a custom dataset show that CNNs outperform MestreNagao sums on the LMFDB dataset while demonstrating comparable performance on the custom dataset. This is joint work with Domagoj Vlah. Additionally, we will elaborate on a recent project with Zvonimir Bujanović and Lukas Novak. We'll explain how the recently observed phenomenon of murmurations of elliptic curves can help us understand fluctuations in the averages of MestreNagao sums, leading to improved classification quality.


Last modified: 16.11.2022 