Using Generative Adversarial Networks (GANs) to Produce Elliptic Curves of Specified Rank

John Cox

Prior knowledge:
No previous knowledge expected


Rank is a key property of elliptic curves that is widely studied, yet difficult to calculate with seemingly no pattern given an elliptic curve's coefficients. Utilizing Generative Adverserial Networks (GANs), it is possible to generate coefficients of elliptic curves of specified rank. This project proposes GANs as a new method for discovering elliptic curves of a specified rank.


The intended audience of this talk includes those interested in emerging methods of machine learning and its applications. The talk will be tailored to be inclusive of those with limited knowledge of machine learning. No knowledge of elliptic curves is necessary. The talk will be broken down into three sections. First, background on elliptic curves, their rank, and why they are interesting. Second, a brief introduction to GANs and how their architecture can help solve the rank problem, including the specific architecture of the GAN model I use in the problem. Third, results of the project.