Dr. Barinder Banwait (HRI, Allahabad)
We begin the talk by illustrating some of the motivation for studying elliptic curves, including the congruent number problem which the ancient Greeks considered, as well as modern-day cryptography. We then recall Mazur's theorem on rational isogenies of prime degree, and present our algorithmic work which provides, conditional upon the Generalised Riemann Hypothesis, a method to extend Mazur's theorem to quadratic fields, yielding the first examples of the determination of prime degree isogenies since Mazur's work in the 70s. A live-demo of the Sage and PARI/GP implementations of the algorithm will be given.
Meeting ID: 947 0910 0636