Computing Elliptic Curves over Q(√5)

Опубликовано 12 августа 2016, 2:06

I will discuss creating (conjectural) tables of elliptic curves over Q(√5) ordered by conductor up to the first curve of rank 2. We computed these curves by first computing weight (2,2) Hilbert modular forms over Q(√5) using an algorithm of Lassina Dembélé. Using various methods we constructed the (conjecturally) corresponding elliptic curves. I will also discuss newer work towards partially extending these results to the first curve of rank 3. This is joint work with Jonathan Bober, Joanna Gaski, Ariah Klages-Mundt, Benjamin LeVeque, R. Andrew Ohana, Sebastian Pancratz, Ashwath Rabindranath, Paul Sharaba, Ari Shnidman, William Stein, and Christelle Vincent.