Computing Elliptic Curves over Q(√5)

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Microsoft Research
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Published on ● Video Link: https://www.youtube.com/watch?v=fnG45EqCofw


Duration: 52:13
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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.



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