A database of elliptic curves over Q(sqrt 5): a first report

@article{Bober2013ADO,
  title={A database of elliptic curves over Q(sqrt 5): a first report},
  author={Jonathan W. Bober and Alyson Deines and Ariah Klages-Mundt and Benjamin L{\'e}v{\^e}que and R. Andrew Ohana and Ashwath Rabindranath and Paul Sharaba and William A. Stein},
  journal={arXiv: Number Theory},
  year={2013}
}
We describe a tabulation of (conjecturally) modular elliptic curves over the field Q(sqrt(5)) up to the first curve of rank 2. Using an efficient implementation of an algorithm of Lassina Dembele, we computed tables of Hilbert modular forms of weight (2,2) over Q(sqrt(5)), and via a variety of methods we constructed corresponding elliptic curves, including (again, conjecturally) all elliptic curves over Q(sqrt(5)) that have conductor with norm less than or equal to 1831. 

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