Tenth Algorithmic Number Theory Symposium ANTS-X University of California, San Diego July 9 – 13, 2012 Tenth Algorithmic Number Theory Symposium (ANTS-X) July 9 – 13, 2012

A database of elliptic curves over Q(sqrt(5)) -- First report

Jonathan Bober, Alyson Deines, Ariah Klages-Mundt, Benjamin LeVeque, R. Andrew Ohana, Ashwath Rabindranath, Paul Sharaba, and William Stein

Abstract: We describe a tabulation of (conjecturally) modular elliptic curves over the field Q(sqrt{5}) up to the first elliptic curve of rank 2. Using an efficient implementation of an algorithm of Lassina Dembélé, 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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