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ABSTRACT: 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.