Abstract

We describe a tabulation of (conjecturally) modular elliptic curves over the field $\mathbb{Q}\left(\sqrt{\mathfrak{5}}\right)$ up to the first elliptic curve of rank $\mathfrak{2}$. Using an efficient implementation of an algorithm of Lassina Dembélé, we computed tables of Hilbert modular forms of weight $\left(\mathfrak{2},\mathfrak{2}\right)$ over $\mathbb{Q}\left(\sqrt{\mathfrak{5}}\right)$, and via a variety of methods we constructed corresponding elliptic curves, including (again, conjecturally) all elliptic curves over $\mathbb{Q}\left(\sqrt{\mathfrak{5}}\right)$ that have conductor with norm less than or equal to 1831.

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Mathematical Subject Classification 2010

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