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arXiv · 1202.6612

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·William Stein
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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.

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Jonathan Bober, Alyson Deines, Ariah Klages-Mundt, Benjamin LeVeque, R. Andrew Ohana, Ashwath Rabindranath, Paul Sharaba, William Stein. 2012-02-29. A Database of Elliptic Curves over Q(sqrt(5)) - First Report. https://arxiv.org/abs/1202.6612

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