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<html>
<head>
<title>A Database of Elliptic Curves over Q(sqrt(5))---First Report</title>
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<br><br><br>
<h1 align="center">A Database of Elliptic Curves over Q(sqrt(5))---First Report</h1>
<h2 align="center">Submitted</h2>
<h3 align="center">
by Jonathan Bober, Alyson Deines, Ariah Klages-Mundt, Benjamin
LeVeque, R. Andrew Ohana, Ashwath Rabindranath, Paul Sharaba, William
Stein<br>
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<table width="507" border="0" align="center" cellpadding="10" bgcolor="#990000">
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<th><a href="sqrt5.pdf">Download it now as a PDF</a></th>
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<th><a href="http://arxiv.org/abs/1202.6612">View the Paper at arXiv.org</a></th>
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<th><a href="tables/">Some Relevant Tables</a></th>
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<th><a href="https://github.com/williamstein/sqrt5/">Github Repository</a></th>
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<hr>
<p align="center"><strong>Abstract</strong></p>
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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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