A Database of Elliptic Curves over Q(sqrt(5))  First Report
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.
 Publication:

arXiv eprints
 Pub Date:
 February 2012
 DOI:
 10.48550/arXiv.1202.6612
 arXiv:
 arXiv:1202.6612
 Bibcode:
 2012arXiv1202.6612B
 Keywords:

 Mathematics  Number Theory
 EPrint:
 17 pages