Tenth Algorithmic Number Theory Symposium ANTSX

A database of elliptic curves over Q(sqrt(5))  First report
Jonathan Bober, Alyson Deines, Ariah KlagesMundt, Benjamin LeVeque, R. Andrew Ohana, Ashwath Rabindranath, Paul Sharaba, and William Stein
Abstract: We describe a tabulation of (conjecturally) modular elliptic curves over the field Q(sqrt{5}) up to the first elliptic curve of rank 2. Using an efficient implementation of an algorithm of Lassina Dembélé, 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.
Files available: paper (PDF)
© 201112 Kiran S. Kedlaya (with thanks to Pierrick Gaudry and Emmanuel Thomé)
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