A. Deines: Dembele's Algorithm for Modular Elliptic Curves Over Real Quadratic Fields
May 13, 2011 in Padelford C401 at 3:30pm
Abstract
From the Eichler-Shimura construction we know that for each newform of weight 2 and level
with rational Fourier coefficients, there exists an elliptic curve
over
attached to
. We can instead work over
, a real quadratic number field with narrow class number one, instead of over
. Let
be a Hilbert newform of weight 2 and level
with rational Fourier coefficients, where
is an integral ideal of
. It is a conjecture that for every
there is an elliptic curve
over
attached to
. Recently Dembele has developed an algorithm which computes the (candidate) elliptic curve
under the assumption that the Eichler-Shimura conjecture is true. I will discuss Dembele's algorithm, give an example, and discuss the status of implementing this algorithm in Sage.