A. Deines: Dembele's Algorithm for Modular Elliptic Curves Over Real Quadratic Fields
May 13, 2011 in Padelford C401 at 3:30pm
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.