CoCalc Public Fileswww / wiki / seminar(2f)nt(2f)20110513.html
Author: William A. Stein
Compute Environment: Ubuntu 18.04 (Deprecated)
seminar/nt/20110513
 [top] [TitleIndex] [WordIndex]

# A. Deines: Dembele's Algorithm for Modular Elliptic Curves Over Real Quadratic Fields

## 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.

2013-05-11 18:34