Computing modular degrees using \(L\)-functions
Let \(E\) be an elliptic curve of conductor \(N\) defined over \(\mathbb Q\). There exists a modular parametrization \(\varphi\) from \(X_0(N)\) to \(E.\) By results of \textit{D. Zagier} [Can. Math. Bull. 28, 372--384 (1985; Zbl 0579.14027)] and \textit{G. Shimura} [Pure Appl. Math. 29, 783--804 (1976; Zbl 0348.10015)] one can compute the degree of \(\varphi\) once the critical value \(L(\text{Sym}^2(E),2)\) is known. The author proposes an algorithm which calculates this value and seems to be faster than \textit{J. E. Cremona}'s [Algorithms for modular elliptic curves, Cambridge University Press (1997; Zbl 0872.14041)], at least for large conductor.
scientific article; zbMATH DE number 2184618