Darmon, Henri; Daub, Michael; Lichtenstein, Sam; Rotger, Victor Algorithms for Chow-Heegner points via iterated integrals. (English) Zbl 1378.11059 Math. Comput. 84, No. 295, 2505-2547 (2015). Summary: Let \( E_{/\mathbb{Q}}\) be an elliptic curve of conductor \(N\) and let \(f\) be the weight 2 newform on \(\Gamma_0(N)\) associated to it by modularity. Building on an idea of S. Zhang, an article by Darmon, Rotger, and Sols [H. Darmon et al., Publ. Math. Besançon. Algèbre et Théorie des Nombres 2012/2, 19-46 (2012; Zbl 1332.11054)] describes the construction of so-called Chow-Heegner points, \(P_{T,f}\in E({\bar {\mathbb{Q}}})\), indexed by algebraic correspondences \(T\subset X_0(N)\times X_0(N)\). It also gives an analytic formula, depending only on the image of \(T\) in cohomology under the complex cycle class map, for calculating \(P_{T,f}\) numerically via Chen’s theory of iterated integrals. The present work describes an algorithm based on this formula for computing the Chow-Heegner points to arbitrarily high complex accuracy, carries out the computation for all elliptic curves of rank 1 and conductor \(N< 100\) when the cycles \(T\) arise from Hecke correspondences, and discusses several important variants of the basic construction. Cited in 8 Documents MSC: 11F67 Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols 11G05 Elliptic curves over global fields 11Y16 Number-theoretic algorithms; complexity 14C15 (Equivariant) Chow groups and rings; motives Citations:Zbl 1332.11054 Software:ecdata; SageMath PDFBibTeX XMLCite \textit{H. Darmon} et al., Math. Comput. 84, No. 295, 2505--2547 (2015; Zbl 1378.11059) Full Text: DOI References: [1] Agashe, Amod; Ribet, Kenneth; Stein, William A., The Manin constant, Pure Appl. Math. 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