Let be an elliptic curve over the rational numbers. It is known, by the work of Bombieri and Zannier, that if has full rational 2-torsion, the number of rational points with Weil height bounded by is . In this paper we exploit the method of descent via 2-isogeny to extend this result to elliptic curves with just one nontrivial rational 2-torsion point. Moreover, we make use of a result of Petsche to derive the stronger upper bound for these curves and to remove a deep transcendence theory ingredient from the proof.
Cite this article
Francesco Naccarato, Counting rational points on elliptic curves with a rational 2-torsion point. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 32 (2021), no. 3, pp. 499–509DOI 10.4171/RLM/945