Abstract:Let E/Q be an elliptic curve over the rational numbers. It is known, by the work of Bombieri and Zannier, that if E has full rational 2-torsion, the number N E (B) of rational points with Weil height bounded by B is exp O log B √ log log B. 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 N E (B) = exp O log B log log B for these… Show more
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