Torsion points on elliptic curves in Weierstrass form

Habegger, Philipp. (2013) Torsion points on elliptic curves in Weierstrass form. Annali della Scuola Normale di Pisa - Classe di Scienze, 12 (3). pp. 687-715.

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We prove that there are only finitely many complex numbers a and b with 4a3+27b2≠0 such that the three points (1,∗),(2,∗), and (3,∗) are simultaneously torsion on the elliptic curve defined in Weierstrass form by y2=x3+ax+b. This gives an affirmative answer to a question raised by Masser and Zannier. We thus confirm a special case in two dimensions of the relative Manin-Mumford Conjecture formulated by Pink and Masser-Zannier.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Zahlentheorie (Habegger)
UniBasel Contributors:Habegger, Philipp
Item Type:Article, refereed
Article Subtype:Research Article
Publisher:Scuola Normale Superiore
Note:Publication type according to Uni Basel Research Database: Journal article
Identification Number:
Last Modified:26 Jan 2018 14:29
Deposited On:26 Jan 2018 14:29

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