Torsion points on elliptic curves in Weierstrass form
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 12 (2013) no. 3, pp. 687-715.

We prove that there are only finitely many complex numbers a and b with 4a 3 +27b 2 0 such that the three points (1,*),(2,*), and (3,*) are simultaneously torsion points on the elliptic curve defined in Weierstrass form by y 2 =x 3 +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.

Publié le :
Classification : 14H52, 14G40, 11G05, 11U09
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     author = {Habegger, Philipp},
     title = {Torsion points on elliptic curves in {Weierstrass} form},
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     volume = {Ser. 5, 12},
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Habegger, Philipp. Torsion points on elliptic curves in Weierstrass form. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 12 (2013) no. 3, pp. 687-715. http://www.numdam.org/item/ASNSP_2013_5_12_3_687_0/

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