Torsion points on elliptic curves in Weierstrass form
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 12 (2013) no. 3, p. 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.

Published online : 2019-02-21
Classification:  14H52,  14G40,  11G05,  11U09
@article{ASNSP_2013_5_12_3_687_0,
     author = {Habegger, Philipp},
     title = {Torsion points on elliptic curves in Weierstrass form},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 12},
     number = {3},
     year = {2013},
     pages = {687-715},
     zbl = {1281.14026},
     mrnumber = {3137460},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2013_5_12_3_687_0}
}
Habegger, Philipp. Torsion points on elliptic curves in Weierstrass form. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 12 (2013) no. 3, pp. 687-715. http://www.numdam.org/item/ASNSP_2013_5_12_3_687_0/

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