Displaying similar documents to “The canonical height of an algebraic point on an elliptic curve.”

S -integral points on elliptic curves - Notes on a paper of B. M. M. de Weger

Emanuel Herrmann, Attila Pethö (2001)

Journal de théorie des nombres de Bordeaux

Similarity:

In this paper we give a much shorter proof for a result of B.M.M de Weger. For this purpose we use the theory of linear forms in complex and p -adic elliptic logarithms. To obtain an upper bound for these linear forms we compare the results of Hajdu and Herendi and Rémond and Urfels.

Counting elliptic curves of bounded Faltings height

Ruthi Hortsch (2016)

Acta Arithmetica

Similarity:

We give an asymptotic formula for the number of elliptic curves over ℚ with bounded Faltings height. Silverman (1986) showed that the Faltings height for elliptic curves over number fields can be expressed in terms of modular functions and the minimal discriminant of the elliptic curve. We use this to recast the problem as one of counting lattice points in a particular region in ℝ².