Modular invariant and good reduction of elliptic curves.

Salvador Comalada; Enric Nart

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Displaying similar documents to “Modular invariant and good reduction of elliptic curves.”

Stickelberger elements and modular parametrizations of elliptic curves.

Glenn Stevens (1989)

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The number of elliptic curves over Q with conductor N.

Joseph H. Silverman, Armand Brumer (1996)

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ndependence of Modular Units on Tate Curves.

Serge Lang, Daniel S. Kubert (1979)

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Points of Order p on Elliptic Curves Over Q(...p).

S. Kamienny (1982)

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A Cuspidal Class Number Formula for the Modular Curves X1(N).

Jing Yu (1980)

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Modular parametrizations of certain elliptic curves

Matija Kazalicki, Koji Tasaka (2014)

Acta Arithmetica

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Kaneko and Sakai (2013) recently observed that certain elliptic curves whose associated newforms (by the modularity theorem) are given by the eta-quotients can be characterized by a particular differential equation involving modular forms and Ramanujan-Serre differential operator. In this paper, we study certain properties of the modular parametrization associated to the elliptic curves over ℚ, and as a consequence we generalize and explain some of their findings. ...

Counting elliptic curves of bounded Faltings height

Ruthi Hortsch (2016)

Acta Arithmetica

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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.