Geodesic
Counting elliptic curves of bounded Faltings height
Ruthi Hortsch1
1 Department of Mathematics, 2-239A Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge, MA 02139, U.S.A.
Acta Arithmetica, Tome 173 (2016) no. 3, pp. 239-253.

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We give an asymptotic formula for the number of elliptic curves over $\mathbb Q$ 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 $\mathbb R^2$.
DOI : 10.4064/aa8204-2-2016
Keywords: asymptotic formula number elliptic curves mathbb bounded faltings height silverman showed faltings height elliptic curves number fields expressed terms modular functions minimal discriminant elliptic curve recast problem counting lattice points particular region nbsp mathbb

Ruthi Hortsch 1

1 Department of Mathematics, 2-239A Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge, MA 02139, U.S.A. 
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Ruthi Hortsch. Counting elliptic curves of bounded Faltings height. Acta Arithmetica, Tome 173 (2016) no. 3, pp. 239-253. doi : 10.4064/aa8204-2-2016. http://geodesic.mathdoc.fr/articles/10.4064/aa8204-2-2016/

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