Counting elliptic curves of bounded Faltings height

Ruthi Hortsch. "Counting elliptic curves of bounded Faltings height." Acta Arithmetica 173.3 (2016): 239-253. <http://eudml.org/doc/286416>.

@article{RuthiHortsch2016,
abstract = {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.},
author = {Ruthi Hortsch},
journal = {Acta Arithmetica},
keywords = {elliptic curves; faltings height; arithmetic statistics},
language = {eng},
number = {3},
pages = {239-253},
title = {Counting elliptic curves of bounded Faltings height},
url = {http://eudml.org/doc/286416},
volume = {173},
year = {2016},
}

TY - JOUR
AU - Ruthi Hortsch
TI - Counting elliptic curves of bounded Faltings height
JO - Acta Arithmetica
PY - 2016
VL - 173
IS - 3
SP - 239
EP - 253
AB - 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.
LA - eng
KW - elliptic curves; faltings height; arithmetic statistics
UR - http://eudml.org/doc/286416
ER -