Points of Finite Order of Elliptic Curves with Complex Multiplication.
Loren D. Olson (1974/75)
Manuscripta mathematica
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Loren D. Olson (1974/75)
Manuscripta mathematica
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Ian Connell (1994)
Manuscripta mathematica
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Rose, Harvey E. (2000)
Experimental Mathematics
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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.
Cremona, John E., Mazur, Barry (2000)
Experimental Mathematics
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Hizuru Yamagishi (1998)
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Clemens Fuchs, Rafael von Känel, Gisbert Wüstholz (2011)
Acta Arithmetica
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Rubin, Karl, Silverberg, Alice (2000)
Experimental Mathematics
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Lisa Berger (2012)
Acta Arithmetica
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Andrej Dujella, Kálmán Győry, Ákos Pintér (2012)
Acta Arithmetica
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Gang Yu (2005)
Acta Arithmetica
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Jörn Steuding, Annegret Weng (2005)
Acta Arithmetica
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Toshihiro Hadano (1982)
Manuscripta mathematica
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Alf Van Der Poorten (1980)
Mémoires de la Société Mathématique de France
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Tom Fisher (2015)
Acta Arithmetica
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We compute equations for the families of elliptic curves 9-congruent to a given elliptic curve. We use these to find infinitely many non-trivial pairs of 9-congruent elliptic curves over ℚ, i.e. pairs of non-isogenous elliptic curves over ℚ whose 9-torsion subgroups are isomorphic as Galois modules.
D.W. Masser, G. Wüstholz (1990)
Inventiones mathematicae
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