Universal bounds on the torsion of elliptic curves
Daniel Sion Kubert (1979)
Compositio Mathematica
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Daniel Sion Kubert (1979)
Compositio Mathematica
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Touafek, Nouressadat (2008)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Horst G. Zimmer (1977)
Mémoires de la Société Mathématique de France
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Emanuel Herrmann, Attila Pethö (2001)
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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 -adic elliptic logarithms. To obtain an upper bound for these linear forms we compare the results of Hajdu and Herendi and Rémond and Urfels.
Franz Lemmermeyer (2003)
Acta Arithmetica
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Everest, Graham, Ward, Thomas (1998)
Experimental Mathematics
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Campbell, Garikai (2003)
Journal of Integer Sequences [electronic only]
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Graham Everest, Patrick Ingram, Valéry Mahé, Shaun Stevens (2008)
Acta Arithmetica
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Bas Edixhoven (1993-1994)
Séminaire Bourbaki
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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.
Dorian Goldfeld, Lucien Szpiro (1995)
Compositio Mathematica
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J. F. Voloch (1990)
Compositio Mathematica
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