From the elliptic regulator to exotic relations.
Touafek, Nouressadat (2008)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Touafek, Nouressadat (2008)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Rose, Harvey E. (2000)
Experimental Mathematics
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P. G. Walsh (2009)
Acta Arithmetica
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J. Bochnak, J. Huisman (1992)
Mathematische Annalen
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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.
Franz Lemmermeyer (2003)
Acta Arithmetica
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Joseph H. Silverman (2012)
Acta Arithmetica
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Rubin, Karl, Silverberg, Alice (2000)
Experimental Mathematics
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Clemens Fuchs, Rafael von Känel, Gisbert Wüstholz (2011)
Acta Arithmetica
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D.W. Masser, G. Wüstholz (1990)
Inventiones mathematicae
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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.
Lisa Berger (2012)
Acta Arithmetica
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Daniel S. Kubert (1994)
Inventiones mathematicae
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Gang Yu (2005)
Acta Arithmetica
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Joseph H. Silverman, Armand Brumer (1996)
Manuscripta mathematica
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M. Anderson, David W. Masser (1980)
Mathematische Zeitschrift
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