Elliptic curves with bounded ranks in function field towers
Lisa Berger (2012)
Acta Arithmetica
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Lisa Berger (2012)
Acta Arithmetica
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Kevin James, Gang Yu (2006)
Acta Arithmetica
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Ritabrata Munshi (2009)
Acta Arithmetica
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Rose, Harvey E. (2000)
Experimental Mathematics
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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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Amílcar Pacheco (2003)
Acta Arithmetica
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Cremona, John E., Mazur, Barry (2000)
Experimental Mathematics
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Amílcar Pacheco (2010)
Acta Arithmetica
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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.
Gang Yu (2005)
Acta Arithmetica
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Armand Brumer, Oisín McGuinness (1992)
Inventiones mathematicae
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Alf Van Der Poorten (1980)
Mémoires de la Société Mathématique de France
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Dujella, Andrej, Janfada, Ali S., Salami, Sajad (2009)
Journal of Integer Sequences [electronic only]
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Andrej Dujella, Kálmán Győry, Ákos Pintér (2012)
Acta Arithmetica
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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.
Jörn Steuding, Annegret Weng (2005)
Acta Arithmetica
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