On the number of large integer points on elliptic curves
P. G. Walsh (2009)
Acta Arithmetica
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P. G. Walsh (2009)
Acta Arithmetica
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Andrew Bremner (2003)
Acta Arithmetica
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Franz Lemmermeyer (2003)
Acta Arithmetica
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Sungkon Chang (2010)
Acta Arithmetica
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Touafek, Nouressadat (2008)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Joseph H. Silverman (2012)
Acta Arithmetica
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Sheldon Kamienny (1986)
Bulletin de la Société Mathématique de France
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Chernousov, V., Guletskiĭ, V. (2001)
Documenta Mathematica
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Rubin, Karl, Silverberg, Alice (2000)
Experimental Mathematics
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Huaning Liu, Tao Zhan, Xiaoyun Wang (2009)
Acta Arithmetica
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Takaaki Kagawa (2001)
Acta Arithmetica
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Konstantinos A. Draziotis (2007)
Colloquium Mathematicae
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We study the Ljunggren equation Y² + 1 = 2X⁴ using the "multiplication by 2" method of Chabauty.
Masanari Kida (1996)
Acta Arithmetica
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Masanari Kida (2001)
Journal de théorie des nombres de Bordeaux
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We prove that the -invariant of an elliptic curve defined over an imaginary quadratic number field having good reduction everywhere satisfies certain Diophantine equations under some hypothesis on the arithmetic of the quadratic field. By solving the Diophantine equations explicitly in the rings of quadratic integers, we show the non-existence of such elliptic curve for certain imaginary quadratic fields. This extends the results due to Setzer and Stroeker.
Tim Dokchitser, Vladimir Dokchitser (2009)
Acta Arithmetica
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S. Kamienny (1982)
Mathematische Annalen
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