On the number of large integer points on elliptic curves
P. G. Walsh (2009)
Acta Arithmetica
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Displaying similar documents to “Ranks of quadratic twists of an elliptic curve”
On the number of large integer points on elliptic curves
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Some families of non-congruent numbers
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Acta Arithmetica
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From the elliptic regulator to exotic relations.
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Elliptic Carmichael numbers and elliptic Korselt criteria
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Bulletin de la Société Mathématique de France
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2-torsion of the Brauer group of an elliptic curve: Generators and relations.
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Experimental Mathematics
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Large families of elliptic curve pseudorandom binary sequences
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Acta Arithmetica
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Determination of elliptic curves with everywhere good reduction over real quadratic fields ℚ(√(3p))
Takaaki Kagawa (2001)
Acta Arithmetica
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The Ljunggren equation revisited
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.
On a characterization of Shimura's elliptic curve over ℚ(√37)
Masanari Kida (1996)
Acta Arithmetica
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Good reduction of elliptic curves over imaginary quadratic fields
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.
Elliptic curves with all quadratic twists of positive rank
Tim Dokchitser, Vladimir Dokchitser (2009)
Acta Arithmetica
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Points of Order p on Elliptic Curves Over Q(...p).
S. Kamienny (1982)
Mathematische Annalen
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