Rank computations for the congruent number elliptic curves.
Rogers, Nicholas F. (2000)
Experimental Mathematics
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Displaying similar documents to “Mordell-Weil ranks of families of elliptic curves associated to Pythagorean triples”
Rank computations for the congruent number elliptic curves.
Rational points on some elliptic surfaces
Enrico Jabara (2012)
Acta Arithmetica
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The average rank of elliptic curves I. With Appendix "The Explicit formula for elliptic curves over function fields" by Oisín McGuinness.
Armand Brumer, Oisín McGuinness (1992)
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A search for high rank congruent number elliptic curves.
Dujella, Andrej, Janfada, Ali S., Salami, Sajad (2009)
Journal of Integer Sequences [electronic only]
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Families of elliptic curves of high rank with nontrivial torsion group over ℚ
Leopoldo Kulesz (2003)
Acta Arithmetica
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On certain twisted families of elliptic curves of rank 8.
Hizuru Yamagishi (1998)
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Integer Points and the Rank of Thue Elliptic Curves.
Joseph H. Silvermann (1982)
Inventiones mathematicae
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On Some Elliptic Curves Defined Over ... of Free Rank ... 9.
Kumiko Nakata (1979)
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An infinite family of elliptic curves over Q with large rank via Néron's method.
Tesuji Shioda (1991)
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Elliptic curves with bounded ranks in function field towers
Lisa Berger (2012)
Acta Arithmetica
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Ranks of elliptic curves in cubic extensions
Tim Dokchitser (2007)
Acta Arithmetica
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Elliptic curves of high rank with nontrivial torsion group over .
Kulesz, Leopoldo, Stahlke, Colin (2001)
Experimental Mathematics
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Quadratic twists of elliptic curves with small Selmer rank
Sungkon Chang (2010)
Acta Arithmetica
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Q(T)-rank of elliptic curves and certain limit coming from the local points.
Koh-ichi Nagao (1997)
Manuscripta mathematica
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Rank of elliptic curves associated to Brahmagupta quadrilaterals
Farzali Izadi, Foad Khoshnam, Arman Shamsi Zargar (2016)
Colloquium Mathematicae
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We construct a family of elliptic curves with six parameters, arising from a system of Diophantine equations, whose rank is at least five. To do so, we use the Brahmagupta formula for the area of cyclic quadrilaterals (p³,q³,r³,s³) not necessarily representing genuine geometric objects. It turns out that, as parameters of the curves, the integers p,q,r,s along with the extra integers u,v satisfy u⁶+v⁶+p⁶+q⁶ = 2(r⁶+s⁶), uv = pq, which, by previous work, has infinitely many integer solutions. ...