### 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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Dujella, Andrej, Janfada, Ali S., Salami, Sajad (2009)

Journal of Integer Sequences [electronic only]

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Leopoldo Kulesz (2003)

Acta Arithmetica

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Tesuji Shioda (1991)

Inventiones mathematicae

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Kumiko Nakata (1979)

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Delaunay, C., Duquesne, S. (2003)

Experimental Mathematics

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Armand Brumer, Oisín McGuinness (1992)

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Hizuru Yamagishi (1998)

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Joseph H. Silvermann (1982)

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Julián Aguirre, Fernando Castañeda, Juan Carlos Peral (2000)

Revista Matemática Complutense

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Seven elliptic curves of the form y = x + B x and having rank at least 8 are presented. To find them we use the double descent method of Tate. In particular we prove that the curve with B = 14752493461692 has rank exactly 8.

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. ...

Bremner, Andrew (2000)

International Journal of Mathematics and Mathematical Sciences

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Koh-ichi Nagao (1997)

Manuscripta mathematica

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Sungkon Chang (2010)

Acta Arithmetica

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Kulesz, Leopoldo, Stahlke, Colin (2001)

Experimental Mathematics

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