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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Displaying similar documents to “High rank eliptic curves of the form y2 = x3 + Bx.”
A search for high rank congruent number elliptic curves.
Rank computations for the congruent number elliptic curves.
Rogers, Nicholas F. (2000)
Experimental Mathematics
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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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Numerical investigations related to the derivatives of the -series of certain elliptic curves.
Delaunay, C., Duquesne, S. (2003)
Experimental Mathematics
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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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An interesting family of curves of genus 1.
Bremner, Andrew (2000)
International Journal of Mathematics and Mathematical Sciences
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Rank frequencies for quadratic twists of elliptic curves.
Rubin, Karl, Silverberg, Alice (2001)
Experimental Mathematics
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An infinite family of elliptic curves over Q with large rank via Néron's method.
Tesuji Shioda (1991)
Inventiones mathematicae
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On Some Elliptic Curves Defined Over ... of Free Rank ... 9.
Kumiko Nakata (1979)
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. ...
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)
Inventiones mathematicae
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Integer Points and the Rank of Thue Elliptic Curves.
Joseph H. Silvermann (1982)
Inventiones mathematicae
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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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Tuples of hyperelliptic curves y² = xⁿ+a
Tomasz Jędrzejak, Jaap Top, Maciej Ulas (2011)
Acta Arithmetica
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