Rank computations for the congruent number elliptic curves.
Rogers, Nicholas F. (2000)
Experimental Mathematics
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Displaying similar documents to “Families of elliptic curves of high rank with nontrivial torsion group over ℚ”
Rank computations for the congruent number elliptic curves.
Elliptic curves of high rank with nontrivial torsion group over .
Kulesz, Leopoldo, Stahlke, Colin (2001)
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A search for high rank congruent number elliptic curves.
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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.
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Rank of elliptic curves associated to Brahmagupta quadrilaterals
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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. ...
Q(T)-rank of elliptic curves and certain limit coming from the local points.
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On the Tate-Shafarevich group of semistable elliptic curves with a rational 3-torsion
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