On certain twisted families of elliptic curves of rank 8.
Hizuru Yamagishi (1998)
Manuscripta mathematica
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On certain twisted families of elliptic curves of rank 8.
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Joseph H. Silvermann (1982)
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High rank eliptic curves of the form y = x + Bx.
Julián Aguirre, Fernando Castañeda, Juan Carlos Peral (2000)
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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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Loren D. Olson (1974/75)
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The p-Rank of Artin-Schreier Curves.
Doré Subrao (1975)
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Rank of elliptic curves associated to Brahmagupta quadrilaterals
Farzali Izadi, Foad Khoshnam, Arman Shamsi Zargar (2016)
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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. ...
An interesting family of curves of genus 1.
Bremner, Andrew (2000)
International Journal of Mathematics and Mathematical Sciences
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