## Displaying similar documents to “Rank computations for the congruent number elliptic curves.”

### A search for high rank congruent number elliptic curves.

Journal of Integer Sequences [electronic only]

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Acta Arithmetica

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### An infinite family of elliptic curves over Q with large rank via Néron's method.

Inventiones mathematicae

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### On Some Elliptic Curves Defined Over ... of Free Rank ... 9.

Manuscripta mathematica

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### Numerical investigations related to the derivatives of the $L$-series of certain elliptic curves.

Experimental Mathematics

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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.

Inventiones mathematicae

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### On certain twisted families of elliptic curves of rank 8.

Manuscripta mathematica

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### Integer Points and the Rank of Thue Elliptic Curves.

Inventiones mathematicae

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### High rank eliptic curves of the form y = x + Bx.

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.

### Rank of elliptic curves associated to Brahmagupta quadrilaterals

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. ...

### An interesting family of curves of genus 1.

International Journal of Mathematics and Mathematical Sciences

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### Q(T)-rank of elliptic curves and certain limit coming from the local points.

Manuscripta mathematica

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Acta Arithmetica

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### Elliptic curves of high rank with nontrivial torsion group over $ℚ$.

Experimental Mathematics

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