An interesting family of curves of genus 1.

Bremner, Andrew

Displaying similar documents to “An interesting family of curves of genus 1.”

Rank computations for the congruent number elliptic curves.

Rogers, Nicholas F. (2000)

Experimental Mathematics

Similarity:

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

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

Experimental Mathematics

Similarity:

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

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

Revista Matemática Complutense

Similarity:

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.

A search for high rank congruent number elliptic curves.

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

Journal of Integer Sequences [electronic only]

Similarity:

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

Tesuji Shioda (1991)

Inventiones mathematicae

Similarity:

On the arithmetic of twists of superelliptic curves

Sungkon Chang (2006)

Acta Arithmetica

Similarity:

Families of elliptic curves of high rank with nontrivial torsion group over ℚ

Leopoldo Kulesz (2003)

Acta Arithmetica

Similarity:

Ranks of quadratic twists of elliptic curves

Mark Watkins, Stephen Donnelly, Noam D. Elkies, Tom Fisher, Andrew Granville, Nicholas F. Rogers (2014)

Publications mathématiques de Besançon

Similarity:

We report on a large-scale project to investigate the ranks of elliptic curves in a quadratic twist family, focussing on the congruent number curve. Our methods to exclude candidate curves include 2-Selmer, 4-Selmer, and 8-Selmer tests, the use of the Guinand-Weil explicit formula, and even 3-descent in a couple of cases. We find that rank 6 quadratic twists are reasonably common (though still quite difficult to find), while rank 7 twists seem much more rare. We also describe our inability...