An interesting family of curves of genus 1.
Bremner, Andrew (2000)
International Journal of Mathematics and Mathematical Sciences
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Displaying similar documents to “On the arithmetic of twists of superelliptic curves”
An interesting family of curves of genus 1.
Numerical investigations related to the derivatives of the -series of certain elliptic curves.
Delaunay, C., Duquesne, S. (2003)
Experimental Mathematics
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Tuples of hyperelliptic curves y² = xⁿ+a
Tomasz Jędrzejak, Jaap Top, Maciej Ulas (2011)
Acta Arithmetica
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Rank computations for the congruent number elliptic curves.
Rogers, Nicholas F. (2000)
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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The analytic order of III for modular elliptic curves
J. E. Cremona (1993)
Journal de théorie des nombres de Bordeaux
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In this note we extend the computations described in [4] by computing the analytic order of the Tate-Shafarevich group III for all the curves in each isogeny class ; in [4] we considered the strong Weil curve only. While no new methods are involved here, the results have some interesting features suggesting ways in which strong Weil curves may be distinguished from other curves in their isogeny class.
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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High rank eliptic curves of the form y = x + Bx.
Julián Aguirre, Fernando Castañeda, Juan Carlos Peral (2000)
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.
The p-Rank of Artin-Schreier Curves.
Doré Subrao (1975)
Manuscripta mathematica
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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
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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...
Rigidity of integral curves of rank 2 distributions.
Robert L. Bryant, Lucas Hsu (1993)
Inventiones mathematicae
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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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Classification of Maximal Rank Curves in the Liasion Class Ln.
Giorgio Bolondi, Juan Migliore (1987)
Mathematische Annalen
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