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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Displaying similar documents to “Ranks of elliptic curves in cubic extensions”
A search for high rank congruent number elliptic curves.
Elliptic curves of high rank with nontrivial torsion group over .
Kulesz, Leopoldo, Stahlke, Colin (2001)
Experimental Mathematics
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Integer Points and the Rank of Thue Elliptic Curves.
Joseph H. Silvermann (1982)
Inventiones mathematicae
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Rank computations for the congruent number elliptic curves.
Rogers, Nicholas F. (2000)
Experimental Mathematics
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Reductions of an elliptic curve with almost prime orders
Alina Carmen Cojocaru (2005)
Acta Arithmetica
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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.
Armand Brumer, Oisín McGuinness (1992)
Inventiones mathematicae
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Integral points on elliptic curves defined by simplest cubic fields.
Duquesne, Sylvain (2001)
Experimental Mathematics
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Numerical investigations related to the derivatives of the -series of certain elliptic curves.
Delaunay, C., Duquesne, S. (2003)
Experimental Mathematics
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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.
Families of elliptic curves of high rank with nontrivial torsion group over ℚ
Leopoldo Kulesz (2003)
Acta Arithmetica
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Mordell-Weil ranks of families of elliptic curves associated to Pythagorean triples
Bartosz Naskręcki (2013)
Acta Arithmetica
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We study the family of elliptic curves y² = x(x-a²)(x-b²) parametrized by Pythagorean triples (a,b,c). We prove that for a generic triple the lower bound of the rank of the Mordell-Weil group over ℚ is 1, and for some explicitly given infinite family the rank is 2. To each family we attach an elliptic surface fibered over the projective line. We show that the lower bounds for the rank are optimal, in the sense that for each generic fiber of such an elliptic surface its corresponding...
From the elliptic regulator to exotic relations.
Touafek, Nouressadat (2008)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Some families of non-congruent numbers
Franz Lemmermeyer (2003)
Acta Arithmetica
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On certain twisted families of elliptic curves of rank 8.
Hizuru Yamagishi (1998)
Manuscripta mathematica
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On the number of prime divisors of the order of elliptic curves modulo p
Jörn Steuding, Annegret Weng (2005)
Acta Arithmetica
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