of elliptic curves with sufficient torsion over
Raymond Ross (1992)
Compositio Mathematica
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Raymond Ross (1992)
Compositio Mathematica
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Eriksson, Nicholas (1999)
International Journal of Mathematics and Mathematical Sciences
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M. Ram Murty, Rajiv Gupta (1990)
Inventiones mathematicae
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Dujella, Andrej, Janfada, Ali S., Salami, Sajad (2009)
Journal of Integer Sequences [electronic only]
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Rose, Harvey E. (2000)
Experimental Mathematics
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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.
Andrea Bandini (2008)
Czechoslovak Mathematical Journal
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We explicitly perform some steps of a 3-descent algorithm for the curves , a nonzero integer. In general this will enable us to bound the order of the 3-Selmer group of such curves.
Lemmermeyer, F., Mollin, R. (2003)
Acta Mathematica Universitatis Comenianae. New Series
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Jerzy Browkin, Daniel Davies
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We consider elliptic curves defined over ℚ. It is known that for a prime p > 3 quadratic twists permute the Kodaira classes, and curves belonging to a given class have the same conductor exponent. It is not the case for p = 2 and 3. We establish a refinement of the Kodaira classification, ensuring that the permutation property is recovered by {refined} classes in the cases p = 2 and 3. We also investigate the nonquadratic twists. In the last part of the paper we discuss the number...