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Families of elliptic curves with trivial Mordell-Weil group

Published online by Cambridge University Press:  17 April 2009

Andrzej Dabrowski  and
Małgorzata Wieczorek
Andrzej Dabrowski
Affiliation:
University of Szczecin, Institute of Mathematics, ul. Wielkopolska 15, 70–451 Szczecin, Poland, e-mail: dabrowsk@sus.univ.szczecin.pl
Małgorzata Wieczorek
Affiliation:
University of Szczecin, Institute of Mathematics, ul. Wielkopolska 15, 70–451 Szczecin, Poland, e-mail: dabrowsk@sus.univ.szczecin.pl
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Abstract

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Fix and elliptic curve y2 = x3 + Ax + B, satisfying A, B ∈ ℤ A ≥ |B| > 0. We prove that the associated quadratic family contains infinitely many elliptic curves with trivial Mordell-Weil group.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 62 , Issue 2 , October 2000 , pp. 303 - 306
Copyright
Copyright © Australian Mathematical Society 2000

References

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