Volume 12, Issue 1 (4-2017)                   IJMSI 2017, 12(1): 27-34 | Back to browse issues page

DOI: DOI: 10.7508/ijmsi.2017.01.003

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‎‎In the category of Mordell curves (E_D:y^2=x^3+D) with nontrivial torsion groups we find curves of the generic rank two as quadratic twists of (E_1), ‎and of the generic rank at least two and at least three as cubic twists of (E_1). ‎Previous work‎, ‎in the category of Mordell curves with trivial torsion groups‎, ‎has found infinitely many elliptic curves with rank at least seven as sextic twists of (E_1) cite{Kih}.

Type of Study: Research paper | Subject: Special