:: Volume 12, Number 1 (4-2017) ::
IJMSI 2017, 12(1): 27-34 Back to browse issues page
A Note on Twists of (y^2=x^3+1)
F. Izadi, A. Shamsi Zargar
Abstract:  

‎‎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}.

Keywords: Elliptic curve‎, ‎Mordell curve‎, ‎(Mordell-Weil) rank‎, ‎Twist.
Full-Text [PDF 258 kb]      
Type of Study: Research | Subject: Special



DOI: DOI: 10.7508/ijmsi.2017.01.003


XML     Print


Volume 12, Number 1 (4-2017) Back to browse issues page