TY - JOUR T1 - A Note on Twists of (y^2=x^3+1) TT - JF - IJMSI JO - IJMSI VL - 12 IS - 1 UR - http://ijmsi.ir/article-1-593-en.html Y1 - 2017 SP - 27 EP - 34 KW - Elliptic curve‎ KW - ‎Mordell curve‎ KW - ‎(Mordell-Weil) rank‎ KW - ‎Twist. N2 - ‎‎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}. M3 DOI: 10.7508/ijmsi.2017.01.003 ER -