TY - JOUR
T1 - A Note on Twists of (y^2=x^3+1)
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
ER -