TY - JOUR
JF - IJMSI
JO - IJMSI
VL - 12
IS - 1
PY - 2017
Y1 - 2017/4/01
TI - A Note on Twists of (y^2=x^3+1)
TT -
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}.
SP - 27
EP - 34
AU - Izadi, F.
AU - Shamsi Zargar, A.
AD - Shahid Madani University, Tabriz
KW - Elliptic curve
KW - Mordell curve
KW - (Mordell-Weil) rank
KW - Twist.
UR - http://ijmsi.ir/article-1-593-en.html
DO - DOI: 10.7508/ijmsi.2017.01.003
ER -