Title of article :
A Note on Twists of (y²=x³+1)
Author/Authors :
Izadi ، Farzali Department of Mathematics - Faculty of Science - Urmia University , Shamsi Zargar ، Arman Department of Pure Mathematics - Faculty of Basic Science - Azarbaijan Shahid Madani University
Abstract :
In the category of Mordell curves ED : y²=x³ + D with nontrivial torsion groups we find curves of the generic rank two as quadratic twists of E1, and of the generic rank at least two and at least three as cubic twists of E1. 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 E1.
Keywords :
Elliptic curve , Mordell curve , (Mordell , Weil) rank , Twist
Journal title :
Iranian Journal of Mathematical Sciences and Informatics (IJMSI)
Journal title :
Iranian Journal of Mathematical Sciences and Informatics (IJMSI)
