A Note on Twists of (y^2=x^3+1)

Author(s):

F. Izadi , A. Shamsi Zargar

Abstract:
In the category of Mordell curves (E_D:y^2=x^3) with nontrivial torsion groups we find curves of the generic rank two as quadratic twists of (E_1), ýand of the generic rank at least two and at least three as cubic twists of (E_1). ýPrevious worký, ýin the category of Mordell curves with trivial torsion groupsý, ýhas found infinitely many elliptic curves with rank at least seven as sextic twists of (E_1) cite{Kih}.
Keywords:

Elliptic curveý , ýMordell curveý , ý(Mordell-Weil) ranký , ýTwist

Language:
English
Published:
Iranian Journal of Mathematical Sciences and Informatics, Volume:12 Issue: 1, May 2017
Pages:
27 to 34
https://www.magiran.com/p1674668