Twists of elliptic curves of rank at least four
نویسندگان
چکیده
We give infinite families of elliptic curves over Q such that each curve has infinitely many non-isomorphic quadratic twists of rank at least 4. Assuming the Parity Conjecture, we also give elliptic curves over Q with infinitely many non-isomorphic quadratic twists of odd rank at least 5.
منابع مشابه
A Note on Twists of (y^2=x^3+1)
‎‎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 ...
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