Rank-one quadratic twists of an infinite family of elliptic curves

DOI10.1515/CRELLE.2009.060zbMath1257.11062OpenAlexW2077610384MaRDI QIDQ3647061

Dongho Byeon, Chang Heon Kim, Daeyeol Jeon

Publication date: 27 November 2009

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/crelle.2009.060

zbMATH Keywords

elliptic curvesquadratic twists

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40)

Related Items

Infinitely many elliptic curves of rank exactly two ⋮ Elliptic curves of rank zero satisfying the \(p\)-part of the Birch and Swinnerton-Dyer conjecture ⋮ Elliptic curves with conductor having $n$ prime factors ⋮ Rational torsion on optimal curves and rank-one quadratic twists ⋮ Heegner points on elliptic curves with a rational torsion point ⋮ GOLDFELD’S CONJECTURE AND CONGRUENCES BETWEEN HEEGNER POINTS ⋮ Elliptic curves of rank 1 satisfying the 3-part of the Birch and Swinnerton-Dyer conjecture ⋮ Class number divisibility for imaginary quadratic fields ⋮ DENSITY RESULTS FOR SPECIALIZATION SETS OF GALOIS COVERS

Cites Work

• Heegner points and derivatives of \(L\)-series
• Rank-one twists of a certain elliptic curve
• Non-vanishing of quadratic twists of modular \(L\)-functions
• Modular elliptic curves and Fermat's Last Theorem
• Ring-theoretic properties of certain Hecke algebras
• Canonical periods and congruence formulae
• On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises
• MULTIPLICATIVE SUBGROUPS OF J 0(N) AND APPLICATIONS TO ELLIPTIC CURVES
• Elliptic Curves with no Rational Points
• L-series with nonzero central critical value
• Ranks of quadratic twists of an elliptic curve
• On the density of discriminants of cubic fields. II
• RATIONAL TORSION ON OPTIMAL CURVES