On the equation \(y^2=x(x - 2^m)(x+q - 2^m)\)

DOI10.1016/j.jnt.2006.09.005zbMath1117.11032OpenAlexW1975414132MaRDI QIDQ880062

Andrzej Dąbrowski, Małgorzata Wieczorek

Publication date: 10 May 2007

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2006.09.005

zbMATH Keywords

Mordell-Weil rankElliptic curves2-descent methodquadratic twists by prime numbers

Mathematics Subject Classification ID

Rational points (14G05) Elliptic curves over global fields (11G05) Curves over finite and local fields (11G20) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Primes (11A41)

Related Items (6)

On several families of elliptic curves with arbitrary large Selmer groups ⋮ Integral points on elliptic curves $y^{2}=x(x-2^{m}) (x+p)$ ⋮ On the proportion of rank 0 twists of elliptic curves ⋮ ON TWISTS OF THE FERMAT CUBIC x³ + y³ = 2 ⋮ ON POSITIVE PROPORTION OF RANK-ZERO TWISTS OF ELLIPTIC CURVES OVER ⋮ Integral points on elliptic curves associated with generalized twin primes

Uses Software

• ComputeL

Cites Work

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• The canonical height and integral points on elliptic curves
• Non-vanishing of quadratic twists of modular \(L\)-functions
• Mordell-Weil ranks of quadratic twists of pairs of elliptic curves.
• Integral points in arithmetic progression on \(y^2= x(x^2-n^2)\)
• Explicit 4-descents on an elliptic curve
• Sur certaines hypothèses concernant les nombres premiers
• Signes locaux des courbes elliptiques en 2 et 3
• Invariants des courbes de Frey-Hellegouarch et grands groupes de Tate-Shafarevich
• Computing Special Values of MotivicL-Functions
• The non-vanishing of central values of automorphic \(L\)-functions and Landau-Siegel zeros

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