INTEGRAL POINTS ON CONGRUENT NUMBER CURVES

DOI10.1142/S1793042113500474zbMath1318.11047MaRDI QIDQ2850712

Michael A. Bennett

Publication date: 30 September 2013

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

zbMATH Keywords

elliptic curvescongruent numbersintegral points

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Cubic and quartic Diophantine equations (11D25)

Related Items (4)

Shifted powers in binary recurrence sequences ⋮ Integral points on elliptic curves $y^{2}=x(x-2^{m}) (x+p)$ ⋮ On certain Diophantine equations of the form \(z^2=f(x)^2\pm g(y)^2\) ⋮ Integral points on the elliptic curve $y^2=x^3-4p^2x$

Cites Work

• Elementary results for certain Diophantine equations
• Maximal ranks and integer points on a family of elliptic curves. II.
• Integer points and independent points on the elliptic curve \(y^2=x^3-p^kx\)
• Mock Heegner points and congruent numbers
• Integer solutions to the equation \(y^2=x(x^2\pm p^k)\)
• The polynomial \(X^2+Y^4\) captures its primes
• Solving the Diophantine equation \(y^2=x(x^2 - n^2)\)
• Diophantine analysis and modular forms
• An explicit lower bound for a homogeneous rational linear form in the logarithms of algebraic numbers. II
• Maximal ranks and integer points on a family of elliptic curves
• THE DIOPHANTINE EQUATION A⁴ + 2^δB² = Cⁿ
• The Diophantine equation $b^2X^4-dY^2=1$
• Ternary Diophantine Equations via Galois Representations and Modular Forms
• Galois representations attached to Q-curves and the generalized Fermat equation A 4 + B 2 = C p
• The Diophantine Equation y ² = D x ⁴ +1
• Integer points on the curve $Y^{2}=X^{3}\pm p^{k}X$
• Practical solution of the Diophantine equation $y^2 = x(x+2^ap^b)(x-2^ap^b)$
• Some Remarks on the Diophantine Equations x ² − Dy ⁴ = 1 and x ⁴ − Dy ² = 1
• THE EQUATIONS 3x²−2 = y² AND 8x²−7 = z²

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