On the Equation Y 2 = X(X 2 + p)

DOI10.2307/2007578zbMath0531.10014OpenAlexW2087547970MaRDI QIDQ3312309

Andrew Bremner, J. W. S. Cassels

Publication date: 1984

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2007578

zbMATH Keywords

generatorsrational pointselliptic curvecubic Diophantine equationquartic Diophantine equationMordell conjectureMordell-Weil rank oneSelmer conjecture

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Computer solution of Diophantine equations (11Y50) Cubic and quartic Diophantine equations (11D25)

Related Items (17)

On quartic Diophantine equations with trivial solutions in the Gaussian integers ⋮ On the equation \(Y^ 2=(X+p)(X^ 2+p^ 2)\) ⋮ Indivisible points on families of elliptic curves ⋮ Computer-aided serendipity ⋮ Infinite descent on elliptic curves ⋮ The upper bound estimate of the number of integer points on elliptic curves \(y^2=x^3+p^{2r}x\) ⋮ Higher descents on an elliptic curve with a rational 2-torsion point ⋮ Integral points in arithmetic progression on \(y^2= x(x^2-n^2)\) ⋮ Three constructions of rational points on \(Y^ 2=X^ 3\pm NX\) ⋮ Elliptic curves with rank 0 over number fields ⋮ A family of elliptic curves with rank \(\geq 5\) ⋮ On quadratic solutions of \(x^4+py^4=z^4\) ⋮ A note on the Selmer group of the elliptic curve \(y^ 2=x^ 3+Dx\). ⋮ Mordell-Weil groups and Selmer groups of twin-prime elliptic curves ⋮ Two-descent on some genus two curves ⋮ Unnamed Item ⋮ Bielliptic smooth plane curves and quadratic points

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