On the equation \(Y^ 2=(X+p)(X^ 2+p^ 2)\)

DOI10.1216/rmjm/1181072392zbMath0810.11038OpenAlexW2087828806MaRDI QIDQ1344011

Jaap Top, Roelof J. Stroeker

Publication date: 9 February 1995

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1216/rmjm/1181072392

zbMATH Keywords

elliptic curvesrational solutionSelmer groupShafarevich group

Mathematics Subject Classification ID

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

Related Items (11)

A note on the curve \(Y^2=(X+p)(X^2+p^2)\) ⋮ Infinite descent on elliptic curves ⋮ Application of covering techniques to families of curves. ⋮ On several families of elliptic curves with arbitrary large Selmer groups ⋮ Infinitely many hyperelliptic curves with exactly two rational points ⋮ On elliptic curves with large Tate-Shafarevich groups ⋮ Mordell-Weil groups and Selmer groups of twin-prime elliptic curves ⋮ Two-descent on some genus two curves ⋮ Unnamed Item ⋮ Solving Elliptic Diophantine Equations Avoiding Thue Equations and Elliptic Logarithms ⋮ A remark on prime (non)congruent numbers

Cites Work

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• Zeta-functions of elliptic curves of 2-power conductor
• Three Points of Great Height on Elliptic Curves
• On the Equation Y 2 = X(X 2 + p)
• The Difference Between the Weil Height and the Canonical Height on Elliptic Curves

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