Infinite descent on elliptic curves
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Publication:1915736
DOI10.1216/rmjm/1181072159zbMath0852.11028OpenAlexW2006264362MaRDI QIDQ1915736
Publication date: 5 December 1996
Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1216/rmjm/1181072159
Elliptic curves over global fields (11G05) Number-theoretic algorithms; complexity (11Y16) Elliptic curves (14H52) Computational aspects of algebraic curves (14Q05)
Related Items (30)
Lucas sequences whose 12th or 9th term is a square ⋮ On the Elliptic Logarithm Method for Elliptic Diophantine Equations: Reflections and an Improvement ⋮ Computing a lower bound for the canonical height on elliptic curves over number fields ⋮ Local solubility and height bounds for coverings of elliptic curves ⋮ Elliptic curves associated with simplest quartic fields ⋮ On the difference between the ordinary height and the canonical height on elliptic curves. ⋮ Numerical Investigations Related to the Derivatives of theL-Series of Certain Elliptic Curves ⋮ Infinite descent on elliptic curves ⋮ Some Improvements to 4-Descent on an Elliptic Curve ⋮ Computing a Lower Bound for the Canonical Height on Elliptic Curves over Totally Real Number Fields ⋮ Generators for the elliptic curve \(y^2=x^3-nx\) of rank at least three ⋮ Solving 𝑆-unit, Mordell, Thue, Thue–Mahler and Generalized Ramanujan–Nagell Equations via the Shimura–Taniyama Conjecture ⋮ Visualizing elements of order in the Tate–Shafarevich group of an elliptic curve ⋮ Higher descents on an elliptic curve with a rational 2-torsion point ⋮ Rational points and the elliptic Chabauty method. ⋮ Integral points in arithmetic progression on \(y^2= x(x^2-n^2)\) ⋮ On the Mordell-Weil group of the elliptic curve ⋮ The difference between the ordinary height and the canonical height on elliptic curves ⋮ On the elliptic curve \(y^2= x^3-2rDx\) and factoring integers ⋮ Generators for the elliptic curve \(y^2=x^3-nx\) ⋮ Explicit arithmetic intersection theory and computation of Néron-Tate heights ⋮ Archimedean local height differences on elliptic curves ⋮ Explicit $n$-descent on elliptic curves III. Algorithms ⋮ Generators and integral points on twists of the Fermat cubic ⋮ Computation of Sets of Rational Points of Genus-3 Curves via the Dem'Janenko–Manin Method ⋮ Problèmes D'effectivité sur les Quartiques de Fermat ⋮ The Mordell-Weil bases for the elliptic curve $y^2=x^3-m^2x+m^2$ ⋮ Computing the rank of elliptic curves over real quadratic number fields of class number 1 ⋮ Elliptic binomial diophantine equations ⋮ Height difference bounds for elliptic curves over number fields
Uses Software
Cites Work
- Approximation of conic sections by curvature continuous quartic Bézier curves
- On the difference of the Weil height and the Neron-Tate height
- On the equation \(Y^ 2=(X+p)(X^ 2+p^ 2)\)
- Infinite descent on elliptic curves
- Estimate of the remainder term in Tate's formula
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- On the Equation Y 2 = X(X 2 + p)
- The Difference Between the Weil Height and the Canonical Height on Elliptic Curves
- Construction of Elliptic Curves with Large Rank
- On the Conjecture of Birch and Swinnerton-Dyer for an Elliptic Curve of Rank 3
- Computing rational points on rank 1 elliptic curves via $L$-series and canonical heights
- Solving elliptic diophantine equations by estimating linear forms in elliptic logarithms
- S-integral points on elliptic curves
- Computing integral points on elliptic curves
- Integral points on elliptic curves over number fields
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