Computing rational points on rank 1 elliptic curves via $L$-series and canonical heights

DOI10.1090/S0025-5718-99-01068-6zbMath1042.11036OpenAlexW2064164257MaRDI QIDQ4235523

Joseph H. Silverman

Publication date: 22 March 1999

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-99-01068-6

zbMATH Keywords

canonical heightElliptic curve

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Computer solution of Diophantine equations (11Y50)

Related Items (7)

STARK POINTS AND -ADIC ITERATED INTEGRALS ATTACHED TO MODULAR FORMS OF WEIGHT ONE ⋮ Infinite descent on elliptic curves ⋮ Spreading alerts quietly and the subgroup escape problem ⋮ Integral points and the rank of elliptic curves over imaginary quadratic fields ⋮ On the elliptic curve \(y^2= x^3-2rDx\) and factoring integers ⋮ THE EXPLICIT MORDELL CONJECTURE FOR FAMILIES OF CURVES ⋮ 5-torsion in the Shafarevich-Tate group of a family of elliptic curves

Uses Software

• ecdata

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Heegner points and derivatives of \(L\)-series
• \(p\)-adic \(L\)-functions and rational points on elliptic curves with complex multiplication
• Modular elliptic curves and Fermat's Last Theorem
• Ring-theoretic properties of certain Hecke algebras
• On deformation rings and Hecke rings
• Ellitpic curves and modular functions
• The Difference Between the Weil Height and the Canonical Height on Elliptic Curves

This page was built for publication: Computing rational points on rank 1 elliptic curves via $L$-series and canonical heights