Local solubility and height bounds for coverings of elliptic curves

DOI10.1090/S0025-5718-2012-02587-7zbMath1277.11075arXiv1103.4944OpenAlexW2963701088MaRDI QIDQ2894526

G. F. Sills, Tom A. Fisher

Publication date: 29 June 2012

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

Full work available at URL: https://arxiv.org/abs/1103.4944

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Computer solution of Diophantine equations (11Y50) Heights (11G50) Elliptic curves over local fields (11G07)

Related Items (4)

Local solubility and height bounds for coverings of elliptic curves ⋮ On genus one curves of degree 5 with square-free discriminant ⋮ Minimal genus one curves ⋮ Explicit $n$-descent on elliptic curves III. Algorithms

Uses Software

• Magma
• ecdata

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Minimisation and reduction of 2-, 3- and 4-coverings of elliptic curves
• Height difference bounds for elliptic curves over number fields
• The Magma algebra system. I: The user language
• Visibility of Shafarevich-Tate groups of abelian varieties.
• Infinite descent on elliptic curves
• On the Jacobians of plane cubics
• The Hessian of a genus one curve
• Local solubility and height bounds for coverings of elliptic curves
• Higher descents on an elliptic curve with a rational 2-torsion point
• Counting models of genus one curves
• Explicit 4-descents on an elliptic curve
• Arithmetic on Curves of Genus 1. IV. Proof of the Hauptvermutung.
• Some Improvements to 4-Descent on an Elliptic Curve
• Some ternary Diophantine equations of signature (n, n, 2)
• The invariants of a genus one curve
• How to do a 𝑝-descent on an elliptic curve
• Notes on elliptic curves. I.
• Jacobians of genus one curves.

This page was built for publication: Local solubility and height bounds for coverings of elliptic curves