On binary quartics and the Cassels-Tate pairing

DOI10.1007/s40993-022-00376-zOpenAlexW4297473687MaRDI QIDQ2081522

Tom A. Fisher

Publication date: 13 October 2022

Published in: Research in Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2208.14977

zbMATH Keywords

elliptic curvesTate-Shafarevich groupsCassels-Tate pairing

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Elliptic curves (14H52) Computational aspects of algebraic curves (14Q05)

Uses Software

• Magma
• PARI/GP
• ecdata

Cites Work

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• Coregular spaces and genus one curves
• On the equivalence of binary quartics
• On Cayley's explicit solution to Poncelet's porism
• The Magma algebra system. I: The user language
• The Cassels-Tate pairing and the Platonic solids.
• The Cassels-Tate pairing on polarized Abelian varieties
• Duality theorems for curves over p-adic fields
• Remarques sur un mémoire d'Hermite
• The yoga of the Cassels–Tate pairing
• Arithmetic on Curves of Genus 1. IV. Proof of the Hauptvermutung.
• Second descents for elliptic curves
• Notes on elliptic curves. I.
• Classical invariants and 2-descent on elliptic curves

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