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Journals / Turkish Journal of Mathematics / 1999 / Cilt: 23 - Sayı: 4

On the asymptotic behaviour of Heegner points

Jan NEKOVAR
Norbert SCHAPPACHER
Pages
549–556
Publication Date
2022-11-05
DOI
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⚡ TL;DR(Too Long; Didn't Read)

We prove that all but finitely many Heegner points on a given modular elliptic curve (or, more generally, on a given quotient of the modularJacobian variety $J_0$(N)) are of infinite order in the Mordell-Weil group where they naturally live, i.e., over the corresponding ring class field.

📌 3 Key Takeaways

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Objective & Hypothesis:We prove that all but finitely many Heegner points on a given modular elliptic curve (or, more generally, on a given quotient of the modularJacobian variety $J_0$(N)) are of infinite order in the Mordell-Weil group where they naturally live, i.e., over the corresponding ring class field.
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Key Findings & Data:We prove that all but finitely many Heegner points on a given modular elliptic curve (or, more generally, on a given quotient of the modularJacobian variety $J_0$(N)) are of infinite order in the Mordell-Weil group where they naturally live, i.e., over the corresponding ring class field.
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Conclusion & Impact:We prove that all but finitely many Heegner points on a given modular elliptic curve (or, more generally, on a given quotient of the modularJacobian variety $J_0$(N)) are of infinite order in the Mordell-Weil group where they naturally live, i.e., over the corresponding ring class field.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

We prove that all but finitely many Heegner points on a given modular elliptic curve (or, more generally, on a given quotient of the modularJacobian variety $J_0$(N)) are of infinite order in the Mordell-Weil group where they naturally live, i.e., over the corresponding ring class field.

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Cite This Article

NEKOVAR, J., SCHAPPACHER, N. (2022). On the asymptotic behaviour of Heegner points. Turkish Journal of Mathematics, Cilt: 23 - Sayı: 4, 549–556. https://ajindex.com/articles/608978

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References (3)

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