A divisibility related to the Birch and Swinnerton-Dyer conjecture

DOI10.1016/j.jnt.2022.10.004OpenAlexW4310068205WikidataQ122884311 ScholiaQ122884311MaRDI QIDQ2112722

Mentzelos Melistas

Publication date: 11 January 2023

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

Full work available at URL: https://arxiv.org/abs/2211.08147

zbMATH Keywords

elliptic curveShafarevich-Tate groupBSD conjecturetorsion pointTamagawa number

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Elliptic curves (14H52) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40)

Uses Software

• SageMath
• ecdata

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Torsion and Tamagawa numbers
• Rational torsion on optimal curves and rank-one quadratic twists
• On Néron's classification of elliptic curves of residue characteristics 2 and 3
• The Manin constant. (With an appendix by J. Cremona)
• On the Birch-Swinnerton-Dyer quotients modulo squares
• A note on elliptic curves with a rational 3-torsion point
• Heegner points and derivatives of \(L\)-series
• Modular curves and the Eisenstein ideal
• Calculating root numbers of elliptic curves over \(\mathbb{Q}\)
• Modular elliptic curves and Fermat's Last Theorem
• Ring-theoretic properties of certain Hecke algebras
• Elliptic curves of prime power conductor with Q-rational points of finite order
• On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises
• Algorithm for determining the type of a singular fiber in an elliptic pencil
• Courbes de Weil semi-stables de discriminant une puissance m-ième.
• Structure de torsion des courbes elliptiques sur les corps quadratiques
• The Manin constant in the semistable case
• A conjecture of Gross and Zagier: Case E(ℚ)tor≅ℤ/2ℤ ⊕ ℤ/2ℤ, ℤ/2ℤ ⊕ ℤ/4ℤ or ℤ/2ℤ ⊕ ℤ/6ℤ
• On a conjecture of Agashe
• The Arithmetic of Elliptic Curves
• FINITENESS OF $ \textit{Ø}$ OVER TOTALLY REAL FIELDS
• Elliptic curves with a torsion point
• Signes locaux des courbes elliptiques en 2 et 3
• Elliptic Curves
• Visible evidence for the Birch and Swinnerton-Dyer conjecture for modular abelian varieties of analytic rank zero
• Optimal curves differing by a 3-isogeny
• Local invariants of isogenous elliptic curves
• RATIONAL TORSION ON OPTIMAL CURVES

This page was built for publication: A divisibility related to the Birch and Swinnerton-Dyer conjecture