Torsion of elliptic curves over cyclic cubic fields

DOI10.1090/mcom/3408zbMath1470.11149arXiv1804.06777OpenAlexW2797232339MaRDI QIDQ5380100

Filip Najman, Maarten Derickx

Publication date: 14 June 2019

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

Full work available at URL: https://arxiv.org/abs/1804.06777

zbMATH Keywords

elliptic curvesmodular curvesrational points

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05)

Related Items (7)

A survey on the group of points arising from elliptic curves with a Weierstrass model over a ring ⋮ RANK JUMPS AND GROWTH OF SHAFAREVICH–TATE GROUPS FOR ELLIPTIC CURVES IN -EXTENSIONS ⋮ Torsion groups of elliptic curves over the \(\mathbb{Z}_p\)-extensions of \(\mathbb{Q}\) ⋮ Torsion of rational elliptic curves over different types of cubic fields ⋮ Groups of generalized G‐type and applications to torsion subgroups of rational elliptic curves over infinite extensions of Q ⋮ Elliptic curves with a point of order \(13\) defined over cyclic cubic fields ⋮ Modular curves over number fields and ECM

Uses Software

• Magma
• LMFDB
• GitHub
• chabauty

Cites Work

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• Torsion des courbes elliptiques sur les corps cubiques. (Torsion of elliptic curves over cubic fields)
• Torsion points on elliptic curves and \(q\)-coefficients of modular forms
• Families of elliptic curves over cyclic cubic number fields with prescribed torsion
• Ranks of Elliptic Curves with Prescribed Torsion over Number Fields
• Families of elliptic curves over cubic number fields with prescribed torsion subgroups
• The Mordell–Weil sieve: proving non-existence of rational points on curves
• Vanishing and non-vanishing Dirichlet twists of L -functions of elliptic curves
• Torsion points on elliptic curves defined over quadratic fields
• Fields of definition of elliptic curves with prescribed torsion
• Rational families of 17-torsion points of elliptic curves over number fields
• On the torsion of elliptic curves over cubic number fields
• Constructing elliptic curves over finite fields with prescribed torsion

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