Rational Poncelet

DOI10.1142/S1793042118501580zbMath1440.11096OpenAlexW4211219723MaRDI QIDQ4961429

Jaap Top, Tiemar Mepschen, Johan Los

Publication date: 29 October 2018

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

Full work available at URL: https://doi.org/10.1142/s1793042118501580

zbMATH Keywords

elliptic curvetorsion pointPoncelet closure theorem

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Questions of classical algebraic geometry (51N35) Elliptic curves (14H52)

Related Items (1)

Mazur's rational torsion result for pointless genus one curves: examples

Cites Work

• Unnamed Item
• Gonality of the modular curve \(X_1(N)\)
• Explicit solutions to Poncelet's porism
• Poncelet's theorem and billiard knots
• Poncelet's closure theorem
• Modular curves and the Eisenstein ideal
• Torsion points on elliptic curves and \(q\)-coefficients of modular forms
• Beppo Levi and the arithmetic of elliptic curves
• Bicentennial of the Great Poncelet Theorem (1813–2013): Current advances
• Ranks of Elliptic Curves with Prescribed Torsion over Number Fields
• Poncelet problem for rational conics
• Families of elliptic curves over cubic number fields with prescribed torsion subgroups
• Families of elliptic curves over quartic number fields with prescribed torsion subgroups
• Explicit determination of nontrivial torsion structures of elliptic curves over quadratic number fields
• The closure theorem of Poncelet
• Elliptical billiards and Poncelet’s theorem
• Torsion subgroups of elliptic curves over quintic and sextic number fields
• The Poncelet Grid and Billiards in Ellipses

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