Explicit points on the Legendre curve

DOI10.1016/j.jnt.2013.09.010zbMath1297.11055arXiv1002.3313OpenAlexW3022085934MaRDI QIDQ2637184

Douglas L. Ulmer

Publication date: 7 February 2014

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

Full work available at URL: https://arxiv.org/abs/1002.3313

zbMATH Keywords

elliptic curvesranksconjecture of Birch and Swinnerton-Dyer

Mathematics Subject Classification ID

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

Related Items (10)

Explicit points on \(y^2+xy-t^dy=x^3\) and related character sums ⋮ On the distribution of balanced subgroups ⋮ Analogue of the Brauer-Siegel theorem for Legendre elliptic curves ⋮ ON THE FIBRES OF AN ELLIPTIC SURFACE WHERE THE RANK DOES NOT JUMP ⋮ Rational curves on elliptic surfaces ⋮ Explicit Arithmetic of Jacobians of Generalized Legendre Curves Over Global Function Fields ⋮ Curves and Jacobians over Function Fields ⋮ Explicit L-functions and a Brauer–Siegel theorem for Hessian elliptic curves ⋮ Arithmetic of abelian varieties in Artin-Schreier extensions ⋮ On the Brauer-Siegel ratio for abelian varieties over function fields

Cites Work

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• \(L\)-functions with large analytic rank and abelian varieties with large algebraic rank over function fields
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• Intersection numbers of sections of elliptic surfaces
• The rank of elliptic curves
• On Balanced Subgroups of the Multiplicative Group
• Algorithm for determining the type of a singular fiber in an elliptic pencil
• Park City lectures on elliptic curves over function fields
• The Arithmetic of Elliptic Curves
• Elliptic Curves
• On Mordell–Weil groups of Jacobians over function fields
• Modular Forms

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