Behaviour of the Order of Tate–Shafarevich Groups for the Quadratic Twists of $$X_0(49)$$

DOI10.1007/978-3-319-45032-2_4zbMath1398.11087OpenAlexW2577972809MaRDI QIDQ5273370

Andrzej Dąbrowski, Tomasz Jędrzejak, Lucjan Szymaszkiewicz

Publication date: 6 July 2017

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-45032-2_4

zbMATH Keywords

elliptic curvesTate-Shafarevich groupquadratic twistsCohen-Lenstra heuristicsdistribution of central \(L\)-values

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Computer solution of Diophantine equations (11Y50) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40)

Related Items (5)

Orders of Tate-Shafarevich groups for the Neumann-Setzer type elliptic curves ⋮ Orders of Tate–Shafarevich groups for the cubic twists of $X_0(27)$ ⋮ A heuristic for boundedness of ranks of elliptic curves ⋮ Elliptic curves with exceptionally large analytic order of the Tate–Shafarevich groups ⋮ Behaviour of the Order of Tate–Shafarevich Groups for the Quadratic Twists of $$X_0(49)$$

Uses Software

• PARI/GP

Cites Work

• The effect of torsion on the distribution of \(\text Ш\) among quadratic twists of an elliptic curve
• Moments and distribution of central \(L\)-values of quadratic twists of elliptic curves
• Heegner points and derivatives of \(L\)-series
• Tate-Shafarevich groups and L-functions of elliptic curves with complex multiplication
• Rational points on elliptic curves with complex multiplication by the ring of integers in \({\mathbb{Q}}(\sqrt{-7})\)
• On the conjecture of Birch and Swinnerton-Dyer
• The Iwasawa Main Conjectures for \(\mathrm{GL}_{2}\)
• Random Matrix Theory and the Fourier Coefficients of Half-Integral-Weight Forms
• On the Distribution of Analytic Values on Quadratic Twists of Elliptic Curves
• Some Heuristics about Elliptic Curves
• The powers of logarithm for quadratic twists
• Heuristics on class groups and on Tate-Shafarevich groups
• FINITENESS OF $ E(\mathbf{Q})$ AND $ \textrm{Ø}(E,\mathbf{Q})$ FOR A SUBCLASS OF WEIL CURVES
• On the conjecture of Birch and Swinnerton-Dyer
• Quadratic twists of elliptic curves
• Behaviour of the Order of Tate–Shafarevich Groups for the Quadratic Twists of $$X_0(49)$$
• Integral moments of L-functions
• MOMENTS OF THE ORDERS OF TATE–SHAFAREVICH GROUPS
• Random matrix theory and \(\zeta(1/2+it)\).

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