Elliptic curves and lower bounds for class numbers

DOI10.1016/j.jnt.2020.05.001zbMath1481.11109arXiv2001.07332OpenAlexW3028580367WikidataQ114157190 ScholiaQ114157190MaRDI QIDQ2187113

Ken Ono, Michael J. Griffin

Publication date: 2 June 2020

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

Full work available at URL: https://arxiv.org/abs/2001.07332

zbMATH Keywords

elliptic curvesclass numbers

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Class numbers, class groups, discriminants (11R29)

Related Items (4)

Bilinear forms in Weyl sums for modular square roots and applications ⋮ Heights of points on elliptic curves over ℚ ⋮ Quadratic twists of elliptic curves and class numbers ⋮ On class numbers, torsion subgroups, and quadratic twists of elliptic curves

Cites Work

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• Class pairings and isogenies on elliptic curves
• Heegner points and derivatives of \(L\)-series
• Sums involving the values at negative integers of \(L\)-functions of quadratic characters
• Homomorphisms from the group of rational points on elliptic curves to class groups of quadratic number fields
• A complete determination of the complex quadratic fields of class-number one
• Diophantine analysis and modular forms
• The Difference Between the Weil Height and the Canonical Height on Elliptic Curves
• Gauss’ class number problem for imaginary quadratic fields
• Elliptic Curves and Class Groups of Quadratic Fields
• Class numbers of imaginary quadratic fields
• The Mordell--Weil bases for the elliptic curve of the form $y^2=x^3-m^2x+n^2$
• Heights and the specialization map for families of abelian varieties.
• Linear forms in the logarithms of algebraic numbers

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