Legendre polynomials and complex multiplication. I.

DOI10.1016/J.JNT.2010.03.009zbMath1200.11093OpenAlexW2051575897MaRDI QIDQ982524

Patrick Morton

Publication date: 7 July 2010

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2010.03.009

zbMATH Keywords

finite fieldelliptic curvefactorizationLegendre polynomial

Mathematics Subject Classification ID

Elliptic curves (14H52) Polynomials over finite fields (11T06) Elliptic curves over local fields (11G07)

Related Items (8)

Explicit congruences for class equations ⋮ On the Galois groups of Legendre polynomials ⋮ Explicit identities for invariants of elliptic curves ⋮ Counting points on hyperelliptic curves of type \(y^2=x^{2g+1}+ax^{g+1}+bx\) ⋮ On the Hasse invariants of the Tate normal forms \(E_5\) and \(E_7\) ⋮ The cubic Fermat equation and complex multiplication on the Deuring normal form ⋮ The Hasse invariant of the Tate normal form \(E_5\) and the class number of \(\mathbb{Q}(\sqrt{-5l})\) ⋮ The number of linear factors of supersingular polynomials and sporadic simple groups

Cites Work

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• The cubic Fermat equation and complex multiplication on the Deuring normal form
• Systems of orthogonal polynomials arising from the modular \(j\)-function.
• Class numbers of quadratic fields, Hasse invariants of elliptic curves, and the supersingular polynomial
• Explicit identities for invariants of elliptic curves
• Die Typen der Multiplikatorenringe elliptischer Funktionenkörper
• Zur Theorie der abstrakten elliptischen Funktionenkörper III. Die Struktur des Meromorphismenrings. Die Riemannsche Vermutung.

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