Supersingular parameters of the Deuring normal form

DOI10.1007/s11139-012-9459-6zbMath1307.14048OpenAlexW1982777350MaRDI QIDQ744839

Patrick Morton

Publication date: 26 September 2014

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-012-9459-6

zbMATH Keywords

elliptic curvessupersingularalgebraic function fieldsDeuring normal formcubic Fermat curve

Mathematics Subject Classification ID

Elliptic curves (14H52) Dedekind eta function, Dedekind sums (11F20) Higher degree equations; Fermat's equation (11D41) Algebraic functions and function fields in algebraic geometry (14H05)

Cites Work

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• The cubic Fermat equation and complex multiplication on the Deuring normal form
• Algebraic function fields and codes
• Monogénéité de l'anneau des entiers de certains corps de classes de rayon. (Monogeneity of the ring of integers of certain ray class fields)
• Cubic theta functions.
• Class numbers of quadratic fields, Hasse invariants of elliptic curves, and the supersingular polynomial
• Explicit identities for invariants of elliptic curves
• Solutions of the cubic Fermat equation in ring class fields of imaginary quadratic fields (as periodic points of a 3-adic algebraic function)
• Eta Products and Theta Series Identities
• Rational analogues of Ramanujan's series for 1/π
• Realising wreath products of cyclic groups as Galois groups
• Some Cubic Modular Identities of Ramanujan
• A Cubic Counterpart of Jacobi's Identity and the AGM
• An identity for the Dedekind eta-function involving two independent complex variables
• A simple proof of an expansion of an eta-quotient as a Lambert series
• Note on an eta identity presented by B. C. Berndt and W. B. Hart

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