Computing modular polynomials and isogenies of rank two Drinfeld modules over finite fields

DOI10.1090/conm/754/15148zbMath1469.11178OpenAlexW3046517850MaRDI QIDQ4998642

Matthew Greenberg, Perlas C. Caranay, Renate Scheidler

Publication date: 9 July 2021

Published in: 75 Years of Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/conm/754/15148

zbMATH Keywords

\(j\)-invariantisogenyendomorphism ringDrinfeld modular polynomialisogeny volcanorank 2 Drinfeld module

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Algebraic number theory computations (11Y40) Drinfel'd modules; higher-dimensional motives, etc. (11G09)

Related Items

Computing the Characteristic Polynomial of Endomorphisms of a finite Drinfeld Module using Crystalline Cohomology

Cites Work

• Computing isogeny volcanoes of composite degree
• Zur Arithmetik von Drinfeld-Moduln
• On finite Drinfeld modules
• A product expansion for the discriminant function of Drinfeld modules of rank two
• Drinfeld modular curves
• On the coefficients of Drinfeld modular forms
• On the modular equation for Drinfeld modules of rank 2
• On the singular Drinfeld modules of rank 2
• Von Staudt for \(\mathbb F_q[T\)]
• On the coefficients of the Drinfeld modular equation
• On the Drinfeld modular polynomial \(\Phi_ T(X,Y)\)
• Isogenies of Drinfeld modules over finite fields
• Drinfeld modular polynomials in higher rank
• Computing the endomorphism ring of an ordinary elliptic curve over a finite field
• Isogeny volcanoes
• On the evaluation of modular polynomials
• Computing modular polynomials in quasi-linear time
• On the coefficients of the transformation polynomials for the elliptic modular function
• Modular forms for Fr [T.]
• The algebraist’s upper half-plane
• Probabilistic Algorithms in Finite Fields
• ELLIPTIC MODULES
• Polynomial Multiplication over Finite Fields in Time \( O(n \log n \)
• Computing the Characteristic Polynomial of a Finite Rank Two Drinfeld Module
• Modular polynomials via isogeny volcanoes
• Frobenius distributions of Drinfeld modules over finite fields
• Computing Modular Polynomials
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