Computing newforms using supersingular isogeny graphs

DOI10.1007/s40993-022-00392-zzbMath1499.11183arXiv2010.10745OpenAlexW3093596071MaRDI QIDQ2100578

Alex Cowan

Publication date: 24 November 2022

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

Full work available at URL: https://arxiv.org/abs/2010.10745

zbMATH Keywords

sparse matrices\(q\)-expansionsWiedemann's algorithm

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Holomorphic modular forms of integral weight (11F11) Algebraic number theory computations (11Y40)

Uses Software

• LMFDB
• GitHub

Cites Work

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• Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves
• Modeling the distribution of ranks, Selmer groups, and Shafarevich-Tate groups of elliptic curves
• Cryptographic hash functions from expander graphs
• Supersingular isogeny graphs and endomorphism rings: reductions and solutions
• Refined dimensions of cusp forms, and equidistribution and bias of signs
• Modular elliptic curves and Fermat's Last Theorem
• Ring-theoretic properties of certain Hecke algebras
• A heuristic for boundedness of ranks of elliptic curves
• Counting elliptic curves with prescribed torsion
• On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises
• Isogeny volcanoes
• Towards Quantum-Resistant Cryptosystems from Supersingular Elliptic Curve Isogenies
• Some Heuristics about Elliptic Curves
• The Arithmetic of Elliptic Curves
• Solving sparse linear equations over finite fields
• Probabilistic Algorithms in Finite Fields
• Continued Fractions and Linear Recurrences
• Fast Algorithms for Manipulating Formal Power Series
• Computing elliptic curves over $\mathbb {Q}$
• The behavior of the Mordell-Weil group of elliptic curves
• HEURISTICS FOR THE ARITHMETIC OF ELLIPTIC CURVES
• An Algorithm for the Machine Calculation of Complex Fourier Series
• Adventures in Supersingularland

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