Constructing supersingular elliptic curves with a given endomorphism ring

DOI10.1112/S1461157014000254zbMath1326.11029arXiv1301.6875OpenAlexW3105729405WikidataQ61914013 ScholiaQ61914013MaRDI QIDQ2878828

Ilya Chevyrev, Steven D. Galbraith

Publication date: 5 September 2014

Published in: LMS Journal of Computation and Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.6875

zbMATH Keywords

endomorphism ringsupersingular elliptic curve

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) General ternary and quaternary quadratic forms; forms of more than two variables (11E20) Curves over finite and local fields (11G20) Finite ground fields in algebraic geometry (14G15) Quaternion and other division algebras: arithmetic, zeta functions (11R52) Quadratic forms (reduction theory, extreme forms, etc.) (11H55)

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On sign changes of cusp forms and the halting of an algorithm to construct a supersingular elliptic curve with a given endomorphism ring ⋮ Selectivity in definite quaternion algebras ⋮ Cycles in the Supersingular ℓ-Isogeny Graph and Corresponding Endomorphisms ⋮ Endomorphism rings of supersingular elliptic curves over \(\mathbb{F}_p\)

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