An algorithm to compute the number of points on elliptic curves of \(j\)-invariant 0 or 1728 over a finite field

DOI10.1007/BF02845114zbMath0797.11096OpenAlexW2068852025MaRDI QIDQ1313211

Juan G. Tena Ayuso, Carlos Munuera

Publication date: 20 October 1994

Published in: Rendiconti del Circolo Matemàtico di Palermo. Serie II (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02845114

zbMATH Keywords

algorithmelliptic curvesfinite fieldrational points

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Elliptic curves (14H52) Finite ground fields in algebraic geometry (14G15) Complex multiplication and moduli of abelian varieties (11G15) Computational aspects of algebraic curves (14Q05)

Related Items (2)

On isogeny graphs of supersingular elliptic curves over finite fields ⋮ Locally recoverable codes from rational maps

Cites Work

• Primality of the number of points on an elliptic curve over a finite field
• Resolution of ambiguities in the evaluation of cubic and quartic Jacobsthal sums
• Classi di isomorfismo delle cubiche di \(F_q\).
• Frobenius distributions in \(\mathrm{GL}_2\)-extensions. Distribution of Frobenius automorphisms in \(\mathrm{GL}_2\)-extensions of the rational numbers
• Elliptic Curves Over Finite Fields and the Computation of Square Roots mod p
• A quantitative version of Siegel's theorem: integral points on elliptic curves and Catalan curves.
• A simple and fast probabilistic algorithm for computing square roots modulo a prime number (Corresp.)
• A note on square roots in finite fields
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