2, 3, 5, Legendre: ± Trace Ratios in Families of Elliptic Curves

DOI10.1080/10586458.2010.10390623zbMath1295.14026OpenAlexW2032127771MaRDI QIDQ2911504

Nicholas M. Katz

Publication date: 31 August 2012

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.em/1317758091

zbMATH Keywords

finite fieldelliptic curvetrace of Frobeniuscanonical lifting

Mathematics Subject Classification ID

Elliptic curves (14H52) Curves over finite and local fields (11G20) Finite ground fields in algebraic geometry (14G15) Complex multiplication and moduli of abelian varieties (11G15) Complex multiplication and abelian varieties (14K22)

Related Items (1)

On isogeny classes of Edwards curves over finite fields

Cites Work

• Nonsingular plane cubic curves over finite fields
• Frobenius distributions in \(\mathrm{GL}_2\)-extensions. Distribution of Frobenius automorphisms in \(\mathrm{GL}_2\)-extensions of the rational numbers
• Variétés abeliennes ordinaires sur un corps fini
• Isogeny classes of abelian varieties over finite fields
• Die Typen der Multiplikatorenringe elliptischer Funktionenkörper
• Lang–Trotter revisited

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