Coverings of elliptic curves with complex multiplication by hyperelliptic curves and character sums

DOI10.1006/jnth.1997.2070zbMath0874.11044OpenAlexW2051260171MaRDI QIDQ1358795

Franck Leprévost, François Morain

Publication date: 23 June 1997

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

Full work available at URL: https://doi.org/10.1006/jnth.1997.2070

zbMATH Keywords

hyperelliptic curvescharacter sumscoverings of elliptic curves with complex multiplicationnormalizing conditions

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Elliptic curves (14H52) Other character sums and Gauss sums (11T24) Complex multiplication and moduli of abelian varieties (11G15)

Related Items (8)

Parametric families of elliptic curves with cyclic \(\mathbb F_p\)-rational points groups ⋮ Congruences for Brewer sums ⋮ Congruences involving \({2k\choose k}^2{3k\choose k}\) ⋮ Computing the cardinality of CM elliptic curves using torsion points ⋮ HYPERELLIPTIC CURVES, CARTIER — MANIN MATRICES AND LEGENDRE POLYNOMIALS ⋮ Trace of Frobenius endomorphism of an elliptic curve with complex multiplication ⋮ CONGRUENCES CONCERNING LEGENDRE POLYNOMIALS III ⋮ Generating Genus Two Hyperelliptic Curves over Large Characteristic Finite Fields

Uses Software

• PARI/GP
• ECPP

Cites Work

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• On Primes of the Form u 2 + 5v 2
• On the Evaluation of Brewer's Character Sums

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