scientific article

zbMath0708.14020MaRDI QIDQ3490122

Noam D. Elkies

Publication date: 1989

Full work available at URL: http://www.numdam.org/item?id=CM_1989__72_2_165_0

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zbMATH Keywords

real embeddinginfinitely many primes of supersingular reduction

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Global ground fields in algebraic geometry (14G25)

Related Items (11)

Arithmetic exceptionality of generalized Lattès maps ⋮ The square sieve and a Lang-Trotter question for generic abelian varieties ⋮ Lang–Trotter revisited ⋮ Exceptional splitting of reductions of abelian surfaces ⋮ Singularities and radical initial ideals ⋮ Explicit small heights in infinite non-abelian extensions ⋮ Supersingular primes for points on \(X_{0}(p)/w_{p}\) ⋮ CM liftings of supersingular elliptic curves ⋮ Exceptional isogenies between reductions of pairs of elliptic curves ⋮ On the Birch and Swinnerton-Dyer conjecture for elliptic curves over totally real number fields ⋮ Potential modularity for elliptic curves and some applications

Cites Work

• The existence of infinitely many supersingular primes for every elliptic curve over \(\mathbb Q\).
• Frobenius distributions in \(\mathrm{GL}_2\)-extensions. Distribution of Frobenius automorphisms in \(\mathrm{GL}_2\)-extensions of the rational numbers
• Die Typen der Multiplikatorenringe elliptischer Funktionenkörper
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