Products of CM elliptic curves

DOI10.1007/s13348-010-0029-1zbMath1237.11027OpenAlexW2050019333MaRDI QIDQ644468

Ernst Kani

Publication date: 4 November 2011

Published in: Collectanea Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13348-010-0029-1

zbMATH Keywords

abelian varietyelliptic curvecomplex multiplicationisomorphichomomorphism ringideal class

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Complex multiplication and moduli of abelian varieties (11G15) Algebraic moduli of abelian varieties, classification (14K10) Complex multiplication and abelian varieties (14K22)

Related Items (18)

Sato–Tate groups of abelian threefolds: a preview of the classification ⋮ Abelian varieties isogenous to a power of an elliptic curve ⋮ Computing base extensions of ordinary abelian varieties over finite fields ⋮ Grothendieck groups of categories of abelian varieties ⋮ Explicit uniform bounds for Brauer groups of singular \(K3\) surfaces ⋮ Principally polarized squares of elliptic curves with field of moduli equal to \(\mathbb{Q}\) ⋮ Endomorphism algebras of geometrically split abelian surfaces over \(\mathbb{Q} \) ⋮ Products of CM elliptic curves ⋮ Computing square-free polarized abelian varieties over finite fields ⋮ Extensions of CM elliptic curves and orbit counting on the projective line ⋮ Jacobians isomorphic to a product of two elliptic curves and ternary quadratic forms ⋮ Elements of given order in Tate-Shafarevich groups of abelian varieties in quadratic twist families ⋮ Algebraic maps constant on isomorphism classes of unpolarized abelian varieties are constant ⋮ The structure of the group of rational points of an abelian variety over a finite field ⋮ On CM points away from the Torelli locus ⋮ Elliptic subcovers of a curve of genus 2. I: The isogeny defect ⋮ Computing abelian varieties over finite fields isogenous to a power ⋮ Spanning the isogeny class of a power of an elliptic curve

Cites Work

• Products of CM elliptic curves
• Binary quadratic forms. An algorithmic approach
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• Principally Polarized Ordinary Abelian Varieties Over Finite Fields
• Abelian varieties over finite fields
• Isogenous Generic Elliptic Curves
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