A lower bound for the canonical height on elliptic curves over abelian extensions.

DOI10.1016/j.jnt.2003.07.001zbMath1053.11052arXivmath/0305041OpenAlexW1996015125MaRDI QIDQ1427990

Joseph H. Silverman

Publication date: 14 March 2004

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

Full work available at URL: https://arxiv.org/abs/math/0305041

zbMATH Keywords

\(j\)-invariantelliptic curveLehmer's conjecturecomplex multiplicationramificationcanonical heightformal grouptorsion point

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Abelian varieties of dimension (> 1) (11G10) Heights (11G50) Arithmetic ground fields for abelian varieties (14K15) Global ground fields in algebraic geometry (14G25)

Related Items (10)

The local Lehmer inequality for Drinfeld modules ⋮ The Lehmer inequality and the Mordell-Weil theorem for Drinfeld modules ⋮ Small height and infinite nonabelian extensions ⋮ On the properties of Northcott and Narkiewicz for elliptic curves ⋮ Cyclotomic and abelian points in backward orbits of rational functions ⋮ Explicit small heights in infinite non-abelian extensions ⋮ Some consequences of Masser's counting theorem on elliptic curves ⋮ Torsion homology growth and cycle complexity of arithmetic manifolds ⋮ On the ranks of elliptic curves in families of quadratic twists over number fields ⋮ Intersections of subgroups and subvarieties. I

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