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Height difference bounds for elliptic curves over number fields

โœ Scribed by J.E. Cremona; M. Prickett; Samir Siksek


Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
266 KB
Volume
116
Category
Article
ISSN
0022-314X

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A lower bound for the canonical height o
โœ Joseph H. Silverman ๐Ÿ“‚ Article ๐Ÿ“… 2004 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 296 KB

Let E=K be an elliptic curve defined over a number field, let ฤฅ be the canonical height on E; and let K ab =K be the maximal abelian extension of K: Extending work of M. Baker (IMRN 29 (2003) 1571-1582), we prove that there is a constant CรฐE=Kรž40 so that every nontorsion point PAEรฐK ab รž satisfies ฤฅ