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Elliptic divisibility sequences over certain curves

โœ Scribed by Patrick Ingram

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
160 KB
Volume
123
Category
Article
ISSN
0022-314X

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โœฆ Synopsis

Let n 5 be an integer. We provide an effective method for finding all elliptic curves in short Weierstrass form E/Q with j (E) โˆˆ {0, 1728} and all P โˆˆ E(Q) such that the nth term in the elliptic divisibility sequence defined by P over E fails to have a primitive divisor. In particular, we improve recent results of Everest, Mclaren, and Ward on the Zsigmondy bounds of elliptic divisibility sequences associated with congruent number curves.

๐Ÿ“œ SIMILAR VOLUMES

Modularity of CM elliptic curves over di
Modularity of CM elliptic curves over division fields
โœ Naoki Murabayashi ๐Ÿ“‚ Article ๐Ÿ“… 2008 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 91 KB

Let E be a CM elliptic curve defined over an algebraic number field F . In general E will not be modular over F . In this paper, we determine extensions of F , contained in suitable division fields of E, over which E is modular. Under some weak assumptions on E, we construct a minimal subfield of di