✦ LIBER ✦

Modularity of CM elliptic curves over division fields

✍ Scribed by Naoki Murabayashi

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 91 KB
Volume: 128
Category: Article
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2007.01.011

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✦ Synopsis

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 division fields over which E is modular.

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