Families of curves with Galois action and their L-functions
نویسندگان
چکیده
منابع مشابه
Elliptic Curves with Maximal Galois Action on Their Torsion Points
Given an elliptic curve E over a number field k, the Galois action on the torsion points of E induces a Galois representation, ρE : Gal(k/k) → GL2(b Z). For a fixed number field k, we describe the image of ρE for a “random” elliptic curve E over k. In particular, if k 6= Q is linearly disjoint from the cyclotomic extension of Q, then ρE will be surjective for “most” elliptic curves over k.
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2015
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2015.02.015