Elliptic curves with full 2-torsion and maximal adelic Galois representations
نویسندگان
چکیده
منابع مشابه
Elliptic curves with full 2-torsion and maximal adelic Galois representations
In 1972, Serre showed that the adelic Galois representation associated to a non-CM elliptic curve over a number field has open image in GL2(Ẑ). In [Gre10], Greicius develops necessary and sufficient criteria for determining when this representation is actually surjective and exhibits such an example. However, verifying these criteria turns out to be difficult in practice; Greicius describes tes...
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Let K be a number field. The Gal(K/K)-action on the the torsion of an elliptic curve E/K gives rise to an adelic representation ρE : Gal(K/K) → GL2(Ẑ). From an analysis of maximal closed subgroups of GL2(Ẑ) we derive useful necessary and sufficient conditions for ρE to be surjective. Using these conditions, we compute an example of a number field K and an elliptic curve E/K that admits a surjec...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2014
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-2014-02804-4