Elliptic curves with surjective adelic Galois representations

Details Elliptic curves with surjective adelic Galois representations Elliptic curves with surjective adelic Galois representations

2009-01-16

arxiv.org/abs/0901.2513v3

Mathematics

Number Theory

Mildly revised version, accepted for publication by Experimental Mathematics.

Scientific paper

We prove useful necessary and sufficient conditions for an elliptic curve
over a number field to admit a surjective adelic Galois representation. Using
these conditions, we compute an example of a number field K and an elliptic
curve E/K whose corresponding adelic representation is surjective.

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