Elliptic curves with surjective adelic Galois representations

Abstract

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.

Mildly revised version, accepted for publication by Experimental Mathematics.

References in corpus (2)

• Elliptic curves with maximal Galois action on their torsion points
• Almost all elliptic curves are Serre curves