Abstract
A Q -curve is an elliptic curve E over Q ¯ which is isogenous to all its Galois conjugates. Serre's conjecture implies that Q -curves are modular. This means that E is a Q ¯ -simple factor of J 1 ( N ) for some level N. In this paper we will introduce Q -motives which are generalizations of Q -curves and present basic properties of Q -motives. Their properties are proved under some standard conjectures for motives.
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