Abstract
This paper is a survey on the arithmetic of ℚ-curves: the elliptic curves defined over number fields which are isogenous to all their Galois conjugates. Our purpose is to review some results concerning their basic properties such as: the moduli classification, fields of definition, relationship with abelian varieties of GL2-type, and optimal quotients. Most of the results were separately published before and our aim here is to reinforce a global presentation. What we call “central” Q-curves will constitute the leitmotif.
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González, J., Lario, JC., Quer, J. (2004). Arithmetic of ℚ-Curves. In: Cremona, J.E., Lario, JC., Quer, J., Ribet, K.A. (eds) Modular Curves and Abelian Varieties. Progress in Mathematics, vol 224. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7919-4_9
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DOI: https://doi.org/10.1007/978-3-0348-7919-4_9
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