Abstract
Let H be the Hilbert class field of an imaginary quadratic field K. An elliptic curve E over H with complex multiplication by K is called a ℚ-curve if E is isogenous over H to all its Galois conjugates. We classify ℚ-curves over H, relating them with the cohomology group H2(H/ℚ, +1). The structures of the abelian varieties over ℚ obtained from ℚ-curves by restriction of scalars are investigated.
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Nakamura, T. (2004). Elliptic ℚ-Curves with Complex Multiplication. 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_13
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DOI: https://doi.org/10.1007/978-3-0348-7919-4_13
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9621-4
Online ISBN: 978-3-0348-7919-4
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