Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 56, Number 2 (2004), 635-648.
A classification of -curves with complex multiplication
Let be the Hilbert class field of an imaginary quadratic field . An elliptic curve over with complex multiplication by is called a -curve if is isogenous over to all its Galois conjugates. We classify -curves over , relating them with the cohomology group . The structures of the abelian varieties over obtained from -curves by restriction of scalars are investigated.
J. Math. Soc. Japan, Volume 56, Number 2 (2004), 635-648.
First available in Project Euclid: 3 October 2007
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NAKAMURA, Tetsuo. A classification of $Q$ -curves with complex multiplication. J. Math. Soc. Japan 56 (2004), no. 2, 635--648. doi:10.2969/jmsj/1191418649. https://projecteuclid.org/euclid.jmsj/1191418649