On fields of definition of torsion points of elliptic curves with complex multiplication

Details On fields of definition of torsion points of elliptic curves with complex multiplication On fields of definition of torsion points of elliptic curves with complex multiplication

2009-09-09

arxiv.org/abs/0909.1661v2

Proceeding of the American Mathematical Society 139, no. 6, 1961-1969 (2011)

Mathematics

Number Theory

To appear in Proceeding of the American Mathematical Society

Scientific paper

10.1090/S0002-9939-2010-10621-4

For any elliptic curve E defined over the rationals with complex multiplication and for every prime p, we describe the image of the mod p Galois representation attached to E. We deduce information about the field of definition of torsion points of these curves, in particular we classify all cases where there are torsion points over Galois number fields not containing the field of definition of the CM.

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