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The Selmer groups and the ambiguous ideal class groups of cubic fields
Published online by Cambridge University Press: 17 April 2009
Abstract
In this paper, we study a family of elliptic curves with CM by which also admits a ℚ-rational isogeny of degree 3. We find a relation between the Selmer groups of the elliptic curves and the ambiguous ideal class groups of certain cubic fields. We also find some bounds for the dimension of the 3-Selmer group over ℚ, whose upper bound is also an upper bound of the rank of the elliptic curve.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 54 , Issue 2 , October 1996 , pp. 267 - 274
- Copyright
- Copyright © Australian Mathematical Society 1996
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