A formula for the Selmer group of a rational three-isogeny
A formula is given for the dimension of the Selmer group of the rational three-isogeny of elliptic curves of the form y^2=x^3+a(x-b)^2. The formula is in terms of the three-ranks of the quadratic number fields Q(\sqrt{a}) and Q(\sqrt{-3a}) and various aspects of the arithmetic of these number fields...
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| Format: | Artikel |
| Sprache: | eng |
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| Zusammenfassung: | A formula is given for the dimension of the Selmer group of the rational
three-isogeny of elliptic curves of the form y^2=x^3+a(x-b)^2. The formula is
in terms of the three-ranks of the quadratic number fields Q(\sqrt{a}) and
Q(\sqrt{-3a}) and various aspects of the arithmetic of these number fields. In
addition a duality theorem is used to relate the dimension of the Selmer group
of the three-isogeny with the dimension of the Selmer group of its dual
isogeny. |
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| DOI: | 10.48550/arxiv.math/9906068 |