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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| creator | DeLong, Matt |
| description | 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. |
| doi_str_mv | 10.48550/arxiv.math/9906068 |
| format | Article |
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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
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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
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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.</abstract><doi>10.48550/arxiv.math/9906068</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Number Theory |
| title | A formula for the Selmer group of a rational three-isogeny |
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