On the equation \(y^2 = x^3 - pqx\) (Q2337582)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the equation \(y^2 = x^3 - pqx\) |
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On the equation \(y^2 = x^3 - pqx\) (English)
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20 November 2019
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Summary: We consider certain quartic twists of an elliptic curve. We establish the rank of these curves under the Birch and Swinnerton-Dyer conjecture and obtain bounds on the size of Shafarevich-Tate group of these curves. We also establish a reduction between the problem of factoring integers of a certain form and the problem of computing rational points on these twists.
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quartic twists of elliptic curve
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rank
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Birch--Swinnerton-Dyer conjecture
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bounds on size of Shafarevich-Tate group
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