![Open Access](https://i-scholar.in/lib/pkp/templates/images/icons/fulltextgreen.png)
![Restricted Access](https://i-scholar.in/lib/pkp/templates/images/icons/fulltextred.png)
![Open Access](https://i-scholar.in/lib/pkp/templates/images/icons/fulltextgreen.png)
![Open Access](https://i-scholar.in/lib/pkp/templates/images/icons/fulltext_open_medium.gif)
![Restricted Access](https://i-scholar.in/lib/pkp/templates/images/icons/fulltextred.png)
![Restricted Access](https://i-scholar.in/lib/pkp/templates/images/icons/fulltext_restricted_medium.gif)
Pell Surfaces and Elliptic Curves
Subscribe/Renew Journal
Let Em be the elliptic curve y2 = x3 − m, where m is a squarefree positive integer and −m ≡ 2, 3 (mod 4). Let Cl(K)[3] denote the 3-torsion subgroup of the ideal class group of the quadratic field K = Q( √ −m). Let S3 : y2 + mz2 = x3 be the Pell surface. We show that the collection of primitive integral points on S3 coming from the elliptic curve Em do not form a group with respect to the binary operation given by Hambleton and Lemmermeyer. We also show that there is a group homomorphism κ from rational points of Em to Cl(K)[3] using 3-descent on Em, whose kernel contains 3Em(Q). We also explain how our homomorphism κ, the homomorphism ψ of Hambleton and Lemmermeyer and the homomorphism φ of Soleng are related.
User
Subscription
Login to verify subscription
Font Size
Information
![](https://i-scholar.in/public/site/images/abstractview.png)
Abstract Views: 179
![](https://i-scholar.in/public/site/images/pdfview.png)
PDF Views: 0