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https://gnanaganga.inflibnet.ac.in:8443/jspui/handle/123456789/6321
Title: | Pell Surfaces and Elliptic Curves |
Authors: | K. J. Manasa B. R. Shankar |
Issue Date: | 2016 |
Publisher: | Journal of the Ramanujan Mathematical Society |
Abstract: | Let Em be the elliptic curve y2 = x3 a�� m, where m is a squarefree positive integer and a��m a�� 2, 3 (mod 4). Let Cl(K)[3] denote the 3-torsion subgroup of the ideal class group of the quadratic field K = Q( a�� a��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. |
URI: | http://gnanaganga.inflibnet.ac.in:8080/jspui/handle/123456789/6321 |
Appears in Collections: | Articles to be qced |
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