Open AccessOn the Equation y 2 = x 3 - p q x
Author(s) -
Iftikhar Ahamath Burhanuddin,
Ming-Deh A. Huang
Publication year - 2014
Publication title -
journal of numbers
Language(s) - English
Resource type - Journals
eISSN - 2356-7511
pISSN - 2314-842X
DOI - 10.1155/2014/825634
Subject(s) - conjecture , quartic function , elliptic curve , mathematics , rank (graph theory) , combinatorics , algorithm , pure mathematics
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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