Title of article
On the rank of certain parametrized elliptic curves
Author/Authors
Hadavand, A. Department of mathematics - Arak Branch, Islamic Azad university
Pages
10
From page
13
To page
22
Abstract
In this paper the family of elliptic curves over Q given by the equation Ep : Y 2 = (X − p) 3 + X3 + (X + p) 3 where p is a prime number, is studied. It is shown that the maximal rank of the elliptic curves is at most 3 and some conditions under which we have rank(Ep(Q)) = 0 or rank(Ep(Q)) = 1 or rank(Ep(Q)) ≥ 2 are given.
Keywords
Elliptic Curve , Selmer Group
Journal title
نظريه تقريب و كاربردهاي آن
Serial Year
2015
Record number
2492983
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