On the rank of certain parametrized elliptic curves

محورهای موضوعی : Applied Mathematics

Ali Hadavand ¹

1 - aDepartment of mathematics, Arak Branch, Islamic Azad university, Arak, Iran.

تاریخ دریافت : 1395/06/03 تاریخ پذیرش : 1394/05/23 تاریخ انتشار : 1395/09/11

کلید واژه: Elliptic Curve, Selmer Group,

چکیده مقاله :

In this paper the family of elliptic curves over Q given by the equation Ep :Y2 = (X - p)3 + X3 + (X + p)3 where p is a prime number, is studied. Itis shown that the maximal rank of the elliptic curves is at most 3 and someconditions under which we have rank(Ep(Q)) = 0 or rank(Ep(Q)) = 1 orrank(Ep(Q))≥2 are given.

چکیده انگلیسی:

In this paper the family of elliptic curves over Q given by the equation Ep :Y2 = (X - p)3 + X3 + (X + p)3 where p is a prime number, is studied. Itis shown that the maximal rank of the elliptic curves is at most 3 and someconditions under which we have rank(Ep(Q)) = 0 or rank(Ep(Q)) = 1 orrank(Ep(Q))≥2 are given.

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