On the rank of certain parametrized elliptic curves

الموضوعات :

Ali Hadavand ¹

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

تاريخ الإرسال : 21 الأربعاء , ذو القعدة, 1437 تاريخ التأكيد : 29 الجمعة , شوال, 1436 تاريخ الإصدار : 02 الخميس , ربيع الأول, 1438

الکلمات المفتاحية: Elliptic Curve, Selmer Group,

ملخص المقالة :

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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