FAMILY OF ELLIPTIC CURVES E(p,q)‎: ‎y2=x2-p2x+q2

Mehrdad Khazali, Hassan Daghigh

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In this paper we show that for any two primes p and q greater than 5, the
elliptic curve E(p,q) : y2 = x3 − p2x + q2 has rank at least 2. We will also provide two
independent points on E(p,q). Then we will show that, conjecturally, the family {E(p,q)}
contains an infinite subfamily of rank three elliptic curves.

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