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FAMILY OF ELLIPTIC CURVES <em>E<sup></em>(<em>p</em>,<em>q</em>)</sup>: <em>y</em><sup>2</sup>=<em>x</em><sup>2</sup>-<em>p</em><sup>2</sup><em>x</em>+<em>q</em><sup>2</sup>
In this paper we show that for any two primes p and q greater than 5, theelliptic curve E(p,q) : y2 = x3 − p2x + q2 has rank at least 2. We will also provide twoindependent points on E(p,q). Then we will show that, conjecturally, the family {E(p,q)}contains an …