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On families of elliptic curves E_(p,q):y²=x³-pqx that intersect the same line L_(a,b):y=a/bx of rational slope
Eldar Sultanow, Anja Jeschke, Amir Darwish Tfiha, Madjid Tehrani, William J Buchanan
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Let p and q be two distinct odd primes, p<q and E_(p,q):y²=x³-pqx be an elliptic curve. Fix a line L_(a.b):y=a/bx where a∈ℤ,b∈ℕ and (a,b)=1. We study sufficient conditions that p and q must satisfy so that there are infinitely many elliptic curves E_(p,q) that intersect L_(a,b).
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