On the Elliptic Curves of the Form $y^2 = x^3 − pqx$
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Abstract:
By the Mordell- Weil theorem, the group of rational points on an elliptic curve over a number field is a finitely generated abelian group. This paper studies the rank of the family Epq:y2=x3-pqx of elliptic curves, where p and q are distinct primes. We give infinite families of elliptic curves of the form y2=x3-pqx with rank two, three and four, assuming a conjecture of Schinzel and Sierpinski is true.
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Journal title
volume 10 issue None
pages 77- 86
publication date 2015-10
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