Glasnik Matematicki, Vol. 44, No.1 (2009), 83-87.

MAXIMAL RANKS AND INTEGER POINTS ON A FAMILY OF ELLIPTIC CURVES

P. G. Walsh

Abstract.   We extend a result of Spearman which provides a sufficient condition for elliptic curves of the form y² = x³ - px, with p a prime, to have Mordell-Weil rank 2. As in Spearman's work, the condition given here involves the existence of integer points on these curves.

2000 Mathematics Subject Classification.   11G05.

Key words and phrases.   Elliptic curve, prime number.

DOI: 10.3336/gm.44.1.04

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