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

### MAXIMAL RANKS AND INTEGER POINTS ON A FAMILY
OF ELLIPTIC CURVES

### P. G. Walsh

Department of Mathematics, University of Ottawa,
585 King Edward St., Ottawa, Ontario, K1N-6N5, Canada

*e-mail:* `gwalsh@uottawa.ca`

**Abstract.** We extend a result of Spearman which provides a sufficient condition
for elliptic curves of the form *y*^{2} = *x*^{3} - *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.

**Full text (PDF)** (free access)
DOI: 10.3336/gm.44.1.04

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MathSciNet
CrossRef

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