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A Note on Arithmetic Progressions on Elliptic Curves
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Garikai Campbell

Department of Mathematics and Statistics

Swarthmore College

Swarthmore, PA 19081

USA

**Abstract:**
Andrew Bremner
(*Experiment. Math.* **8** (1999), 409-413)
has described a technique for producing infinite
families of elliptic curves containing length 7 and length 8 arithmetic
progressions. This note describes another way to produce infinite families
of elliptic curves containing length 7 and length 8 arithmetic progressions. We
illustrate how the technique articulated here gives an easy way to produce an
elliptic curve containing a length 12 progression and an infinite family of
elliptic curves containing a length 9 progression, with the caveat that these
curves are not in Weierstrass form.

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Received February 5, 2003;
revised version received February 7, 2003.
Published in *Journal of Integer Sequences* February 25, 2003.

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