Geodesic
A note on arithmetic progressions on elliptic curves
Journal of integer sequences, Tome 6 (2003) no. 1
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.
Classification : 11G05, 11B25
Keywords: elliptic curves, arithmetic progression 
@article{JIS_2003__6_1_a5,
     author = {Campbell,  Garikai},
     title = {A note on arithmetic progressions on elliptic curves},
     journal = {Journal of integer sequences},
     year = {2003},
     volume = {6},
     number = {1},
     zbl = {1022.11026},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2003__6_1_a5/}
}
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Campbell,  Garikai. A note on arithmetic progressions on elliptic curves. Journal of integer sequences, Tome 6 (2003) no. 1. http://geodesic.mathdoc.fr/item/JIS_2003__6_1_a5/