Geodesic
A note on arithmetic progressions on quartic elliptic curves
Journal of integer sequences, Tome 8 (2005) no. 3
G. Campbell described a technique for producing infinite families of quartic elliptic curves containing a length-9 arithmetic progression. He also gave an example of a quartic elliptic curve containing a length-12 arithmetic progression. In this note we give a construction of an infinite family of quartics on which there is an arithmetic progression of length 10. Then we show that there exists an infinite family of quartics containing a sequence of length 12. Full version: pdf, dvi, ps, latex
Classification : 11G05, 11B25
Keywords: elliptic curves, arithmetic progression 
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     author = {Ulas,  Maciej},
     title = {A note on arithmetic progressions on quartic elliptic curves},
     journal = {Journal of integer sequences},
     year = {2005},
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     number = {3},
     zbl = {1068.11039},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2005__8_3_a6/}
}
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Ulas,  Maciej. A note on arithmetic progressions on quartic elliptic curves. Journal of integer sequences, Tome 8 (2005) no. 3. http://geodesic.mathdoc.fr/item/JIS_2005__8_3_a6/