Geodesic
Combinatorial Aspects of Elliptic Curves
Séminaire lotharingien de combinatoire, Tome 56 (2006-2007) Cet article a éte moissonné depuis la source Séminaire Lotharingien de Combinatoire website

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Given an elliptic curve C, we study here Nk = #C(Fqk), the number of points of C over the finite field Fqk. This sequence of numbers, as k runs over positive integers, has numerous remarkable properties of a combinatorial flavor in addition to the usual number theoretical interpretations. In particular, we prove that Nk = -Wk(q,-N1), where Wk(q,t) is a (q,t)-analogue of the number of spanning trees of the wheel graph. Additionally we develop a determinantal formula for Nk, where the eigenvalues can be explicitly written in terms of q, N1, and roots of unity. We also discuss here a new sequence of bivariate polynomials related to the factorization of Nk, which we refer to as elliptic cyclotomic polynomials because of their various properties. 

@article{SLC_2006-2007_56_a5,
     author = {Gregg Musiker},
     title = {Combinatorial {Aspects} of {Elliptic} {Curves}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2006-2007},
     volume = {56},
     url = {http://geodesic.mathdoc.fr/item/SLC_2006-2007_56_a5/}
}
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JO  - Séminaire lotharingien de combinatoire
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VL  - 56
UR  - http://geodesic.mathdoc.fr/item/SLC_2006-2007_56_a5/
ID  - SLC_2006-2007_56_a5
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%D 2006-2007
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%U http://geodesic.mathdoc.fr/item/SLC_2006-2007_56_a5/
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Gregg Musiker. Combinatorial Aspects of Elliptic Curves. Séminaire lotharingien de combinatoire, Tome 56 (2006-2007). http://geodesic.mathdoc.fr/item/SLC_2006-2007_56_a5/