On Symmetries of Elliptic Nets and Valuations of Net Polynomials
  Under certain conditions, we prove that the set of zeros of an elliptic net forms an Abelian group. We present two applications of this fact. Firstly we give a generalization of a theorem of Ayad on valuations of division polynomials in the context of net polynomials. Secondly we generalize a theorem of Ward on symmetry of elliptic divisibility sequences to the case of elliptic nets. 
Amir Akbary, Jeff Bleaney, and Soroosh Yazdani
math.NT