We consider elliptic curves over global fields of positive characteristic with two distinct marked non-trivial rational points. Restricting to a certain subfamily of the universal one, we show that the average size of the 2-Selmer groups of these curves exists, in a natural sense, and equals 12. Along the way, we consider a map from these 2-Selmer groups to the moduli space of -torsors over an algebraic curve, where is isogenous to , and show that the images of 2-Selmer elements under this map become equidistributed in the limit.
Cite this article
Jack A. Thorne, On the Average Number of 2-Selmer Elements of Elliptic Curves over with Two Marked Points. Doc. Math. 24 (2019), pp. 1179–1223DOI 10.4171/DM/702