Counting Multisections in Conic Bundles over a Curve defined over F_q
  For a given conic bundle X over a curve C defined over F_q, we count irreducible branch covers of C in X of degree d and height e>>1. As a special case, we get the number of algebraic numbers of degree d and height e over the function field F_q (C). 
Seyfi Turkelli