Cyclicity of elliptic curves over function fields
Karabina, Koray (2005) Cyclicity of elliptic curves over function fields. [Thesis]
Let K be a global function field over a finite field F containing q elements. Let E be an elliptic curve defined over K. For a prime P in K we can reduce the elliptic curve mod P and get an elliptic curve over a finite extension of F. The group of points on the reduced elliptic curve is either a cyclic group or it is a product of two cyclic groups. We determine the Dirichlet density of the primes in K such that the reduced curve has a cyclic group structure.
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