  Let p be a rational prime and N a positive integer which is prime to p. Let W
be the p-adic weight space for GL_{2,Q}. Let C_N be the p-adic Coleman-Mazur
eigencurve of tame level N. In this paper, we prove that any irreducible
component of C_N which is of finite degree over W is in fact finite over W.
  Combined with an argument of Chenevier and a conjecture of
Coleman-Mazur-Buzzard-Kilford (which has been proven in special cases, and for
general quaternionic eigencurves) this shows that the only finite degree
components of the eigencurve are the ordinary components.
