In this paper we show that the critical Eisenstein series of weight 2, E2critp, defines a smooth point in the eigen-curve C(l), where l is a prime different from p. We also show that E2critp,ordl defines a smooth point in the full eigencurve Cfull(l) and E2critp,ordl1,ordl2 defines a non-smooth point in the full eigencurve Cfull(l1l2). Further, we show that C(l) is étale over the weight space at the point defined by E2critp. As a consequence, we show that level lowering conjecture of Paulin fails to hold at E2critp,ordl. © Société Arithmétique de Bordeaux, 2015.