(The two fibers over 0 are non-isomorphic elliptic curves, so the fibration "X" is certainly not isomorphic to the fibration "E"×C over all of C.)

Then the fibration "X" has a fiber of multiplicity 2 over 0, and otherwise looks like "E"×C.We say that "X" is obtained by applying a logarithmic transformation of order 2 to "E"×C with center 0.