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Let n : X -> C be an elliptic surface defined over a number field k . We consider the field K in which all the sections are defined. Assuming that thê '-invariant is nonconstant, K is again a number field. We describe the primes of possible ramification of the extension K/k in terms of the configuration of the points of bad fibers in C . Aside from few possible exceptions, K/k is unramified outside of the primes of bad reduction of C and the primes p for which two or more points of bad fibersdoi:10.1090/s0002-9939-1992-1116264-0 fatcat:qryvybtz3vaijbk6442ohayzaa