High-precision measurements are made of Z boson production in proton-antiproton collisions at √s = 1.96 TeV recorded by the Collider Detector at Fermilab, using the electron decay channel. The cross-section times branching ratio is measured to be ?Z · Br(Z → e+e-) = (255.7 ± 2.4stat ± 5.2sys ± 15.2lum)pb in a dataset of 194 pb-1 collected between March 2002 and June 2003. This agrees well with theoretical predictions. The cross-section for W boson production in the electron channel has also been measured in the subset of this dataset of 72 pb-1 collected up until January 2003. Using this smaller dataset the ratio of cross-sections is determined to be R ≡ ?W · Br(W → e?)/?Z · Br(Z → ee) = 10.82 ± 0.18stat ± 0.16sys. Combining these results with measurements made in the muon channel gives R = 10.92 ± 0.15stat ± 0.14sys (e + ? channels), from which the branching ratio of the W to electrons and muons, and the total width of the W, have been extracted: Br(W → l?) = 0.1089 ± 0.0022 (l = e,?); ?(W) = 2078.8 ± 41.4 MeV, which are in good agreement with the Standard Model values and with other measurements. The CKM quark mixing matrix element.