[en] In this diploma thesis the elastic J/ψ vector meson photoproduction (ep→eJ/ψp) is studied in the decay channel J/ψ→e⁺e^- with the H1 detector at the electron proton collider HERA. The data from the runs of the year 2007 with an integrated luminosity of 62.4 pb^-1 are used. In this time HERA operated with tree different proton energies E_p called high (920 GeV), medium (575 GeV) and low (460 GeV) with integrated luminosities 45.5 (high), 5.96 (medium) and 10.9 pb^-1 (low). The kinematical region of vertical stroke t vertical stroke <1.2 GeV², where t is the four momentum transfer at the proton vertex, and Q_e²<1 GeV (photoproduction) is used. Further the range of the centre of mass energy in the photon proton rest frame, W_γp, is restricted to 40 GeV< W_γp<110 GeV (high), 20 GeV< W_γp<80 GeV (medium) and 20 GeV< W_γp<100 GeV (low). The differential cross section as a function of vertical stroke t vertical stroke is well described by an exponential, dσ /d vertical stroke t vertical stroke ∝ e^{-b₀verticalstroketverticalstroke}, which yields to b₀=4.4±0.2(stat.). The cross section as a function of W_γp is fitted by a power law, dσ/dW_γp∝W^δ_γp, and gives δ=0.66±0.07(stat.). (orig.)