The primary frequency and time standard, defined via a transition frequency of caesium-133, is realized by microwave clocks reaching relative uncertainties in the 10−^16 level. This performance has been surpassed by state-of-the-art lattice clocks, with transition frequencies in the optical regime, leading to two orders of magnitude lower uncertainties. The key to this performance is the confinement in the Lamb-Dicke regime at the magic wavelength enabling a Doppler- and recoil-free spectroscopy with a first-order suppressed AC Stark shift. In atomic clocks, several effects contribute to the uncertainty of the transition frequency. Through continuous global characterization efforts, the individual uncertainty of these effects have been subsequently reduced. Yet one effect, namely the frequency shift induced by blackbody radiation has been identified as a dominant contribution which is difficult to overcome by technical means. In this regard, magnesium-24 excels as a species of choice as its blackbody radiation sensitivity is one order of magnitude lower than in the most frequently used atomic clock species. Furthermore, magnesium offers a relatively simple electronic structure which enables theoretical support through high-precision calculations. This thesis features the first characterization of a magnesium optical lattice clock operating at the magic wavelength. The characterization of the magnesium frequency standard presented in this thesis depends essentially on the resolution of the transition linewidth, which could be reduced from kHz range to 51(3) Hz in a complementing work. The realization of a transition linewidth with a quality factor of Q = 1.3 × 10^13 has contributed to an improved determination of the magic wavelength within this thesis to 468.4106(2) nm. Compared to earlier work, this represents an improvement of two orders of magnitude. Furthermore, the lower transition linewidth also allowed the first observation of the probe AC Stark shift and thus the first characterization of effects in the lattice that falsify the frequency of the trapped magnesium atoms. Overall, the relative uncertainty of the frequency-related effects influencing the clock transition could be determined to be 7.1 × 10^−15. The dominant contributions can be assigned to tunneling broadening and the lattice and probe AC Stark effects, induced by the probe and lattice light. All these effects can be traced back to technical limitations and are part of future work. Following the characterization, a first frequency comparison between the magnesium lattice clock against the primary frequency standard as well as the ytterbium ion clock at the PTB has been performed and thus a first realization of a lattice based frequency standard with magnesium atoms was demonstrated. The determined transition frequency of 655 058 646 681 864.1(5.3) Hz complies with former measurements. The primary frequency and time standard, defined via a transition frequency of caesium-133, is realized by microwave clocks reaching relative uncertainties in the 10^−16 level. This performance has been surpassed by state-of-the-art lattice clocks, with transition frequencies in the optical regime, leading to two orders of magnitude lower uncertainties. The key to this performance is the confinement in the Lamb-Dicke regime at the magic wavelength enabling a Doppler- and recoil-free spectroscopy with a first-order suppressed AC Stark shift. In atomic clocks, several effects contribute to the uncertainty of the transition frequency. Through continuous global characterization efforts, the individual uncertainty of these effects have been subsequently reduced. Yet one effect, namely the frequency shift induced by blackbody radiation has been identified as a dominant contribution which is difficult to overcome by technical means. In this regard, magnesium-24 excels as a species of choice as its blackbody radiation sensitivity is one order of magnitude lower than in the most frequently used atomic clock species. Furthermore, magnesium offers a relatively simple electronic structure which enables theoretical support through high-precision calculations. This thesis features the first characterization of a magnesium optical lattice clock operating at the magic wavelength. The characterization of the magnesium frequency standard presented in this thesis depends essentially on the resolution of the transition linewidth, which could be reduced from kHz range to 51(3) Hz in a complementing work. The realization of a transition linewidth with a quality factor of Q = 1.3 × 10^13 has contributed to an improved determination of the magic wavelength within this thesis to 468.4106(2) nm. Compared to earlier work, this represents an improvement of two orders of magnitude. Furthermore, the lower transition linewidth also allowed the first observation of the probe AC Stark shift and thus the first characterization of effects in the lattice that falsify the frequency of the trapped magnesium atoms. Overall, the relative uncertainty of the frequency-related effects influencing the clock transition could be determined to be 7.1 × 10^−15. The dominant contributions can be assigned to tunneling broadening and the lattice and probe AC Stark effects, induced by the probe and lattice light. All these effects can be traced back to technical limitations and are part of future work. Following the characterization, a first frequency comparison between the magnesium lattice clock against the primary frequency standard as well as the ytterbium ion clock at the PTB has been performed and thus a first realization of a lattice based frequency standard with magnesium atoms was demonstrated. The determined transition frequency of 655 058 646 681 864.1(5.3) Hz complies with former measurements.