  The hadronic leading-order (hlo) contribution to the lepton anomalous
magnetic moments $a_l^\mathrm{hlo}$ of the Standard Model leptons still
accounts for the dominant source of the uncertainty of the Standard Model
estimates. We present the results of an investigation of the hadronic leading
order anomalous magnetic moments of the electron, muon and tau lepton from
first principles in twisted mass lattice QCD. With lattice data for multiple
pion masses in the range $230 \mathrm{~MeV} \lesssim m_{PS} \lesssim 490
\mathrm{~MeV}$, multiple lattice volumes and three lattice spacings we perform
the extrapolation to the continuum and to the physical pion mass and check for
all systematic uncertainties in the lattice calculation. As a result we
calculate $a_{l}^\mathrm{hlo}$ for the three Standard Model leptons with
controlled statistical and systematic error in agreement with phenomenological
determinations using dispersion relations and experimental data. In addition,
we also give a first estimate of the hadronic leading order anomalous magnetic
moments from simulations directly at the physical value of the pion mass.
