  Context: There are currently three pulsars firmly detected by imaging
atmospheric Cherenkov telescopes (IACTs), two of them reaching TeV energies,
challenging models of very-high-energy (VHE) emission in pulsars. More precise
observations are needed to better characterize pulsar emission at these
energies. The LST-1 is the prototype of the Large-Sized Telescope, that will be
part of the Cherenkov Telescope Array Observatory (CTAO). Its improved
performance over previous IACTs makes it well suited for studying pulsars.
Aims: To study the Crab pulsar emission with the LST-1, improving and
complementing the results from other telescopes. These observations can also be
used to characterize the potential of the LST-1 to study other pulsars and
detect new ones. Methods: We analyzed a total of $\sim$103 hours of gamma-ray
observations of the Crab pulsar conducted with the LST-1 in the period from
September 2020 to January 2023. The observations were carried out at zenith
angles less than 50 degrees. A new analysis of the Fermi-LAT data was also
performed, including $\sim$14 years of observations. Results: The Crab pulsar
phaseogram, long-term light-curve, and phase-resolved spectra are reconstructed
with the LST-1 from 20 GeV to 450 GeV for P1 and up to 700 GeV for P2. The
pulsed emission is detected with a significance of 15.2$\sigma$. The two
characteristic emission peaks of the Crab pulsar are clearly detected
(>10$\sigma$), as well as the so-called bridge emission (5.7$\sigma$). We find
that both peaks are well described by power laws, with spectral indices of
$\sim$3.44 and $\sim$3.03 respectively. The joint analysis of Fermi-LAT and
LST-1 data shows a good agreement between both instruments in the overlapping
energy range. The detailed results obtained in the first observations of the
Crab pulsar with LST-1 show the potential that CTAO will have to study this
type of sources.
