  Ultra-short period planets have orbital periods of less than one day. Since
their masses and radii can be determined to a higher precision than long-period
planets, they are the preferred targets to determine the density of planets
which constrains their composition. The K2-106 system is particularly
interesting because it contains two planets of nearly identical masses. One is
a high density USP, the other is a low-density planet that has an orbital
period of 13 days. Combining the Gaia DR3 results with new ESPRESSO data allows
us to determine the masses and radii of the two planets more precisely than
before. We find that the USP K2-106b has a density consistent with an
Earth-like composition, and K2-106c is a low-density planet that presumably has
an extended atmosphere. We measure a radius of Rp=1.676-0.037+0.037 REarth, a
mass of Mp=7.80-0.70+0.71 MEarth and a density of rho=9.09-0.98+0.98 gcm-3 for
K2-106b. For K2-106c, we derive Rp=2.84-0.08+0.10 REarth, Mp=7.3-2.4+2.5
MEarth, and a density of rho= 1.72-0.58+0.66 gcm-3. We finally discuss the
possible structures of the two planets with respect to other low-mass planets.
