We announce the discovery of the transiting planet CoRoT-13b. Ground based follow-up in CFHT and IAC80 confirmed CoRoTs observations. The mass of the planet was measured with the HARPS spectrograph and the properties of the host star were obtained analyzing HIRES spectra from the Keck telescope. It is a hot Jupiter-like planet with an orbital period of 4.04 days, 1.3 Jupiter masses, 0.9 Jupiter radii, and a density of 2.34 g cm-3. It orbits a G0V star with Teff=5945K, M*=1.09 Msun, R*=1.01 Rsun, solar metallicity, a lithium content of +1.45 dex, and an estimated age between 0.12 and 3.15 Gyr. The lithium abundance of the star is consistent with its effective temperature, activity level, and age range derived from the stellar analysis. The density of the planet is extreme for its mass. It implies the existence of an amount of heavy elements with a mass between about 140 and 300 Mearth.
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