  Most of the currently known planets are small worlds with radii between that
of the Earth and that of Neptune. The characterization of planets in this
regime shows a large diversity in compositions and system architectures, with
distributions hinting at a multitude of formation and evolution scenarios.
Using photometry from the K2 satellite and radial velocities measured with the
HARPS and CORALIE spectrographs, we searched for planets around the bright and
slightly evolved Sun-like star HD 137496. We precisely estimated the stellar
parameters, $M_*$ = 1.035 +/- 0.022 $M_\odot$, $R_*$ = 1.587 +/- 0.028
$R_\odot$, $T_\text{eff}$ = 5799 +/- 61 K, together with the chemical
composition of the slightly evolved star. We detect two planets orbiting HD
137496. The inner planet, HD 137496 b, is a super-Mercury (an Earth-sized
planet with the density of Mercury) with a mass of $M_b$ = 4.04 +/- 0.55
$M_\oplus$, a radius of $R_b = 1.31_{-0.05}^{+0.06} R_\oplus,$ and a density of
$\rho_b = 10.49_{-1.82}^{+2.08}$ $\mathrm{g cm^{-3}}$. With an interior
modeling analysis, we find that the planet is composed mainly of iron, with the
core representing over 70% of the planet's mass ($M_{core}/M_{total} =
0.73^{+0.11}_{-0.12}$). The outer planet, HD 137496 c, is an eccentric ($e$ =
0.477 +/- 0.004), long period ($P$ = $479.9_{-1.1}^{+1.0}$ days) giant planet
($M_c\sin i_c$ = 7.66 +/- 0.11 $M_{Jup}$) for which we do not detect a transit.
HD 137496 b is one of the few super-Mercuries detected to date. The accurate
characterization reported here enhances its role as a key target to better
understand the formation and evolution of planetary systems. The detection of
an eccentric long period giant companion also reinforces the link between the
presence of small transiting inner planets and long period gas giants.
