  In the hydrodynamic framework of heavy-ion collisions, elliptic flow, $v_2$,
is sensitive to the quadrupole deformation, $\beta$, of the colliding ions.
This enables one to test whether the established knowledge on the low-energy
structure of nuclei is consistent with collider data from high-energy
experiments. We derive a formula based on generic scaling laws of hydrodynamics
to relate the difference in $v_2$ measured between collision systems that are
close in size to the value of $\beta$ of the respective species. We validate
our formula in simulations of 238U+238U and 197Au+197Au collisions at top
Relativistic Heavy Ion Collider (RHIC) energy, and subsequently apply it to
experimental data. Using the deformation of 238U from low-energy experiments,
we find that RHIC $v_2$ data implies $0.16 \lesssim |\beta| \lesssim 0.20$ for
197Au nuclei, i.e., significantly more deformed than reported in the
literature, posing an interesting puzzle in nuclear phenomenology.
