We systematically investigate the normal and superconducting properties of non-centrosymmetric ReZr using magnetization, heat capacity, and electrical resistivity measurements. Resistivity measurements indicate ReZr has poor metallic behavior and is dominated by disorder. ReZr undergoes a superconducting transition at $T_{} = \left(6.75\pm0.05\right)$ K. Magnetization measurements give a lower critical field, mT. The Werthamer-Helfand-Hohenberg model is used to approximate the upper critical field T which is close to the Pauli limiting field of 12.35 T and which could indicate singlet-triplet mixing. However, low-temperature specific-heat data suggest that ReZr is an isotropic, fully gapped s-wave superconductor with enhanced electron-phonon coupling. Unusual flux pinning resulting in a peak effect is observed in the magnetization data, indicating an unconventional vortex state.

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