Zero group velocity modes can be utilized in many applications in both optics and acoustics. There exists numerous realizations of metamaterials with ZGVs at higher dispersion branches. However, to engineer the lowest dispersion branch to retain ZGVs, non-local metamaterials with couplings beyond the nearest neighbor are usually at play (i.e., roton like dispersion). To date, there exists no realization of roton-like dispersion for the lowest branch without non-local couplings. Non-locality, while rich in dynamics, can render designs rather complex. Here, we provide the first experimental evidence of a ZGV point for the lowest dispersion branch within the first Brillouin zone with local interactions. We utilize nonlinear magnetic lattices as a platform to sculpt our dispersion. Our findings might enable the realization of exotic metamaterials with simple designs.