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We present a ground-based near-infrared search for lensed supernovae behindthe massive cluster Abell 1689 at z=0.18, one of the most powerfulgravitational telescopes that nature provides. Our survey was based onmulti-epoch $J$-band observations with the HAWK-I instrument on VLT, withsupporting optical data from the Nordic Optical Telescope. Our search resultedin the discovery of five high-redshift, $0.671<z<1.703$, photometricallyclassified core-collapse supernovae with magnifications in the range $\Delta m$= $-0.31$ to $-1.58$ mag, as calculated from lensing models in the literature.Thanks to the power of the lensing cluster, the survey had the sensitivity todetect supernovae up to very high-redshifts, $z$$\sim$$3$, albeit for a limitedregion of space. We present a study of the core-collapse supernova rates for$0.4\leq z< 2.9$, and find good agreement with both previous estimates, and thepredictions from the star formation history. During our survey, we alsodiscovered 2 type Ia supernovae in A1689 cluster members, which allowed us todetermine the cluster Ia rate to be $0.14^{+0.19}_{-0.09}\pm0.01$$\rm{SNuB}$$\,h^2$ (SNuB$\equiv 10^{-12} \,\rm{SNe} \, L^{-1}_{\odot,B}yr^{-1}$). The cluster rate normalized by the stellar mass is$0.10^{+0.13}_{-0.06}\pm0.02$ in $\rm SNuM$$\,h^2$ (SNuM$\equiv 10^{-12}\,\rm{SNe} \, M^{-1}_{\odot} yr^{-1}$). Furthermore, we explore the optimalfuture survey for improving the core-collapse supernova rate measurements at$z\gtrsim2$ using gravitational telescopes, as well as for the detections withmultiply lensed images, and find that the planned WFIRST space mission hasexcellent prospects. Massive clusters can be used as gravitational telescopesto significantly expand the survey range of supernova searches, with importantimplications for the study of the high-$z$ transient universe.

High-redshift supernova rates measured with the gravitational telescope A1689