We analyze the properties of a multiply-imaged Lyman-alpha (Lya) emitter at z=5.75 identified through SHARDS Frontier Fields intermediate-band imaging of the Hubble Frontier Fields (HFF) cluster Abell 370. The source, A370-L57, has low intrinsic luminosity (M_UV~-16.5), steep UV spectral index (beta=-2.4+/-0.1), and extreme rest-frame equivalent width of Lya (EW(Lya)=420+180-120 AA). Two different gravitational lens models predict high magnification (mu~10--16) for the two detected counter-images, separated by 7, while a predicted third counter-image (mu~3--4) is undetected. We find differences of ~50% in magnification between the two lens models, quantifying our current systematic uncertainties. Integral field spectroscopy of A370-L57 with MUSE shows a narrow (FWHM=204+/-10 km/s) and asymmetric Lya profile with an integrated luminosity L(Lya)~10^42 erg/s. The morphology in the HST bands comprises a compact clump (r_e<100 pc) that dominates the Lya and continuum emission and several fainter clumps at projected distances <1 kpc that coincide with an extension of the Lya emission in the SHARDS F823W17 and MUSE observations. The latter could be part of the same galaxy or an interacting companion. We find no evidence of contribution from AGN to the Lya emission. Fitting of the spectral energy distribution with stellar population models favors a very young (t<10 Myr), low mass (M*~10^6.5 Msun), and metal poor (Z<4x10^-3) stellar population. Its modest star formation rate (SFR~1.0 Msun/yr) implies high specific SFR (sSFR~2.5x10^-7 yr^-1) and SFR density (Sigma_SFR ~ 7-35 Msun/yr/kpc^2). The properties of A370-L57 make it a good representative of the population of galaxies responsible for cosmic reionization.
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