  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.
