We use deep VLT optical and near-IR spectroscopy and deep Spitzer/IRAC imaging to examine the properties of two of the most luminous Ly \alpha emitters at z = 5.7 . The continuum red-ward of the Ly \alpha line is clearly detected in both objects , thus facilitating a relatively accurate measurement ( 10–20 % uncertainties ) of the observed rest-frame equivalent widths , which are around 160 \mathrm { \AA } for both objects . Through detailed modelling of the profile of the Ly \alpha line with a 3-D Monte-Carlo radiative transfer code , we estimate the intrinsic rest-frame equivalent width of Ly \alpha and find values that are around 300 \mathrm { \AA } , which is at the upper end of the range allowed for very young , moderately metal-poor star-forming galaxies . However , the uncertainties are large and values as high as 700 \mathrm { \AA } are permitted by the data . Both Ly \alpha emitters are detected at 3.6 \mu m in deep images taken with the Spitzer Space Telescope . We use these measurements , the measurement of the continuum red-ward of Ly \alpha and other photometry to constrain the spectral energy distributions of these very luminous Ly \alpha emitters and to compare them to three similar Ly \alpha emitters from the literature . The contribution from nebular emission is included in our models : excluding it results in significantly higher masses . Four of the five Ly \alpha emitters have masses of the order of \sim 10 ^ { 9 } M _ { \odot } Â and fairly high specific star-formation rates ( \ga 10–100 Gyr ^ { -1 } ) . While our two Ly \alpha emitters appear similar in terms of the observed Ly \alpha rest-frame equivalent width , they are quite distinct from each other in terms of age , mass and star formation history . Evidence for dust is found in all objects , and emission from nebular lines often make a dominant contribution to the rest frame 3.6 \mu m flux . Rich in emission lines , these objects are prime targets for the next generation of extremely large telescopes , JWST and ALMA .