Context :

Aims : We present a study of the very high energy ( VHE ; E > 100 GeV ) \gamma -ray emission of the blazar PKS 1424+240 observed with the MAGIC telescopes .
The primary aim of this paper is the multiwavelength spectral characterization and modeling of this blazar , which is made particularly interesting by the recent discovery of a lower limit of its redshift of z \geq 0.6 and makes it a promising candidate to be the most distant VHE source .

Methods : The source has been observed with the MAGIC telescopes in VHE \gamma rays for a total observation time of \sim 33.6 h from 2009 to 2011 .
A detailed analysis of its \gamma -ray spectrum and time evolution has been carried out .
Moreover , we have collected and analyzed simultaneous and quasi-simultaneous multiwavelength data .

Results : The source was marginally detected in VHE \gamma rays during 2009 and 2010 , and later , the detection was confirmed during an optical outburst in 2011 .
The combined significance of the stacked sample is \sim 7.2 \sigma .
The differential spectra measured during the different campaigns can be described by steep power laws with the indices ranging from 3.5 \pm 1.2 to 5.0 \pm 1.7 .
The MAGIC spectra corrected for the absorption due to the extragalactic background light connect smoothly , within systematic errors , with the mean spectrum in 2009-2011 observed at lower energies by the Fermi -LAT .
The absorption-corrected MAGIC spectrum is flat with no apparent turn down up to 400 GeV .
The multiwavelength light curve shows increasing flux in radio and optical bands that could point to a common origin from the same region of the jet .
The large separation between the two peaks of the constructed non-simultaneous spectral energy distribution also requires an extremely high Doppler factor if an one zone synchrotron self-Compton model is applied .
We find that a two-component synchrotron self-Compton model describes the spectral energy distribution of the source well , if the source is located at z \sim 0.6 .

Conclusions :