Invariant theory for the elliptic normal quintic, I. Twists of X(5). Fisher, T. Math. Ann., 356(2):589–616, 2013.
Invariant theory for the elliptic normal quintic, I. Twists of X(5) [link]Paper  doi  bibtex   
@Article{	  fis:13,
  author	= {Fisher, Tom},
  title		= {Invariant theory for the elliptic normal quintic, {I}.
		  {T}wists of {X}(5)},
  journal	= {Math. Ann.},
  fjournal	= {Mathematische Annalen},
  volume	= {356},
  year		= {2013},
  number	= {2},
  pages		= {589--616},
  issn		= {0025-5831},
  doi		= {10.1007/s00208-012-0850-9},
  url		= {http://dx.doi.org/10.1007/s00208-012-0850-9}
}
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