The Variety which is an invariant of degree four and is given by the equation
References
Burkhardt, H. ``Untersuchungen aus dem Gebiet der hyperelliptischen Modulfunctionen. II.'' Math. Ann. 38, 161-224, 1890.
Burkhardt, H. ``Untersuchungen aus dem Gebiet der hyperelliptischen Modulfunctionen. III.'' Math. Ann. 40, 313-343, 1892.
Hunt, B. ``The Burkhardt Quartic.'' Ch. 5 in The Geometry of Some Special Arithmetic Quotients.
New York: Springer-Verlag, pp. 168-221, 1996.