Burkhardt Quartic

The Variety which is an invariant of degree four and is given by the equation

$$y_0^4-y_0(y_1^3+y_2^3+y_3^3+y_4^3)+3y_1y_2y_3y_4=0.$$

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.