An algebraic curve over a Field is an equation , where is a Polynomial in and with Coefficients in . A nonsingular algebraic curve is an algebraic curve over which has no Singular Points over . A point on an algebraic curve is simply a solution of the equation of the curve. A -Rational Point is a point on the curve, where and are in the Field .

**References**

Griffiths, P. A. *Introduction to Algebraic Curves.* Providence, RI: Amer. Math. Soc., 1989.

© 1996-9

1999-05-25