Introduction

This online help node and the nodes below it describe rational curves (those of type CrvRat) and the specialised category of conic curves (those of type CrvCon). Curves whose genus is zero, rational curves, can be parametrised when defined over a field but only once a point defined over that field is known. Conic curves may be defined over any ring. However, if a solution to the conic is sought then the conic must be defined over the integers or the rationals, or it must be the case that the coefficients of the defining polynomial coerce into the rationals.