 This means that over a field formula_2 with charformula_41 every hyperelliptic curve of genus formula_5 is isomorphic to one given by an equation of the form formula_52 where formula_16 is a monic polynomial of degree formula_11 and the curve has no singular points.Note that for curves of this form it is easy to check whether the non-singularity criterion is met.A point formula_25 on the curve is singular if and only if formula_56 and formula_57.