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ELLIPTIC CUBIC

Cartesian equation:
with
.
Cartesian parametrization: where is the associated Weierstrass function (cf [Eymard Lafond] p. 220). |

An elliptic cubic is a cubic without singularities.

Any elliptic cubic is projectively equivalent to a divergent parabola, whose equation is given above, or to a Chasles cubic, or a cubic hyperbola.

Examples: the non-rational circular cubics, the Lamé cubic, the Humbert cubic.

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© Robert FERRÉOL 2017