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Elliptic Curves [HB 91]
Removals and Changes:
- Elliptic curves can now be created from general schemes instead of only
hyperelliptic curves.
Similarly, elliptic curves can now be created from a general scheme and a
point rather than a curve and a point.
Only one map is returned in each case but it is birational.
- Redesigned routines to put a curve of genus 1 into Weierstrass form. Many
commonly occurring cases are recognised and handled more efficiently.
The system will automatically choose the most appropriate method.
- Elliptic curves may now be created by specifying the polynomials,
similar to the hyperelliptic case. To resolve a naming conflict
the former intrinsic EllipticCurve(j) has been changed to
EllipticCurveFromjInvariant(j).
New features:
- Elliptic curves can be created from a curve of genus 1 and a place
of degree 1.
- HyperellipticPolynomials of an elliptic curve can be retrieved
as for hyperelliptic curves.
- Elliptic curves can be created from the corresponding hyperelliptic
polynomials.
- The DualIsogeny of an isogeny of an elliptic curve can be obtained
as well as the TwoIsogeny of a point of an elliptic curve.
Subsections
Next: Elliptic Curves over the
Up: Algebraic Geometry
Previous: Function Fields and Divisors