Elliptic Curve

Get doctest coverage up to 100%

Period Lattice

• Make it so precision can be specified (in bits)
• Make an abstract "period lattice" class

Implement Tate's algorithm over number fields

• This means porting Cremona's code. David Roe started on this.
• This will give computation of conductors over number fields.

Compute the Neron-Tate canonical height of points on elliptic curves over number fields

• Start with David Kohel and Martin Giraud: package/Geometry/CrvEll/anf_height.m

Reorganize and refactor the ell_rational_field file

1. separate out all the L-series commands into an L-series class, e.g., like padic_lseries right now.

Compute E(F_q) and/or #E(F_q)

• Implement smart baby step-giant step (Albrecht, Sutherland)

Compute with L-series of elliptic curves over number fields

• Use Dokchitser to compute L-function

Sympow improvement

• Improve Sage wrapper (a lot)
• In particular, should autogenerate the needed data files.