# 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

- 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.