Code
Caution: these procedures are supplied as-is: errors may occur, so if you find any, let me know!
I've created an eds class and supporting heights procedures: the full version of Shipsey's algorithm (and some examination of the input to best apply it) is used; beware that this can give division by zero errors in finite fields. These procedures allow for estimates of heights of points of elliptic curves defined over number fields, a feature currently lacking in PARI/GP (and hence SAGE). Documentation and discussion is available here and here. For an alternative algorithm, without the risk of division by zero, see below.
The generalisation of EDS to elliptic nets allows for computation of the Tate Pairing. For SAGE, the classes ellnet2d and ellnet1d, plus supporting procedures tate, are enough (save finding the order of a point) to jump straight in: here are some examples. These classes are essentially an implementation of Stange's algorithm, details of which are here.
Specific to pairing, a slightly quicker algorithm is described here. A faster implementation based on this is available as a replacement for ellnet2d.
ellnet1d is actually another eds class; so can be used for height estimates; there's some information about that.
Many tasks for manipulating groups of rational points can be described purely in terms of the group operations (rather than exploiting special properties of the group at hand). To save recreating these each time, I've created some Maple procedures, generic_group (Maple 9 version), for manipulating abstract groups. They currently support multiplication by m, the discrete logarithm problem and order determination: see this post.
ella implements the group law (addition and inversion) for an elliptic curve over the rationals or a (prime) finite field, designed for use with the generic group procedures described above. It also generates the assorted coefficients associated to a curve. There is some brief documentation.
jac implements the group law (addition and inversion) for the jacobian of a genus 2 hyperelliptic curve over a (prime) finite field, designed for use with the generic group procedures described above. Random point and divisor generation is also included. There is some brief documentation.