Function: ellheight
Section: elliptic_curves
C-Name: ellheight0
Prototype: GGD2,L,p
Help: ellheight(E,x,{flag=2}): canonical height of point x on elliptic curve
 E (assumed to be a minimal model). flag is optional and selects the algorithm
 used to compute the Archimedean local height. Its meaning is 0: use
 theta-functions, 1: use Tate's method, 2: use Mestre's AGM.
Doc: global \idx{N\'eron-Tate height} of the point $z$ on the elliptic curve
 $E$ (defined over $\Q$), given by a standard minimal integral model. $E$
 must be an \kbd{ell} as output by \kbd{ellinit}. \fl selects the algorithm
 used to compute the Archimedean local height. If $\fl=0$, this computation
 is done using sigma and theta-functions and a trick due to J.~Silverman. If
 $\fl=1$, use Tate's $4^n$ algorithm. If $\fl=2$, use Mestre's AGM algorithm.
 The latter is much faster than the other two, both in theory (converges
 quadratically) and in practice.
Variant: Also available is \fun{GEN}{ghell}{GEN E, GEN x, long prec}
 ($\fl=2$).
