L-series derivatives

["Tom Womack" <tom@womack.net>]

Is there any particular reason why computing L(s) for an elliptic curve is
an in-built command, whilst to compute L' you have to do something like

E = ellinit([0,0,0,0,32757])
N = ellglobalred(E)[1]
X = 2*Pi/sqrt(N)
VV = eint1(X,2^19)
WW = ellan(E,2^19)
sum(i=1,2^19,2*VV[i]*WW[i]/i)

and there's no obvious way of computing L^(r) for higher derivatives?

The L-series functions also seem to take an enormous amount of memory in the
case where the conductor is reasonably large; I understand that you have to
sum sqrt(N) or so terms of the series, but for the above case the conductor
is 10^11 and you can sum the 2^19 terms in well under two minutes on a
P3/500.

Do there exist algorithms which are a bit more memory-efficient, even at the
cost of perhaps taking a bit longer?

Tom