Derivation in finite fields

[Benedikt Berghammer <benedikt.berghammer@unibw.de>]

Hi all,

I'm new in working with PARI and have the following problem. I'm working 
on a script for computing the Weil-Pairing over finite fields after 
Miller's algorithm.

In one step I need to get the line tangent to an Elliptic Curve E at a 
point P. For computing the gradient of this tangent I need to compute 
the derivation of the square root.

For example I have the Elliptic Curve E=x^3-48*x+1 in the field p=1009.
When trying
Mod(deriv(sqrt(x^3-48*x+1)),1009) I get the following error in PARI: 
Mod: incorrect type in Rg_to_Fl.

Is there any possibility to compute such derivations in PARI or has PARI 
maybe functions for computing such a tangent line?

Thanks

Benedikt

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