Re: one-bit estimate of Reg*Sha

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

On Sun, Sep 14, 2025 at 07:17:09PM +0200, Bill Allombert wrote:
> Dear PARI-dev,
> 
> For number fields under GRH it is possible to compute the product h*R
> analytically to a fixed floating point precision in polynomial time.
> 
> Is there a similar result for the product Reg Sha of a rank-1 elliptic curves ?
> That is, computing lfun(E,1,1) with very low precision.
> 
> I just need B such that B <= Reg Sha <= 2*B.

Another question:

Let E an elliptic cuve of conductor N, D a fundamental discriminant prime to N,
and E_D the twist of E by D. 
Is it possible to compute L'_{E_D}(1) faster than for a 
generic curve of conductor ~ N*D^2 ?
(for example in time O(sqrt(N*D)) instead of O(sqrt(N*D^2)))

Cheers,
Bill.