Bill Allombert on Sun, 07 Nov 2021 22:50:17 +0100

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ellrank and Cassels pairing

Dear PARI developers,

We have updated ellrank to compute the Cassels pairing.
As the result the output is now a 4 component vector:
[r,R,s,L] where r, R, and L are as before and s is the 2-rank of

Compared to the previous version we have old_R = new_R + s,
so the new version is more accurate.

For example:
? ellrank(ellinit([0,0,0,-1,351298031616]))
%1 = [3,3,2,[[-1,592704],[1,592704],[-7056,84]]]
instead of 
%1 = [3,5,[[-1,592704],[1,592704],[-7056,84]]]

So now, we know that the rank is exactly 3.