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 Sha[2]/2Sha[4]. 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. Cheers, Bill.